M7160 Ordinary Differential Equations II

Faculty of Science
Spring 2024
Extent and Intensity
2/1/0. 5 credit(s). Type of Completion: zk (examination).
Taught in person.
Teacher(s)
doc. RNDr. Michal Veselý, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Michal Veselý, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 19. 2. to Sun 26. 5. Wed 13:00–14:50 MS1,01016
  • Timetable of Seminar Groups:
M7160/01: Mon 19. 2. to Sun 26. 5. Wed 15:00–15:50 MS1,01016, M. Veselý
Prerequisites
M5160 Ord. Differential Equations I
Mathematical analysis: Differential calculus of functions of several variables, integral calculus, sequences and series of numbers and functions, metric spaces, complex functions of a real variable.
Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformations and matrices, canonical form of a matrix.
Differential equations: Linear and non-linear systems of ordinary differential equations, stability theory, autonomous equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is focused on systems of non-linear differential equations with the Carathéodory right-hand side. The following questions are studied in detail: the existence of solutions of the Cauchy problem; the extendibility of solutions; and the existence of global solutions.
Learning outcomes
At the end of the course, students will be able to:
define and interpret the basic notions used in the mentioned fields;
formulate relevant mathematical theorems and statements and to explain methods of their proofs;
use effective techniques utilized in the subject areas;
analyse selected problems from the topics of the course.
Syllabus
  • The Carathéodory class of functions
  • Absolutely continuous functions
  • The Carathéodory theorem for higher-order differential equations
  • Extendibility of solutions of the Cauchy problem
  • Lower and upper solutions of the Cauchy problem
  • Set of solutions of the Cauchy problem
  • Differential and integral inequalities
  • Global solutions of the Cauchy problem
  • Uniqueness of solutions of the Cauchy problem
Literature
    recommended literature
  • HARTMAN, Philip. Ordinary differential equations. 2nd ed. Philadelphia, Pa.: SIAM, 2002, xx, 612 s. ISBN 0-89871-510-5. info
  • CODDINGTON, Earl A. and Norman LEVINSON. Theory of ordinary differential equations. New York: McGraw-Hill, 1955, 429 s. info
  • KIGURADZE, Ivan. Okrajové úlohy pro systémy lineárních obyčejných diferenciálních rovnic. 1. vyd. Brno: Masarykova univerzita, 1997, 183 s. ISBN 80-210-1664-7. info
    not specified
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice. 2. vyd. Brno: Masarykova univerzita, 2001, 207 s. ISBN 8021025891. info
  • KURZWEIL, Jaroslav. Obyčejné diferenciální rovnice : úvod do teorie obyčejných diferenciálních rovnic v reálném oboru. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1978, 418 s. info
Teaching methods
Lectures, seminars
Assessment methods
The final oral exam (60 minutes) for 20 points. For successfull examination (the grade at least E), the student needs 10 points or more.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught once in two years.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2000, Autumn 2002, Autumn 2004, Autumn 2006, Autumn 2008, Spring 2011, Spring 2014, Spring 2016, spring 2018, Spring 2020, Spring 2022.

M7160 Ordinary Differential Equations II

Faculty of Science
Spring 2022
Extent and Intensity
2/1/0. 5 credit(s). Type of Completion: zk (examination).
Taught in person.
Teacher(s)
doc. RNDr. Michal Veselý, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Michal Veselý, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 14:00–15:50 M3,01023
  • Timetable of Seminar Groups:
M7160/01: Wed 16:00–16:50 M3,01023, M. Veselý
Prerequisites
M5160 Ord. Differential Equations I
Mathematical analysis: Differential calculus of functions of several variables, integral calculus, sequences and series of numbers and functions, metric spaces, complex functions of a real variable.
Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformations and matrices, canonical form of a matrix.
Differential equations: Linear and non-linear systems of ordinary differential equations, stability theory, autonomous equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is focused on systems of non-linear differential equations with the Carathéodory right-hand side. The following questions are studied in detail: the existence of solutions of the Cauchy problem; the extendibility of solutions; and the existence of global solutions.
Learning outcomes
At the end of the course, students will be able to:
define and interpret the basic notions used in the mentioned fields;
formulate relevant mathematical theorems and statements and to explain methods of their proofs;
use effective techniques utilized in the subject areas;
analyse selected problems from the topics of the course.
Syllabus
  • The Carathéodory class of functions
  • Absolutely continuous functions
  • The Carathéodory theorem for higher-order differential equations
  • Extendibility of solutions of the Cauchy problem
  • Lower and upper solutions of the Cauchy problem
  • Set of solutions of the Cauchy problem
  • Differential and integral inequalities
  • Global solutions of the Cauchy problem
  • Uniqueness of solutions of the Cauchy problem
Literature
    recommended literature
  • HARTMAN, Philip. Ordinary differential equations. 2nd ed. Philadelphia, Pa.: SIAM, 2002, xx, 612 s. ISBN 0-89871-510-5. info
  • CODDINGTON, Earl A. and Norman LEVINSON. Theory of ordinary differential equations. New York: McGraw-Hill, 1955, 429 s. info
  • KIGURADZE, Ivan. Okrajové úlohy pro systémy lineárních obyčejných diferenciálních rovnic. 1. vyd. Brno: Masarykova univerzita, 1997, 183 s. ISBN 80-210-1664-7. info
    not specified
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice. 2. vyd. Brno: Masarykova univerzita, 2001, 207 s. ISBN 8021025891. info
  • KURZWEIL, Jaroslav. Obyčejné diferenciální rovnice : úvod do teorie obyčejných diferenciálních rovnic v reálném oboru. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1978, 418 s. info
Teaching methods
Lectures, seminars
Assessment methods
The final oral exam (60 minutes) for 20 points. For successfull examination (the grade at least E), the student needs 10 points or more.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught once in two years.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2000, Autumn 2002, Autumn 2004, Autumn 2006, Autumn 2008, Spring 2011, Spring 2014, Spring 2016, spring 2018, Spring 2020, Spring 2024.

M7160 Ordinary Differential Equations II

Faculty of Science
Spring 2020
Extent and Intensity
2/1/0. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Michal Veselý, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Michal Veselý, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Fri 12:00–13:50 M4,01024
  • Timetable of Seminar Groups:
M7160/01: Fri 14:00–14:50 M4,01024, M. Veselý
Prerequisites
M5160 Ord. Differential Equations I
Mathematical analysis: Differential calculus of functions of several variables, integral calculus, sequences and series of numbers and functions, metric spaces, complex functions of a real variable.
Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformations and matrices, canonical form of a matrix.
Differential equations: Linear and non-linear systems of ordinary differential equations, stability theory, autonomous equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is focused on systems of non-linear differential equations with the Carathéodory right-hand side. The following questions are studied in detail: the existence of solutions of the Cauchy problem; the extendibility of solutions; and the existence of global solutions.
Learning outcomes
At the end of the course, students will be able to:
define and interpret the basic notions used in the mentioned fields;
formulate relevant mathematical theorems and statements and to explain methods of their proofs;
use effective techniques utilized in the subject areas;
analyse selected problems from the topics of the course.
Syllabus
  • The Carathéodory class of functions
  • Absolutely continuous functions
  • The Carathéodory theorem for higher-order differential equations
  • Extendibility of solutions of the Cauchy problem
  • Lower and upper solutions of the Cauchy problem
  • Set of solutions of the Cauchy problem
  • Differential and integral inequalities
  • Global solutions of the Cauchy problem
  • Uniqueness of solutions of the Cauchy problem
Literature
    recommended literature
  • HARTMAN, Philip. Ordinary differential equations. 2nd ed. Philadelphia, Pa.: SIAM, 2002, xx, 612 s. ISBN 0-89871-510-5. info
  • CODDINGTON, Earl A. and Norman LEVINSON. Theory of ordinary differential equations. New York: McGraw-Hill, 1955, 429 s. info
  • KIGURADZE, Ivan. Okrajové úlohy pro systémy lineárních obyčejných diferenciálních rovnic. 1. vyd. Brno: Masarykova univerzita, 1997, 183 s. ISBN 80-210-1664-7. info
    not specified
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice. 2. vyd. Brno: Masarykova univerzita, 2001, 207 s. ISBN 8021025891. info
  • KURZWEIL, Jaroslav. Obyčejné diferenciální rovnice : úvod do teorie obyčejných diferenciálních rovnic v reálném oboru. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1978, 418 s. info
Teaching methods
Lectures, seminars
Assessment methods
The final oral exam (60 minutes) for 20 points. For successfull examination (the grade at least E), the student needs 10 points or more.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught once in two years.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2000, Autumn 2002, Autumn 2004, Autumn 2006, Autumn 2008, Spring 2011, Spring 2014, Spring 2016, spring 2018, Spring 2022, Spring 2024.

