M7160 Ordinary Differential Equations II
Faculty of ScienceSpring 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:
- 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
- Mathematical Analysis (programme PřF, N-MA)
- 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.
M7160 Ordinary Differential Equations II
Faculty of ScienceSpring 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:
- 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
- Mathematical Analysis (programme PřF, N-MA)
- 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.
M7160 Ordinary Differential Equations II
Faculty of ScienceSpring 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:
- 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
- Mathematical Analysis (programme PřF, N-MA)
- 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.
M7160 Ordinary Differential Equations II
Faculty of Sciencespring 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:
- 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
- Mathematical Analysis (programme PřF, N-MA)
- 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.
M7160 Ordinary Differential Equations II
Faculty of ScienceSpring 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:
- 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
- Mathematical Analysis (programme PřF, N-MA)
- 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.
M7160 Ordinary Differential Equations II
Faculty of ScienceSpring 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:
- 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.
M7160 Ordinary Differential Equations II
Faculty of ScienceSpring 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:
- 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.
M7160 Ordinary Differential Equations II
Faculty of ScienceAutumn 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:
- 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.
M7160 Ordinary Differential Equations II
Faculty of ScienceAutumn 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:
- 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.
M7160 Ordinary Differential Equations II
Faculty of ScienceAutumn 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:
- 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.
M7160 Ordinary Differential Equations II
Faculty of ScienceAutumn 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.
M7160 Differential Equations II
Faculty of ScienceAutumn 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.
M7160 Ordinary Differential Equations II
Faculty of ScienceSpring 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
- Mathematical Analysis (programme PřF, N-MA)
- 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.
M7160 Ordinary Differential Equations II
Faculty of ScienceSpring 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
- Mathematical Analysis (programme PřF, N-MA)
- 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.
M7160 Ordinary Differential Equations II
Faculty of ScienceSpring 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
- Mathematical Analysis (programme PřF, N-MA)
- 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.
M7160 Ordinary Differential Equations II
Faculty of ScienceSpring 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
- Mathematical Analysis (programme PřF, N-MA)
- 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.
M7160 Ordinary Differential Equations II
Faculty of ScienceSpring 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
- Mathematical Analysis (programme PřF, N-MA)
- 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.
M7160 Ordinary Differential Equations II
Faculty of ScienceSpring 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.
M7160 Ordinary Differential Equations II
Faculty of ScienceSpring 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.
M7160 Ordinary Differential Equations II
Faculty of ScienceSpring 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.
M7160 Ordinary Differential Equations II
Faculty of ScienceAutumn 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.
M7160 Ordinary Differential Equations II
Faculty of ScienceAutumn 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.
M7160 Ordinary Differential Equations II
Faculty of ScienceAutumn 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.
M7160 Ordinary Differential Equations II
Faculty of ScienceAutumn 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.
M7160 Differential Equations II
Faculty of ScienceAutumn 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.
M7160 Differential Equations II
Faculty of ScienceAutumn 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.
M7160 Ordinary Differential Equations II
Faculty of ScienceSpring 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.
M7160 Ordinary Differential Equations II
Faculty of Sciencespring 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.
M7160 Ordinary Differential Equations II
Faculty of ScienceAutumn 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.
- Enrolment Statistics (recent)