M7160 Ordinary Differential Equations II

Faculty of Science
spring 2018
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Michal Veselý, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 10:00–11:50 M2,01021
  • Timetable of Seminar Groups:
M7160/01: Tue 12:00–12:50 M2,01021, M. Veselý
Prerequisites
M5160 Ord. Differential Equations I
Mathematical analysis: Differential calculus of functions of several variables, integral calculus, sequences and series of numbers and functions, metric spaces, complex functions of a real variable.
Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformations and matrices, canonical form of a matrix.
Differential equations: Linear and non-linear systems of ordinary differential equations, stability theory, autonomous equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is focused on systems of non-linear differential equations with the Carathéodory right-hand side. The following questions are studied in detail: the existence of solutions of the Cauchy problem; the extendibility of solutions; and the existence of global solutions.
Learning outcomes
At the end of the course, students will be able to:
define and interpret the basic notions used in the mentioned fields;
formulate relevant mathematical theorems and statements and to explain methods of their proofs;
use effective techniques utilized in the subject areas;
analyse selected problems from the topics of the course.
Syllabus
  • The Carathéodory class of functions
  • Absolutely continuous functions
  • The Carathéodory theorem for higher-order differential equations
  • Extendibility of solutions of the Cauchy problem
  • Lower and upper solutions of the Cauchy problem
  • Set of solutions of the Cauchy problem
  • Differential and integral inequalities
  • Global solutions of the Cauchy problem
  • Uniqueness of solutions of the Cauchy problem
Literature
    recommended literature
  • HARTMAN, Philip. Ordinary differential equations. 2nd ed. Philadelphia, Pa.: SIAM, 2002, xx, 612 s. ISBN 0-89871-510-5. info
  • CODDINGTON, Earl A. and Norman LEVINSON. Theory of ordinary differential equations. New York: McGraw-Hill, 1955, 429 s. info
  • KIGURADZE, Ivan. Okrajové úlohy pro systémy lineárních obyčejných diferenciálních rovnic. 1. vyd. Brno: Masarykova univerzita, 1997, 183 s. ISBN 80-210-1664-7. info
    not specified
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice. 2. vyd. Brno: Masarykova univerzita, 2001, 207 s. ISBN 8021025891. info
  • KURZWEIL, Jaroslav. Obyčejné diferenciální rovnice : úvod do teorie obyčejných diferenciálních rovnic v reálném oboru. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1978, 418 s. info
Teaching methods
Lectures, seminars
Assessment methods
The final oral exam (60 minutes) for 20 points. For successfull examination (the grade at least E), the student needs 10 points or more.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2000, Autumn 2002, Autumn 2004, Autumn 2006, Autumn 2008, Spring 2011, Spring 2014, Spring 2016, Spring 2020, Spring 2022, Spring 2024.

M7160 Ordinary Differential Equations II

Faculty of Science
Spring 2016
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Michal Veselý, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 12:00–13:50 M3,01023
  • Timetable of Seminar Groups:
M7160/01: Wed 14:00–14:50 M3,01023, M. Veselý
Prerequisites
M5160 Ord. Differential Equations I
Mathematical analysis: Differential calculus of functions of several variables, integral calculus, sequences and series of numbers and functions, metric spaces, complex functions of a real variable.
Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformations and matrices, canonical form of a matrix.
Differential equations: Linear and non-linear systems of ordinary differential equations, stability theory, autonomous equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is focused on systems of non-linear differential equations with the Carathéodory right-hand side. The following questions are studied in detail: the existence of solutions of the Cauchy problem; the extendibility of solutions; and the existence of global solutions. At the end of the course, students should be able to formulate relevant mathematical theorems and their proofs, to use effective techniques utilized in these subject areas, and to analyse selected problems from the topics of the course.
Syllabus
  • The Carathéodory class of functions
  • Absolutely continuous functions
  • The Carathéodory theorem for higher-order differential equations
  • Extendibility of solutions of the Cauchy problem
  • Lower and upper solutions of the Cauchy problem
  • Set of solutions of the Cauchy problem
  • Differential and integral inequalities
  • Global solutions of the Cauchy problem
  • Uniqueness of solutions of the Cauchy problem
Literature
    recommended literature
  • HARTMAN, Philip. Ordinary differential equations. 2nd ed. Philadelphia, Pa.: SIAM, 2002, xx, 612 s. ISBN 0-89871-510-5. info
  • CODDINGTON, Earl A. and Norman LEVINSON. Theory of ordinary differential equations. New York: McGraw-Hill, 1955, 429 s. info
  • KIGURADZE, Ivan. Okrajové úlohy pro systémy lineárních obyčejných diferenciálních rovnic. 1. vyd. Brno: Masarykova univerzita, 1997, 183 s. ISBN 80-210-1664-7. info
    not specified
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice. 2. vyd. Brno: Masarykova univerzita, 2001, 207 s. ISBN 8021025891. info
  • KURZWEIL, Jaroslav. Obyčejné diferenciální rovnice : úvod do teorie obyčejných diferenciálních rovnic v reálném oboru. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1978, 418 s. info
Teaching methods
Lectures, seminars
Assessment methods
The final oral exam (60 minutes) for 20 points. For successfull examination (the grade at least E), the student needs 10 points or more.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught once in two years.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2000, Autumn 2002, Autumn 2004, Autumn 2006, Autumn 2008, Spring 2011, Spring 2014, spring 2018, Spring 2020, Spring 2022, Spring 2024.

M7160 Ordinary Differential Equations II

Faculty of Science
Spring 2014
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Michal Veselý, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Fri 13:00–14:50 M6,01011
  • Timetable of Seminar Groups:
M7160/01: Fri 15:00–15:50 M6,01011, M. Veselý
Prerequisites
M5160 Ord. Differential Equations I
Mathematical analysis: Differential calculus of functions of several variables, integral calculus, sequences and series of numbers and functions, metric spaces, complex functions of a real variable.
Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformations and matrices, canonical form of a matrix.
Differential equations: Linear and non-linear systems of ordinary differential equations, stability theory, autonomous equations.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
The course is focused on systems of non-linear differential equations with the Carathéodory right-hand side. The following questions are studied in detail: the existence of solutions of the Cauchy problem; the extendibility of solutions; and the existence of global solutions. At the end of the course, students should be able to formulate relevant mathematical theorems and their proofs, to use effective techniques utilized in these subject areas, and to analyse selected problems from the topics of the course.
Syllabus
  • The Carathéodory class of functions
  • Absolutely continuous functions
  • The Carathéodory theorem for higher-order differential equations
  • Extendibility of solutions of the Cauchy problem
  • Lower and upper solutions of the Cauchy problem
  • Set of solutions of the Cauchy problem
  • Differential and integral inequalities
  • Global solutions of the Cauchy problem
  • Uniqueness of solutions of the Cauchy problem
Literature
    required literature
  • HARTMAN, Philip. Ordinary differential equations. 2nd ed. Philadelphia, Pa.: SIAM, 2002, xx, 612 s. ISBN 0-89871-510-5. info
  • CODDINGTON, Earl A. and Norman LEVINSON. Theory of ordinary differential equations. New York: McGraw-Hill, 1955, 429 s. info
  • KIGURADZE, Ivan. Okrajové úlohy pro systémy lineárních obyčejných diferenciálních rovnic. 1. vyd. Brno: Masarykova univerzita, 1997, 183 s. ISBN 80-210-1664-7. info
    recommended literature
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice. 2. vyd. Brno: Masarykova univerzita, 2001, 207 s. ISBN 8021025891. info
  • KURZWEIL, Jaroslav. Obyčejné diferenciální rovnice : úvod do teorie obyčejných diferenciálních rovnic v reálném oboru. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1978, 418 s. info
Teaching methods
Lectures, seminars
Assessment methods
The final oral exam (60 minutes) for 20 points. For successfull examination (the grade at least E), the student needs 10 points or more.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2000, Autumn 2002, Autumn 2004, Autumn 2006, Autumn 2008, Spring 2011, Spring 2016, spring 2018, Spring 2020, Spring 2022, Spring 2024.

M7160 Ordinary Differential Equations II

Faculty of Science
Spring 2011
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 12:00–13:50 MS1,01016
  • Timetable of Seminar Groups:
M7160/01: Tue 14:00–14:50 MS1,01016, A. Lomtatidze
Prerequisites
M5160 Ord. Differential Equations I
Mathematical analysis: Differential calculus of functions of one and several variables, integral calculus, sequences and series of numbers and functions, metric spaces, complex function of a real variable. Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformation and matrices, canonical form of a matrix. Differential equations: Linear and nonlinear systems of ordinary differential equations, existence, uniqueness and properties of solutions, elements of the stability theory, autonomous equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives
The theory of differential equations ranks among basic parts of mathematical analysis. The course is focused to systems of nonlinear differential equations with a Carathéodory right-hand side. The following questions are studied in detail: the existence of a solution of the Cauchy problem, extendibility of solutions, global solutions, structure of a solution set of the Cauchy problem, continuous dependence of solutions on parameters. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • Carathéodory class of functions
  • On absolutly continuous functions
  • Cauchy problem
  • Carathéodory theorem for higher-order differential equations
  • Extendibility of solutions of the Cauchy problem
  • Lower and upper solutions of the Cauchy problem
  • On a set of solutions of the Cauchy problem
  • Existence of lower and upper solutions
  • Theorems on differential inequalities
  • Theorems on integral inequalities
  • Global solvability of the Cauchy problem
  • Uniqueness of a solution
  • Correctness of the Cauchy problem
  • Structure of a set of solutions of the Cauchy problem
Literature
  • HARTMAN, Philip. Ordinary differential equations. 2nd ed. Philadelphia, Pa.: SIAM, 2002, xx, 612 s. ISBN 0-89871-510-5. info
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice. 2. vyd. Brno: Masarykova univerzita, 2001, 207 s. ISBN 8021025891. info
  • KIGURADZE, Ivan. Okrajové úlohy pro systémy lineárních obyčejných diferenciálních rovnic. 1. vyd. Brno: Masarykova univerzita, 1997, 183 s. ISBN 80-210-1664-7. info
  • KURZWEIL, Jaroslav. Obyčejné diferenciální rovnice : úvod do teorie obyčejných diferenciálních rovnic v reálném oboru. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1978, 418 s. info
  • CODDINGTON, Earl A. and Norman LEVINSON. Theory of ordinary differential equations. New York: McGraw-Hill, 1955, 429 s. info
Teaching methods
lectures and class exercises
Assessment methods
Teaching: lecture 2 hours a week, seminar 1 hour a week. Examination: written and oral.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught once in two years.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2000, Autumn 2002, Autumn 2004, Autumn 2006, Autumn 2008, Spring 2014, Spring 2016, spring 2018, Spring 2020, Spring 2022, Spring 2024.

M7160 Ordinary Differential Equations II

Faculty of Science
Autumn 2008
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 15:00–16:50 MS2,01022
  • Timetable of Seminar Groups:
M7160/01: Mon 17:00–17:50 MS2,01022, A. Lomtatidze
Prerequisites
M5160 Differential Eqs.&Cont. Models
Mathematical analysis: Differential calculus of functions of one and several variables, integral calculus, sequences and series of numbers and functions, metric spaces, complex function of a real variable. Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformation and matrices, canonical form of a matrix. Differential equations: Linear and nonlinear systems of ordinary differential equations, existence, uniqueness and properties of solutions, elements of the stability theory, autonomous equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives
The theory of differential equations ranks among basic parts of mathematical analysis. The course is concentrated especially to linear differential equations with periodic coefficients, some selected parts from the theory of linear second-order equations, solution of differential equations by means of infinite series, generalization of the concept of a solution and to equations with deviating argument. At the end of this course, students should have advanced knowledges of the theory of ordinary differential equations.
Syllabus
  • 1. Differential inequalities. 2. Selected parts from the theory of linear differential equations - Floquet theory, linear second-order equations (basic properties, Green function, Sturm comparison theorems, Sturm-Liouville boundary-value problem, oscillation theory). 3. Solution of differential equations by means of infinite series. 4. Generalization of the concept of a solution - Carathéodory solution, existence and uniqueness of Carathéodory solutions. 5. Introduction to the theory of differential equations with deviating argument - basic notions, method of steps, existence and uniqueness for delay equations.
Literature
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). 2nd ed. Brno: Masarykova univerzita, 2001, 207 pp. ISBN 80-210-2589-1. info
  • KIGURADZE, Ivan. Okrajové úlohy pro systémy lineárních obyčejných diferenciálních rovnic. 1. vyd. Brno: Masarykova univerzita, 1997, 183 s. ISBN 80-210-1664-7. info
  • KURZWEIL, Jaroslav. Obyčejné diferenciální rovnice : úvod do teorie obyčejných diferenciálních rovnic v reálném oboru. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1978, 418 s. info
  • GREGUŠ, Michal, Marko ŠVEC and Valter ŠEDA. Obyčajné diferenciálne rovnice. 1. vyd. Bratislava: Alfa, vydavateľstvo technickej a ekonomickej literatúry, 1985, 374 s. info
  • Hartman, Philip. Ordinary differential equations. New York-London-Sydney: John Wiley & sons, 1964.
  • El'sgol'c, L. E. Vvedenie v teoriju differencial'nych uravnenij s otklonjajuščimsja argumentom. Moskva
  • Driver, Rodney David. Ordinary and delay differential equations. New York-Heidelberg-Berlin: Springer Verlag, 1977.
Assessment methods
Teaching: lecture 2 hours a week, seminar 1 hour a week. Examination: written and oral.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course is taught once in two years.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2000, Autumn 2002, Autumn 2004, Autumn 2006, Spring 2011, Spring 2014, Spring 2016, spring 2018, Spring 2020, Spring 2022, Spring 2024.

M7160 Ordinary Differential Equations II

Faculty of Science
Autumn 2006
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. Alexander Lomtatidze, DrSc.
Timetable
Tue 17:00–18:50 UM
  • Timetable of Seminar Groups:
M7160/01: Tue 19:00–19:50 UM
Prerequisites
M5160 Differential Eqs.&Cont. Models
Mathematical analysis: Differential calculus of functions of one and several variables, integral calculus, sequences and series of numbers and functions, metric spaces, complex function of a real variable. Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformation and matrices, canonical form of a matrix. Differential equations: Linear and nonlinear systems of ordinary differential equations, existence, uniqueness and properties of solutions, elements of the stability theory, autonomous equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives
The theory of differential equations ranks among basic parts of mathematical analysis. The course is concentrated especially to linear differential equations with periodic coefficients, some selected parts from the theory of linear second-order equations, solution of differential equations by means of infinite series, generalization of the concept of a solution and to equations with deviating argument.
Syllabus
  • 1. Differential inequalities. 2. Selected parts from the theory of linear differential equations - Floquet theory, linear second-order equations (basic properties, Green function, Sturm comparison theorems, Sturm-Liouville boundary-value problem, oscillation theory). 3. Solution of differential equations by means of infinite series. 4. Generalization of the concept of a solution - Carathéodory solution, existence and uniqueness of Carathéodory solutions. 5. Introduction to the theory of differential equations with deviating argument - basic notions, method of steps, existence and uniqueness for delay equations.
Literature
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). 2nd ed. Brno: Masarykova univerzita, 2001, 207 pp. ISBN 80-210-2589-1. info
  • KIGURADZE, Ivan. Okrajové úlohy pro systémy lineárních obyčejných diferenciálních rovnic. 1. vyd. Brno: Masarykova univerzita, 1997, 183 s. ISBN 80-210-1664-7. info
  • KURZWEIL, Jaroslav. Obyčejné diferenciální rovnice : úvod do teorie obyčejných diferenciálních rovnic v reálném oboru. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1978, 418 s. info
  • GREGUŠ, Michal, Marko ŠVEC and Valter ŠEDA. Obyčajné diferenciálne rovnice. 1. vyd. Bratislava: Alfa, vydavateľstvo technickej a ekonomickej literatúry, 1985, 374 s. info
  • Hartman, Philip. Ordinary differential equations. New York-London-Sydney: John Wiley & sons, 1964.
  • El'sgol'c, L. E. Vvedenie v teoriju differencial'nych uravnenij s otklonjajuščimsja argumentom. Moskva
  • Driver, Rodney David. Ordinary and delay differential equations. New York-Heidelberg-Berlin: Springer Verlag, 1977.
Assessment methods (in Czech)
Výuka: přednáška, klasické cvičení. Zkouška: písemná a ústní.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is taught once in two years.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2000, Autumn 2002, Autumn 2004, Autumn 2008, Spring 2011, Spring 2014, Spring 2016, spring 2018, Spring 2020, Spring 2022, Spring 2024.

M7160 Ordinary Differential Equations II

Faculty of Science
Autumn 2004
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. Alexander Lomtatidze, DrSc.
Timetable
Mon 15:00–16:50 UM
  • Timetable of Seminar Groups:
M7160/01: Mon 17:00–17:50 UM, A. Lomtatidze
Prerequisites
M5160 Differential Eqs.&Cont. Models
Mathematical analysis: Differential calculus of functions of one and several variables, integral calculus, sequences and series of numbers and functions, metric spaces, complex function of a real variable. Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformation and matrices, canonical form of a matrix. Differential equations: Linear and nonlinear systems of ordinary differential equations, existence, uniqueness and properties of solutions, elements of the stability theory, autonomous equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives
The theory of differential equations ranks among basic parts of mathematical analysis. The course is concentrated especially to linear differential equations with periodic coefficients, some selected parts from the theory of linear second-order equations, solution of differential equations by means of infinite series, generalization of the concept of a solution and to equations with deviating argument.
Syllabus
  • 1. Differential inequalities. 2. Selected parts from the theory of linear differential equations - Floquet theory, linear second-order equations (basic properties, Green function, Sturm comparison theorems, Sturm-Liouville boundary-value problem, oscillation theory). 3. Solution of differential equations by means of infinite series. 4. Generalization of the concept of a solution - Carathéodory solution, existence and uniqueness of Carathéodory solutions. 5. Introduction to the theory of differential equations with deviating argument - basic notions, method of steps, existence and uniqueness for delay equations.
Literature
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). 2nd ed. Brno: Masarykova univerzita, 2001, 207 pp. ISBN 80-210-2589-1. info
  • KIGURADZE, Ivan. Okrajové úlohy pro systémy lineárních obyčejných diferenciálních rovnic. 1. vyd. Brno: Masarykova univerzita, 1997, 183 s. ISBN 80-210-1664-7. info
  • KURZWEIL, Jaroslav. Obyčejné diferenciální rovnice : úvod do teorie obyčejných diferenciálních rovnic v reálném oboru. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1978, 418 s. info
  • GREGUŠ, Michal, Marko ŠVEC and Valter ŠEDA. Obyčajné diferenciálne rovnice. 1. vyd. Bratislava: Alfa, vydavateľstvo technickej a ekonomickej literatúry, 1985, 374 s. info
  • Hartman, Philip. Ordinary differential equations. New York-London-Sydney: John Wiley & sons, 1964.
  • El'sgol'c, L. E. Vvedenie v teoriju differencial'nych uravnenij s otklonjajuščimsja argumentom. Moskva
  • Driver, Rodney David. Ordinary and delay differential equations. New York-Heidelberg-Berlin: Springer Verlag, 1977.
Assessment methods (in Czech)
Výuka: přednáška, klasické cvičení. Zkouška: písemná a ústní.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is taught once in two years.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2000, Autumn 2002, Autumn 2006, Autumn 2008, Spring 2011, Spring 2014, Spring 2016, spring 2018, Spring 2020, Spring 2022, Spring 2024.

M7160 Ordinary Differential Equations II

Faculty of Science
Autumn 2002
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. Alexander Lomtatidze, DrSc.
Prerequisites
M5160 Differential Eqs.&Cont. Models
Mathematical analysis: Differential calculus of functions of one and several variables, integral calculus, sequences and series of numbers and functions, metric spaces, complex function of a real variable. Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformation and matrices, canonical form of a matrix. Differential equations: Linear and nonlinear systems of ordinary differential equations, existence, uniqueness and properties of solutions, elements of the stability theory, autonomous equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives
The theory of differential equations ranks among basic parts of mathematical analysis. The course is concentrated especially to linear differential equations with periodic coefficients, some selected parts from the theory of linear second-order equations, solution of differential equations by means of infinite series, generalization of the concept of a solution and to equations with deviating argument.
Syllabus
  • 1. Differential inequalities. 2. Selected parts from the theory of linear differential equations - Floquet theory, linear second-order equations (basic properties, Green function, Sturm comparison theorems, Sturm-Liouville boundary-value problem, oscillation theory). 3. Solution of differential equations by means of infinite series. 4. Generalization of the concept of a solution - Carathéodory solution, existence and uniqueness of Carathéodory solutions. 5. Introduction to the theory of differential equations with deviating argument - basic notions, method of steps, existence and uniqueness for delay equations.
Literature
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). 2nd ed. Brno: Masarykova univerzita, 2001, 207 pp. ISBN 80-210-2589-1. info
  • KIGURADZE, Ivan. Okrajové úlohy pro systémy lineárních obyčejných diferenciálních rovnic. 1. vyd. Brno: Masarykova univerzita, 1997, 183 s. ISBN 80-210-1664-7. info
  • KURZWEIL, Jaroslav. Obyčejné diferenciální rovnice : úvod do teorie obyčejných diferenciálních rovnic v reálném oboru. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1978, 418 s. info
  • GREGUŠ, Michal, Marko ŠVEC and Valter ŠEDA. Obyčajné diferenciálne rovnice. 1. vyd. Bratislava: Alfa, vydavateľstvo technickej a ekonomickej literatúry, 1985, 374 s. info
  • Hartman, Philip. Ordinary differential equations. New York-London-Sydney: John Wiley & sons, 1964.
  • El'sgol'c, L. E. Vvedenie v teoriju differencial'nych uravnenij s otklonjajuščimsja argumentom. Moskva
  • Driver, Rodney David. Ordinary and delay differential equations. New York-Heidelberg-Berlin: Springer Verlag, 1977.
Assessment methods (in Czech)
Výuka: přednáška, klasické cvičení. Zkouška: písemná a ústní.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2000, Autumn 2004, Autumn 2006, Autumn 2008, Spring 2011, Spring 2014, Spring 2016, spring 2018, Spring 2020, Spring 2022, Spring 2024.

M7160 Differential Equations II

Faculty of Science
Autumn 2000
Extent and Intensity
2/1/0. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. Alexander Lomtatidze, DrSc.
Prerequisites (in Czech)
M5160 Ord. Differential Equations I
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives
Differential inequalities. Selected parts from the theory of linear differential equations (Floquet theory, linear second-order equations: basic properties, Green function, Sturm comparison theorems, Sturm-Liouville boundary-value problem, oscillation theory). Solution of differential equations by means of infinite series. Generalization of the concept of a solution (Carathéodory solution, existence and uniqueness of Carathéodory solutions). Introduction to the theory of differential equations with deviating argument (basic notions, method of steps, existence and uniqueness for delay equations).
Literature
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice. 1. vyd. Brno: Masarykova univerzita, 1995, 207 s. ISBN 8021011300. info
  • KURZWEIL, Jaroslav. Obyčejné diferenciální rovnice : úvod do teorie obyčejných diferenciálních rovnic v reálném oboru. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1978, 418 s. info
  • GREGUŠ, Michal, Marko ŠVEC and Valter ŠEDA. Obyčajné diferenciálne rovnice. 1. vyd. Bratislava: Alfa, vydavateľstvo technickej a ekonomickej literatúry, 1985, 374 s. info
  • Hartman, Philip. Ordinary differential equations. New York-London-Sydney: John Wiley & sons, 1964.
  • El'sgol'c, L. E. Vvedenie v teoriju differencial'nych uravnenij s otklonjajuščimsja argumentom. Moskva
  • Driver, Rodney David. Ordinary and delay differential equations. New York-Heidelberg-Berlin: Springer Verlag, 1977.
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2002, Autumn 2004, Autumn 2006, Autumn 2008, Spring 2011, Spring 2014, Spring 2016, spring 2018, Spring 2020, Spring 2022, Spring 2024.

M7160 Ordinary Differential Equations II

Faculty of Science
Spring 2025

The course is not taught in Spring 2025

Extent and Intensity
2/1/0. 5 credit(s). Type of Completion: zk (examination).
Taught in person.
Teacher(s)
doc. RNDr. Michal Veselý, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Michal Veselý, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M5160 Ord. Differential Equations I
Mathematical analysis: Differential calculus of functions of several variables, integral calculus, sequences and series of numbers and functions, metric spaces, complex functions of a real variable.
Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformations and matrices, canonical form of a matrix.
Differential equations: Linear and non-linear systems of ordinary differential equations, stability theory, autonomous equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is focused on systems of non-linear differential equations with the Carathéodory right-hand side. The following questions are studied in detail: the existence of solutions of the Cauchy problem; the extendibility of solutions; and the existence of global solutions.
Learning outcomes
At the end of the course, students will be able to:
define and interpret the basic notions used in the mentioned fields;
formulate relevant mathematical theorems and statements and to explain methods of their proofs;
use effective techniques utilized in the subject areas;
analyse selected problems from the topics of the course.
Syllabus
  • The Carathéodory class of functions
  • Absolutely continuous functions
  • The Carathéodory theorem for higher-order differential equations
  • Extendibility of solutions of the Cauchy problem
  • Lower and upper solutions of the Cauchy problem
  • Set of solutions of the Cauchy problem
  • Differential and integral inequalities
  • Global solutions of the Cauchy problem
  • Uniqueness of solutions of the Cauchy problem
Literature
    recommended literature
  • HARTMAN, Philip. Ordinary differential equations. 2nd ed. Philadelphia, Pa.: SIAM, 2002, xx, 612 s. ISBN 0-89871-510-5. info
  • CODDINGTON, Earl A. and Norman LEVINSON. Theory of ordinary differential equations. New York: McGraw-Hill, 1955, 429 s. info
  • KIGURADZE, Ivan. Okrajové úlohy pro systémy lineárních obyčejných diferenciálních rovnic. 1. vyd. Brno: Masarykova univerzita, 1997, 183 s. ISBN 80-210-1664-7. info
    not specified
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice. 2. vyd. Brno: Masarykova univerzita, 2001, 207 s. ISBN 8021025891. info
  • KURZWEIL, Jaroslav. Obyčejné diferenciální rovnice : úvod do teorie obyčejných diferenciálních rovnic v reálném oboru. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1978, 418 s. info
Teaching methods
Lectures, seminars
Assessment methods
The final oral exam (60 minutes) for 20 points. For successfull examination (the grade at least E), the student needs 10 points or more.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2000, Autumn 2002, Autumn 2004, Autumn 2006, Autumn 2008, Spring 2011, Spring 2014, Spring 2016, spring 2018, Spring 2020, Spring 2022, Spring 2024.

M7160 Ordinary Differential Equations II

Faculty of Science
Spring 2023

The course is not taught in Spring 2023

Extent and Intensity
2/1/0. 5 credit(s). Type of Completion: zk (examination).
Taught in person.
Teacher(s)
doc. RNDr. Michal Veselý, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Michal Veselý, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M5160 Ord. Differential Equations I
Mathematical analysis: Differential calculus of functions of several variables, integral calculus, sequences and series of numbers and functions, metric spaces, complex functions of a real variable.
Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformations and matrices, canonical form of a matrix.
Differential equations: Linear and non-linear systems of ordinary differential equations, stability theory, autonomous equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is focused on systems of non-linear differential equations with the Carathéodory right-hand side. The following questions are studied in detail: the existence of solutions of the Cauchy problem; the extendibility of solutions; and the existence of global solutions.
Learning outcomes
At the end of the course, students will be able to:
define and interpret the basic notions used in the mentioned fields;
formulate relevant mathematical theorems and statements and to explain methods of their proofs;
use effective techniques utilized in the subject areas;
analyse selected problems from the topics of the course.
Syllabus
  • The Carathéodory class of functions
  • Absolutely continuous functions
  • The Carathéodory theorem for higher-order differential equations
  • Extendibility of solutions of the Cauchy problem
  • Lower and upper solutions of the Cauchy problem
  • Set of solutions of the Cauchy problem
  • Differential and integral inequalities
  • Global solutions of the Cauchy problem
  • Uniqueness of solutions of the Cauchy problem
Literature
    recommended literature
  • HARTMAN, Philip. Ordinary differential equations. 2nd ed. Philadelphia, Pa.: SIAM, 2002, xx, 612 s. ISBN 0-89871-510-5. info
  • CODDINGTON, Earl A. and Norman LEVINSON. Theory of ordinary differential equations. New York: McGraw-Hill, 1955, 429 s. info
  • KIGURADZE, Ivan. Okrajové úlohy pro systémy lineárních obyčejných diferenciálních rovnic. 1. vyd. Brno: Masarykova univerzita, 1997, 183 s. ISBN 80-210-1664-7. info
    not specified
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice. 2. vyd. Brno: Masarykova univerzita, 2001, 207 s. ISBN 8021025891. info
  • KURZWEIL, Jaroslav. Obyčejné diferenciální rovnice : úvod do teorie obyčejných diferenciálních rovnic v reálném oboru. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1978, 418 s. info
Teaching methods
Lectures, seminars
Assessment methods
The final oral exam (60 minutes) for 20 points. For successfull examination (the grade at least E), the student needs 10 points or more.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2000, Autumn 2002, Autumn 2004, Autumn 2006, Autumn 2008, Spring 2011, Spring 2014, Spring 2016, spring 2018, Spring 2020, Spring 2022, Spring 2024.

M7160 Ordinary Differential Equations II

Faculty of Science
Spring 2021

The course is not taught in Spring 2021

Extent and Intensity
2/1/0. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Michal Veselý, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Michal Veselý, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M5160 Ord. Differential Equations I
Mathematical analysis: Differential calculus of functions of several variables, integral calculus, sequences and series of numbers and functions, metric spaces, complex functions of a real variable.
Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformations and matrices, canonical form of a matrix.
Differential equations: Linear and non-linear systems of ordinary differential equations, stability theory, autonomous equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is focused on systems of non-linear differential equations with the Carathéodory right-hand side. The following questions are studied in detail: the existence of solutions of the Cauchy problem; the extendibility of solutions; and the existence of global solutions.
Learning outcomes
At the end of the course, students will be able to:
define and interpret the basic notions used in the mentioned fields;
formulate relevant mathematical theorems and statements and to explain methods of their proofs;
use effective techniques utilized in the subject areas;
analyse selected problems from the topics of the course.
Syllabus
  • The Carathéodory class of functions
  • Absolutely continuous functions
  • The Carathéodory theorem for higher-order differential equations
  • Extendibility of solutions of the Cauchy problem
  • Lower and upper solutions of the Cauchy problem
  • Set of solutions of the Cauchy problem
  • Differential and integral inequalities
  • Global solutions of the Cauchy problem
  • Uniqueness of solutions of the Cauchy problem
Literature
    recommended literature
  • HARTMAN, Philip. Ordinary differential equations. 2nd ed. Philadelphia, Pa.: SIAM, 2002, xx, 612 s. ISBN 0-89871-510-5. info
  • CODDINGTON, Earl A. and Norman LEVINSON. Theory of ordinary differential equations. New York: McGraw-Hill, 1955, 429 s. info
  • KIGURADZE, Ivan. Okrajové úlohy pro systémy lineárních obyčejných diferenciálních rovnic. 1. vyd. Brno: Masarykova univerzita, 1997, 183 s. ISBN 80-210-1664-7. info
    not specified
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice. 2. vyd. Brno: Masarykova univerzita, 2001, 207 s. ISBN 8021025891. info
  • KURZWEIL, Jaroslav. Obyčejné diferenciální rovnice : úvod do teorie obyčejných diferenciálních rovnic v reálném oboru. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1978, 418 s. info
Teaching methods
Lectures, seminars
Assessment methods
The final oral exam (60 minutes) for 20 points. For successfull examination (the grade at least E), the student needs 10 points or more.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2000, Autumn 2002, Autumn 2004, Autumn 2006, Autumn 2008, Spring 2011, Spring 2014, Spring 2016, spring 2018, Spring 2020, Spring 2022, Spring 2024.

M7160 Ordinary Differential Equations II

Faculty of Science
Spring 2019

The course is not taught in Spring 2019

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Michal Veselý, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M5160 Ord. Differential Equations I
Mathematical analysis: Differential calculus of functions of several variables, integral calculus, sequences and series of numbers and functions, metric spaces, complex functions of a real variable.
Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformations and matrices, canonical form of a matrix.
Differential equations: Linear and non-linear systems of ordinary differential equations, stability theory, autonomous equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is focused on systems of non-linear differential equations with the Carathéodory right-hand side. The following questions are studied in detail: the existence of solutions of the Cauchy problem; the extendibility of solutions; and the existence of global solutions.
Learning outcomes
At the end of the course, students will be able to:
define and interpret the basic notions used in the mentioned fields;
formulate relevant mathematical theorems and statements and to explain methods of their proofs;
use effective techniques utilized in the subject areas;
analyse selected problems from the topics of the course.
Syllabus
  • The Carathéodory class of functions
  • Absolutely continuous functions
  • The Carathéodory theorem for higher-order differential equations
  • Extendibility of solutions of the Cauchy problem
  • Lower and upper solutions of the Cauchy problem
  • Set of solutions of the Cauchy problem
  • Differential and integral inequalities
  • Global solutions of the Cauchy problem
  • Uniqueness of solutions of the Cauchy problem
Literature
    recommended literature
  • HARTMAN, Philip. Ordinary differential equations. 2nd ed. Philadelphia, Pa.: SIAM, 2002, xx, 612 s. ISBN 0-89871-510-5. info
  • CODDINGTON, Earl A. and Norman LEVINSON. Theory of ordinary differential equations. New York: McGraw-Hill, 1955, 429 s. info
  • KIGURADZE, Ivan. Okrajové úlohy pro systémy lineárních obyčejných diferenciálních rovnic. 1. vyd. Brno: Masarykova univerzita, 1997, 183 s. ISBN 80-210-1664-7. info
    not specified
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice. 2. vyd. Brno: Masarykova univerzita, 2001, 207 s. ISBN 8021025891. info
  • KURZWEIL, Jaroslav. Obyčejné diferenciální rovnice : úvod do teorie obyčejných diferenciálních rovnic v reálném oboru. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1978, 418 s. info
Teaching methods
Lectures, seminars
Assessment methods
The final oral exam (60 minutes) for 20 points. For successfull examination (the grade at least E), the student needs 10 points or more.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2000, Autumn 2002, Autumn 2004, Autumn 2006, Autumn 2008, Spring 2011, Spring 2014, Spring 2016, spring 2018, Spring 2020, Spring 2022, Spring 2024.

M7160 Ordinary Differential Equations II

Faculty of Science
Spring 2017

The course is not taught in Spring 2017

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Michal Veselý, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M5160 Ord. Differential Equations I
Mathematical analysis: Differential calculus of functions of several variables, integral calculus, sequences and series of numbers and functions, metric spaces, complex functions of a real variable.
Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformations and matrices, canonical form of a matrix.
Differential equations: Linear and non-linear systems of ordinary differential equations, stability theory, autonomous equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is focused on systems of non-linear differential equations with the Carathéodory right-hand side. The following questions are studied in detail: the existence of solutions of the Cauchy problem; the extendibility of solutions; and the existence of global solutions.
Learning outcomes
At the end of the course, students will be able to:
define and interpret the basic notions used in the mentioned fields;
formulate relevant mathematical theorems and statements and to explain methods of their proofs;
use effective techniques utilized in the subject areas;
analyse selected problems from the topics of the course.
Syllabus
  • The Carathéodory class of functions
  • Absolutely continuous functions
  • The Carathéodory theorem for higher-order differential equations
  • Extendibility of solutions of the Cauchy problem
  • Lower and upper solutions of the Cauchy problem
  • Set of solutions of the Cauchy problem
  • Differential and integral inequalities
  • Global solutions of the Cauchy problem
  • Uniqueness of solutions of the Cauchy problem
Literature
    recommended literature
  • HARTMAN, Philip. Ordinary differential equations. 2nd ed. Philadelphia, Pa.: SIAM, 2002, xx, 612 s. ISBN 0-89871-510-5. info
  • CODDINGTON, Earl A. and Norman LEVINSON. Theory of ordinary differential equations. New York: McGraw-Hill, 1955, 429 s. info
  • KIGURADZE, Ivan. Okrajové úlohy pro systémy lineárních obyčejných diferenciálních rovnic. 1. vyd. Brno: Masarykova univerzita, 1997, 183 s. ISBN 80-210-1664-7. info
    not specified
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice. 2. vyd. Brno: Masarykova univerzita, 2001, 207 s. ISBN 8021025891. info
  • KURZWEIL, Jaroslav. Obyčejné diferenciální rovnice : úvod do teorie obyčejných diferenciálních rovnic v reálném oboru. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1978, 418 s. info
Teaching methods
Lectures, seminars
Assessment methods
The final oral exam (60 minutes) for 20 points. For successfull examination (the grade at least E), the student needs 10 points or more.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2000, Autumn 2002, Autumn 2004, Autumn 2006, Autumn 2008, Spring 2011, Spring 2014, Spring 2016, spring 2018, Spring 2020, Spring 2022, Spring 2024.

M7160 Ordinary Differential Equations II

Faculty of Science
Spring 2015

The course is not taught in Spring 2015

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Michal Veselý, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M5160 Ord. Differential Equations I
Mathematical analysis: Differential calculus of functions of several variables, integral calculus, sequences and series of numbers and functions, metric spaces, complex functions of a real variable.
Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformations and matrices, canonical form of a matrix.
Differential equations: Linear and non-linear systems of ordinary differential equations, stability theory, autonomous equations.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
The course is focused on systems of non-linear differential equations with the Carathéodory right-hand side. The following questions are studied in detail: the existence of solutions of the Cauchy problem; the extendibility of solutions; and the existence of global solutions. At the end of the course, students should be able to formulate relevant mathematical theorems and their proofs, to use effective techniques utilized in these subject areas, and to analyse selected problems from the topics of the course.
Syllabus
  • The Carathéodory class of functions
  • Absolutely continuous functions
  • The Carathéodory theorem for higher-order differential equations
  • Extendibility of solutions of the Cauchy problem
  • Lower and upper solutions of the Cauchy problem
  • Set of solutions of the Cauchy problem
  • Differential and integral inequalities
  • Global solutions of the Cauchy problem
  • Uniqueness of solutions of the Cauchy problem
Literature
    required literature
  • HARTMAN, Philip. Ordinary differential equations. 2nd ed. Philadelphia, Pa.: SIAM, 2002, xx, 612 s. ISBN 0-89871-510-5. info
  • CODDINGTON, Earl A. and Norman LEVINSON. Theory of ordinary differential equations. New York: McGraw-Hill, 1955, 429 s. info
  • KIGURADZE, Ivan. Okrajové úlohy pro systémy lineárních obyčejných diferenciálních rovnic. 1. vyd. Brno: Masarykova univerzita, 1997, 183 s. ISBN 80-210-1664-7. info
    recommended literature
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice. 2. vyd. Brno: Masarykova univerzita, 2001, 207 s. ISBN 8021025891. info
  • KURZWEIL, Jaroslav. Obyčejné diferenciální rovnice : úvod do teorie obyčejných diferenciálních rovnic v reálném oboru. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1978, 418 s. info
Teaching methods
Lectures, seminars
Assessment methods
The final oral exam (60 minutes) for 20 points. For successfull examination (the grade at least E), the student needs 10 points or more.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2000, Autumn 2002, Autumn 2004, Autumn 2006, Autumn 2008, Spring 2011, Spring 2014, Spring 2016, spring 2018, Spring 2020, Spring 2022, Spring 2024.

M7160 Ordinary Differential Equations II

Faculty of Science
Spring 2013

The course is not taught in Spring 2013

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Josef Kalas, CSc. (lecturer)
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable of Seminar Groups
M7160/01: No timetable has been entered into IS.
Prerequisites
M5160 Ord. Differential Equations I
Mathematical analysis: Differential calculus of functions of several variables, integral calculus, sequences and series of numbers and functions, metric spaces, complex functions of a real variable.
Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformations and matrices, canonical form of a matrix.
Differential equations: Linear and non-linear systems of ordinary differential equations, stability theory, autonomous equations.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
The course is focused to systems of non-linear differential equations with the Carathéodory right-hand side. The following questions are studied in detail: the existence of solutions of the Cauchy problem; the extendibility of solutions; and the existence of global solutions. At the end of the course, students should be able to formulate relevant mathematical theorems and their proofs, to use effective techniques utilized in these subject areas, and to analyse selected problems from the topics of the course.
Syllabus
  • The Carathéodory class of functions
  • Absolutely continuous functions
  • The Carathéodory theorem for higher-order differential equations
  • Extendibility of solutions of the Cauchy problem
  • Lower and upper solutions of the Cauchy problem
  • Set of solutions of the Cauchy problem
  • Differential and integral inequalities
  • Global solutions of the Cauchy problem
  • Uniqueness of solutions of the Cauchy problem
Literature
    required literature
  • HARTMAN, Philip. Ordinary differential equations. 2nd ed. Philadelphia, Pa.: SIAM, 2002, xx, 612 s. ISBN 0-89871-510-5. info
  • CODDINGTON, Earl A. and Norman LEVINSON. Theory of ordinary differential equations. New York: McGraw-Hill, 1955, 429 s. info
  • KIGURADZE, Ivan. Okrajové úlohy pro systémy lineárních obyčejných diferenciálních rovnic. 1. vyd. Brno: Masarykova univerzita, 1997, 183 s. ISBN 80-210-1664-7. info
    recommended literature
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice. 2. vyd. Brno: Masarykova univerzita, 2001, 207 s. ISBN 8021025891. info
  • KURZWEIL, Jaroslav. Obyčejné diferenciální rovnice : úvod do teorie obyčejných diferenciálních rovnic v reálném oboru. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1978, 418 s. info
Teaching methods
Lectures, seminars
Assessment methods
Oral exam
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2000, Autumn 2002, Autumn 2004, Autumn 2006, Autumn 2008, Spring 2011, Spring 2014, Spring 2016, spring 2018, Spring 2020, Spring 2022, Spring 2024.

M7160 Ordinary Differential Equations II

Faculty of Science
Spring 2012

The course is not taught in Spring 2012

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M5160 Ord. Differential Equations I
Mathematical analysis: Differential calculus of functions of one and several variables, integral calculus, sequences and series of numbers and functions, metric spaces, complex function of a real variable. Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformation and matrices, canonical form of a matrix. Differential equations: Linear and nonlinear systems of ordinary differential equations, existence, uniqueness and properties of solutions, elements of the stability theory, autonomous equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives
The theory of differential equations ranks among basic parts of mathematical analysis. The course is focused to systems of nonlinear differential equations with a Carathéodory right-hand side. The following questions are studied in detail: the existence of a solution of the Cauchy problem, extendibility of solutions, global solutions, structure of a solution set of the Cauchy problem, continuous dependence of solutions on parameters. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • Carathéodory class of functions
  • On absolutly continuous functions
  • Cauchy problem
  • Carathéodory theorem for higher-order differential equations
  • Extendibility of solutions of the Cauchy problem
  • Lower and upper solutions of the Cauchy problem
  • On a set of solutions of the Cauchy problem
  • Existence of lower and upper solutions
  • Theorems on differential inequalities
  • Theorems on integral inequalities
  • Global solvability of the Cauchy problem
  • Uniqueness of a solution
  • Correctness of the Cauchy problem
  • Structure of a set of solutions of the Cauchy problem
Literature
  • HARTMAN, Philip. Ordinary differential equations. 2nd ed. Philadelphia, Pa.: SIAM, 2002, xx, 612 s. ISBN 0-89871-510-5. info
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice. 2. vyd. Brno: Masarykova univerzita, 2001, 207 s. ISBN 8021025891. info
  • KIGURADZE, Ivan. Okrajové úlohy pro systémy lineárních obyčejných diferenciálních rovnic. 1. vyd. Brno: Masarykova univerzita, 1997, 183 s. ISBN 80-210-1664-7. info
  • KURZWEIL, Jaroslav. Obyčejné diferenciální rovnice : úvod do teorie obyčejných diferenciálních rovnic v reálném oboru. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1978, 418 s. info
  • CODDINGTON, Earl A. and Norman LEVINSON. Theory of ordinary differential equations. New York: McGraw-Hill, 1955, 429 s. info
Teaching methods
lectures and class exercises
Assessment methods
Teaching: lecture 2 hours a week, seminar 1 hour a week. Examination: written and oral.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2000, Autumn 2002, Autumn 2004, Autumn 2006, Autumn 2008, Spring 2011, Spring 2014, Spring 2016, spring 2018, Spring 2020, Spring 2022, Spring 2024.

M7160 Ordinary Differential Equations II

Faculty of Science
Autumn 2009

The course is not taught in Autumn 2009

Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M5160 Differential Eqs.&Cont. Models
Mathematical analysis: Differential calculus of functions of one and several variables, integral calculus, sequences and series of numbers and functions, metric spaces, complex function of a real variable. Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformation and matrices, canonical form of a matrix. Differential equations: Linear and nonlinear systems of ordinary differential equations, existence, uniqueness and properties of solutions, elements of the stability theory, autonomous equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives
The theory of differential equations ranks among basic parts of mathematical analysis. The course is focused to systems of nonlinear differential equations with a Carathéodory right-hand side. The following questions are studied in detail: the existence of a solution of the Cauchy problem, extendibility of solutions, global solutions, structure of a solution set of the Cauchy problem, continuous dependence of solutions on parameters. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • Carathéodory class of functions
  • On absolutly continuous functions
  • Cauchy problem
  • Carathéodory theorem for higher-order differential equations
  • Extendibility of solutions of the Cauchy problem
  • Lower and upper solutions of the Cauchy problem
  • On a set of solutions of the Cauchy problem
  • Existence of lower and upper solutions
  • Theorems on differential inequalities
  • Theorems on integral inequalities
  • Global solvability of the Cauchy problem
  • Uniqueness of a solution
  • Correctness of the Cauchy problem
  • Structure of a set of solutions of the Cauchy problem
Literature
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). 2nd ed. Brno: Masarykova univerzita, 2001, 207 pp. ISBN 80-210-2589-1. info
  • KIGURADZE, Ivan. Okrajové úlohy pro systémy lineárních obyčejných diferenciálních rovnic. 1. vyd. Brno: Masarykova univerzita, 1997, 183 s. ISBN 80-210-1664-7. info
  • KURZWEIL, Jaroslav. Obyčejné diferenciální rovnice : úvod do teorie obyčejných diferenciálních rovnic v reálném oboru. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1978, 418 s. info
  • HARTMAN, Philip. Ordinary Differential Equations. New York: John Wiley and Sons, 1964. info
  • CODDINGTON, Earl A. and Norman LEVINSON. Theory of ordinary differential equations. New York: McGraw-Hill, 1955, 429 s. info
Teaching methods
lectures and class exercises
Assessment methods
Teaching: lecture 2 hours a week, seminar 1 hour a week. Examination: written and oral.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2000, Autumn 2002, Autumn 2004, Autumn 2006, Autumn 2008, Spring 2011, Spring 2014, Spring 2016, spring 2018, Spring 2020, Spring 2022, Spring 2024.

M7160 Ordinary Differential Equations II

Faculty of Science
Autumn 2007

The course is not taught in Autumn 2007

Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M5160 Differential Eqs.&Cont. Models
Mathematical analysis: Differential calculus of functions of one and several variables, integral calculus, sequences and series of numbers and functions, metric spaces, complex function of a real variable. Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformation and matrices, canonical form of a matrix. Differential equations: Linear and nonlinear systems of ordinary differential equations, existence, uniqueness and properties of solutions, elements of the stability theory, autonomous equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives
The theory of differential equations ranks among basic parts of mathematical analysis. The course is concentrated especially to linear differential equations with periodic coefficients, some selected parts from the theory of linear second-order equations, solution of differential equations by means of infinite series, generalization of the concept of a solution and to equations with deviating argument.
Syllabus
  • 1. Differential inequalities. 2. Selected parts from the theory of linear differential equations - Floquet theory, linear second-order equations (basic properties, Green function, Sturm comparison theorems, Sturm-Liouville boundary-value problem, oscillation theory). 3. Solution of differential equations by means of infinite series. 4. Generalization of the concept of a solution - Carathéodory solution, existence and uniqueness of Carathéodory solutions. 5. Introduction to the theory of differential equations with deviating argument - basic notions, method of steps, existence and uniqueness for delay equations.
Literature
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). 2nd ed. Brno: Masarykova univerzita, 2001, 207 pp. ISBN 80-210-2589-1. info
  • KIGURADZE, Ivan. Okrajové úlohy pro systémy lineárních obyčejných diferenciálních rovnic. 1. vyd. Brno: Masarykova univerzita, 1997, 183 s. ISBN 80-210-1664-7. info
  • KURZWEIL, Jaroslav. Obyčejné diferenciální rovnice : úvod do teorie obyčejných diferenciálních rovnic v reálném oboru. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1978, 418 s. info
  • GREGUŠ, Michal, Marko ŠVEC and Valter ŠEDA. Obyčajné diferenciálne rovnice. 1. vyd. Bratislava: Alfa, vydavateľstvo technickej a ekonomickej literatúry, 1985, 374 s. info
  • Hartman, Philip. Ordinary differential equations. New York-London-Sydney: John Wiley & sons, 1964.
  • El'sgol'c, L. E. Vvedenie v teoriju differencial'nych uravnenij s otklonjajuščimsja argumentom. Moskva
  • Driver, Rodney David. Ordinary and delay differential equations. New York-Heidelberg-Berlin: Springer Verlag, 1977.
Assessment methods (in Czech)
Výuka: přednáška, klasické cvičení. Zkouška: písemná a ústní.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2000, Autumn 2002, Autumn 2004, Autumn 2006, Autumn 2008, Spring 2011, Spring 2014, Spring 2016, spring 2018, Spring 2020, Spring 2022, Spring 2024.

M7160 Ordinary Differential Equations II

Faculty of Science
Autumn 2005

The course is not taught in Autumn 2005

Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. Alexander Lomtatidze, DrSc.
Prerequisites
M5160 Differential Eqs.&Cont. Models
Mathematical analysis: Differential calculus of functions of one and several variables, integral calculus, sequences and series of numbers and functions, metric spaces, complex function of a real variable. Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformation and matrices, canonical form of a matrix. Differential equations: Linear and nonlinear systems of ordinary differential equations, existence, uniqueness and properties of solutions, elements of the stability theory, autonomous equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives
The theory of differential equations ranks among basic parts of mathematical analysis. The course is concentrated especially to linear differential equations with periodic coefficients, some selected parts from the theory of linear second-order equations, solution of differential equations by means of infinite series, generalization of the concept of a solution and to equations with deviating argument.
Syllabus
  • 1. Differential inequalities. 2. Selected parts from the theory of linear differential equations - Floquet theory, linear second-order equations (basic properties, Green function, Sturm comparison theorems, Sturm-Liouville boundary-value problem, oscillation theory). 3. Solution of differential equations by means of infinite series. 4. Generalization of the concept of a solution - Carathéodory solution, existence and uniqueness of Carathéodory solutions. 5. Introduction to the theory of differential equations with deviating argument - basic notions, method of steps, existence and uniqueness for delay equations.
Literature
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). 2nd ed. Brno: Masarykova univerzita, 2001, 207 pp. ISBN 80-210-2589-1. info
  • KIGURADZE, Ivan. Okrajové úlohy pro systémy lineárních obyčejných diferenciálních rovnic. 1. vyd. Brno: Masarykova univerzita, 1997, 183 s. ISBN 80-210-1664-7. info
  • KURZWEIL, Jaroslav. Obyčejné diferenciální rovnice : úvod do teorie obyčejných diferenciálních rovnic v reálném oboru. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1978, 418 s. info
  • GREGUŠ, Michal, Marko ŠVEC and Valter ŠEDA. Obyčajné diferenciálne rovnice. 1. vyd. Bratislava: Alfa, vydavateľstvo technickej a ekonomickej literatúry, 1985, 374 s. info
  • Hartman, Philip. Ordinary differential equations. New York-London-Sydney: John Wiley & sons, 1964.
  • El'sgol'c, L. E. Vvedenie v teoriju differencial'nych uravnenij s otklonjajuščimsja argumentom. Moskva
  • Driver, Rodney David. Ordinary and delay differential equations. New York-Heidelberg-Berlin: Springer Verlag, 1977.
Assessment methods (in Czech)
Výuka: přednáška, klasické cvičení. Zkouška: písemná a ústní.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2000, Autumn 2002, Autumn 2004, Autumn 2006, Autumn 2008, Spring 2011, Spring 2014, Spring 2016, spring 2018, Spring 2020, Spring 2022, Spring 2024.

M7160 Ordinary Differential Equations II

Faculty of Science
Autumn 2003

The course is not taught in Autumn 2003

Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. Alexander Lomtatidze, DrSc.
Prerequisites
M5160 Differential Eqs.&Cont. Models
Mathematical analysis: Differential calculus of functions of one and several variables, integral calculus, sequences and series of numbers and functions, metric spaces, complex function of a real variable. Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformation and matrices, canonical form of a matrix. Differential equations: Linear and nonlinear systems of ordinary differential equations, existence, uniqueness and properties of solutions, elements of the stability theory, autonomous equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives
The theory of differential equations ranks among basic parts of mathematical analysis. The course is concentrated especially to linear differential equations with periodic coefficients, some selected parts from the theory of linear second-order equations, solution of differential equations by means of infinite series, generalization of the concept of a solution and to equations with deviating argument.
Syllabus
  • 1. Differential inequalities. 2. Selected parts from the theory of linear differential equations - Floquet theory, linear second-order equations (basic properties, Green function, Sturm comparison theorems, Sturm-Liouville boundary-value problem, oscillation theory). 3. Solution of differential equations by means of infinite series. 4. Generalization of the concept of a solution - Carathéodory solution, existence and uniqueness of Carathéodory solutions. 5. Introduction to the theory of differential equations with deviating argument - basic notions, method of steps, existence and uniqueness for delay equations.
Literature
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). 2nd ed. Brno: Masarykova univerzita, 2001, 207 pp. ISBN 80-210-2589-1. info
  • KIGURADZE, Ivan. Okrajové úlohy pro systémy lineárních obyčejných diferenciálních rovnic. 1. vyd. Brno: Masarykova univerzita, 1997, 183 s. ISBN 80-210-1664-7. info
  • KURZWEIL, Jaroslav. Obyčejné diferenciální rovnice : úvod do teorie obyčejných diferenciálních rovnic v reálném oboru. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1978, 418 s. info
  • GREGUŠ, Michal, Marko ŠVEC and Valter ŠEDA. Obyčajné diferenciálne rovnice. 1. vyd. Bratislava: Alfa, vydavateľstvo technickej a ekonomickej literatúry, 1985, 374 s. info
  • Hartman, Philip. Ordinary differential equations. New York-London-Sydney: John Wiley & sons, 1964.
  • El'sgol'c, L. E. Vvedenie v teoriju differencial'nych uravnenij s otklonjajuščimsja argumentom. Moskva
  • Driver, Rodney David. Ordinary and delay differential equations. New York-Heidelberg-Berlin: Springer Verlag, 1977.
Assessment methods (in Czech)
Výuka: přednáška, klasické cvičení. Zkouška: písemná a ústní.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2000, Autumn 2002, Autumn 2004, Autumn 2006, Autumn 2008, Spring 2011, Spring 2014, Spring 2016, spring 2018, Spring 2020, Spring 2022, Spring 2024.

M7160 Differential Equations II

Faculty of Science
Autumn 2001

The course is not taught in Autumn 2001

Extent and Intensity
2/1/0. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. Alexander Lomtatidze, DrSc.
Prerequisites (in Czech)
M5160 Differential Eqs.&Cont. Models || M6160 Differential Eqs.&Cont. Models
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives
Differential inequalities. Selected parts from the theory of linear differential equations (Floquet theory, linear second-order equations: basic properties, Green function, Sturm comparison theorems, Sturm-Liouville boundary-value problem, oscillation theory). Solution of differential equations by means of infinite series. Generalization of the concept of a solution (Carathéodory solution, existence and uniqueness of Carathéodory solutions). Introduction to the theory of differential equations with deviating argument (basic notions, method of steps, existence and uniqueness for delay equations).
Literature
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice. 1. vyd. Brno: Masarykova univerzita, 1995, 207 s. ISBN 8021011300. info
  • KURZWEIL, Jaroslav. Obyčejné diferenciální rovnice : úvod do teorie obyčejných diferenciálních rovnic v reálném oboru. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1978, 418 s. info
  • GREGUŠ, Michal, Marko ŠVEC and Valter ŠEDA. Obyčajné diferenciálne rovnice. 1. vyd. Bratislava: Alfa, vydavateľstvo technickej a ekonomickej literatúry, 1985, 374 s. info
  • Hartman, Philip. Ordinary differential equations. New York-London-Sydney: John Wiley & sons, 1964.
  • El'sgol'c, L. E. Vvedenie v teoriju differencial'nych uravnenij s otklonjajuščimsja argumentom. Moskva
  • Driver, Rodney David. Ordinary and delay differential equations. New York-Heidelberg-Berlin: Springer Verlag, 1977.
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2000, Autumn 2002, Autumn 2004, Autumn 2006, Autumn 2008, Spring 2011, Spring 2014, Spring 2016, spring 2018, Spring 2020, Spring 2022, Spring 2024.

M7160 Differential Equations II

Faculty of Science
Autumn 1999

The course is not taught in Autumn 1999

Extent and Intensity
2/1/0. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. Alexander Lomtatidze, DrSc.
Prerequisites (in Czech)
M5160 Differential Eqs.&Cont. Models
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Syllabus
  • Differential inequalities. Selected parts from the theory of linear differential equations (Floquet theory, linear second-order equations: basic properties, Green function, Sturm comparison theorems, Sturm-Liouville boundary-value problem, oscillation theory). Solution of differential equations by means of infinite series. Generalization of the concept of a solution (Carathéodory solution, existence and uniqueness of Carathéodory solutions). Introduction to the theory of differential equations with deviating argument (basic notions, method of steps, existence and uniqueness for delay equations).
Literature
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice. 1. vyd. Brno: Masarykova univerzita, 1995, 207 s. ISBN 8021011300. info
  • KURZWEIL, Jaroslav. Obyčejné diferenciální rovnice : úvod do teorie obyčejných diferenciálních rovnic v reálném oboru. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1978, 418 s. info
  • GREGUŠ, Michal, Marko ŠVEC and Valter ŠEDA. Obyčajné diferenciálne rovnice. 1. vyd. Bratislava: Alfa, vydavateľstvo technickej a ekonomickej literatúry, 1985, 374 s. info
  • Hartman, Philip. Ordinary differential equations. New York-London-Sydney: John Wiley & sons, 1964.
  • El'sgol'c, L. E. Vvedenie v teoriju differencial'nych uravnenij s otklonjajuščimsja argumentom. Moskva
  • Driver, Rodney David. Ordinary and delay differential equations. New York-Heidelberg-Berlin: Springer Verlag, 1977.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2000, Autumn 2002, Autumn 2004, Autumn 2006, Autumn 2008, Spring 2011, Spring 2014, Spring 2016, spring 2018, Spring 2020, Spring 2022, Spring 2024.

M7160 Ordinary Differential Equations II

Faculty of Science
Spring 2011 - only for the accreditation
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites (in Czech)
M5160 Differential Eqs.&Cont. Models
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Autumn 2000, Autumn 2002, Autumn 2004, Autumn 2006, Autumn 2008, Spring 2011, Spring 2014, Spring 2016, spring 2018, Spring 2020, Spring 2022, Spring 2024.

M7160 Ordinary Differential Equations II

Faculty of Science
spring 2012 - acreditation

The course is not taught in spring 2012 - acreditation

The information about the term spring 2012 - acreditation is not made public

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M5160 Ord. Differential Equations I
Mathematical analysis: Differential calculus of functions of one and several variables, integral calculus, sequences and series of numbers and functions, metric spaces, complex function of a real variable. Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformation and matrices, canonical form of a matrix. Differential equations: Linear and nonlinear systems of ordinary differential equations, existence, uniqueness and properties of solutions, elements of the stability theory, autonomous equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives
The theory of differential equations ranks among basic parts of mathematical analysis. The course is focused to systems of nonlinear differential equations with a Carathéodory right-hand side. The following questions are studied in detail: the existence of a solution of the Cauchy problem, extendibility of solutions, global solutions, structure of a solution set of the Cauchy problem, continuous dependence of solutions on parameters. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • Carathéodory class of functions
  • On absolutly continuous functions
  • Cauchy problem
  • Carathéodory theorem for higher-order differential equations
  • Extendibility of solutions of the Cauchy problem
  • Lower and upper solutions of the Cauchy problem
  • On a set of solutions of the Cauchy problem
  • Existence of lower and upper solutions
  • Theorems on differential inequalities
  • Theorems on integral inequalities
  • Global solvability of the Cauchy problem
  • Uniqueness of a solution
  • Correctness of the Cauchy problem
  • Structure of a set of solutions of the Cauchy problem
Literature
  • HARTMAN, Philip. Ordinary differential equations. 2nd ed. Philadelphia, Pa.: SIAM, 2002, xx, 612 s. ISBN 0-89871-510-5. info
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice. 2. vyd. Brno: Masarykova univerzita, 2001, 207 s. ISBN 8021025891. info
  • KIGURADZE, Ivan. Okrajové úlohy pro systémy lineárních obyčejných diferenciálních rovnic. 1. vyd. Brno: Masarykova univerzita, 1997, 183 s. ISBN 80-210-1664-7. info
  • KURZWEIL, Jaroslav. Obyčejné diferenciální rovnice : úvod do teorie obyčejných diferenciálních rovnic v reálném oboru. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1978, 418 s. info
  • CODDINGTON, Earl A. and Norman LEVINSON. Theory of ordinary differential equations. New York: McGraw-Hill, 1955, 429 s. info
Teaching methods
lectures and class exercises
Assessment methods
Teaching: lecture 2 hours a week, seminar 1 hour a week. Examination: written and oral.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2000, Autumn 2002, Autumn 2004, Autumn 2006, Autumn 2008, Spring 2011, Spring 2014, Spring 2016, spring 2018, Spring 2020, Spring 2022, Spring 2024.

M7160 Ordinary Differential Equations II

Faculty of Science
Autumn 2007 - for the purpose of the accreditation

The course is not taught in Autumn 2007 - for the purpose of the accreditation

Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. Alexander Lomtatidze, DrSc.
Prerequisites
M5160 Differential Eqs.&Cont. Models
Mathematical analysis: Differential calculus of functions of one and several variables, integral calculus, sequences and series of numbers and functions, metric spaces, complex function of a real variable. Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformation and matrices, canonical form of a matrix. Differential equations: Linear and nonlinear systems of ordinary differential equations, existence, uniqueness and properties of solutions, elements of the stability theory, autonomous equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives
The theory of differential equations ranks among basic parts of mathematical analysis. The course is concentrated especially to linear differential equations with periodic coefficients, some selected parts from the theory of linear second-order equations, solution of differential equations by means of infinite series, generalization of the concept of a solution and to equations with deviating argument.
Syllabus
  • 1. Differential inequalities. 2. Selected parts from the theory of linear differential equations - Floquet theory, linear second-order equations (basic properties, Green function, Sturm comparison theorems, Sturm-Liouville boundary-value problem, oscillation theory). 3. Solution of differential equations by means of infinite series. 4. Generalization of the concept of a solution - Carathéodory solution, existence and uniqueness of Carathéodory solutions. 5. Introduction to the theory of differential equations with deviating argument - basic notions, method of steps, existence and uniqueness for delay equations.
Literature
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). 2nd ed. Brno: Masarykova univerzita, 2001, 207 pp. ISBN 80-210-2589-1. info
  • KIGURADZE, Ivan. Okrajové úlohy pro systémy lineárních obyčejných diferenciálních rovnic. 1. vyd. Brno: Masarykova univerzita, 1997, 183 s. ISBN 80-210-1664-7. info
  • KURZWEIL, Jaroslav. Obyčejné diferenciální rovnice : úvod do teorie obyčejných diferenciálních rovnic v reálném oboru. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1978, 418 s. info
  • GREGUŠ, Michal, Marko ŠVEC and Valter ŠEDA. Obyčajné diferenciálne rovnice. 1. vyd. Bratislava: Alfa, vydavateľstvo technickej a ekonomickej literatúry, 1985, 374 s. info
  • Hartman, Philip. Ordinary differential equations. New York-London-Sydney: John Wiley & sons, 1964.
  • El'sgol'c, L. E. Vvedenie v teoriju differencial'nych uravnenij s otklonjajuščimsja argumentom. Moskva
  • Driver, Rodney David. Ordinary and delay differential equations. New York-Heidelberg-Berlin: Springer Verlag, 1977.
Assessment methods (in Czech)
Výuka: přednáška, klasické cvičení. Zkouška: písemná a ústní.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2000, Autumn 2002, Autumn 2004, Autumn 2006, Autumn 2008, Spring 2011, Spring 2014, Spring 2016, spring 2018, Spring 2020, Spring 2022, Spring 2024.
  • Enrolment Statistics (recent)