M8110 Partial Differential Equations
Faculty of ScienceAutumn 2024
- Extent and Intensity
- 2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). 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
- !( M8300 Part. diff. equations || NOW ( M8300 Part. diff. equations ))
Differential and integral calculus in several variables, basic methods for solving ordinary differential 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
- Geometry (programme PřF, N-MA)
- Mathematical Analysis (programme PřF, N-MA)
- Mathematical Modelling and Numeric Methods (programme PřF, N-MA)
- Course objectives
- The main aim of the course is to analyse the structure and behaviour of the four fundamental linear equations of mathematical physics (Laplace's equation, heat equation, wave equation, and transport equation).
- Learning outcomes
- At the end of the course, in particular, students will be able to:
solve first-order equations;
use the Fourier method;
formulate relevant mathematical theorems and statements and to explain methods of their proofs in the theory of the studied second-order equations;
apply problems from the theory of the studied second-order equations. - Syllabus
- Classification of second-order equations
- Transport equation
- Separation of variables
- Theorem of Cauchy-Kowalevskaya
- Nonlinear first-order equations, method of characteristics
- Method of Fourier's transformation
- Laplace's and Poisson's equation, harmonic functions
- Heat equation
- Wave equation
- Literature
- 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 (probably available only in Czech)
- The course is taught annually.
The course is taught: every week. - Listed among pre-requisites of other courses
- M8300 Partial differential equations
!M8110 && !NOW(M8110)
- M8300 Partial differential equations
M8110 Partial Differential Equations
Faculty of ScienceAutumn 2023
- Extent and Intensity
- 2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). 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 12:00–13:50 M3,01023
- Timetable of Seminar Groups:
- Prerequisites
- !( M8300 Part. diff. equations || NOW ( M8300 Part. diff. equations ))
Differential and integral calculus in several variables, basic methods for solving ordinary differential 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
- Geometry (programme PřF, N-MA)
- Mathematical Analysis (programme PřF, N-MA)
- Mathematical Modelling and Numeric Methods (programme PřF, N-MA)
- Course objectives
- The main aim of the course is to analyse the structure and behaviour of the four fundamental linear equations of mathematical physics (Laplace's equation, heat equation, wave equation, and transport equation).
- Learning outcomes
- At the end of the course, in particular, students will be able to:
solve first-order equations;
use the Fourier method;
formulate relevant mathematical theorems and statements and to explain methods of their proofs in the theory of the studied second-order equations;
apply problems from the theory of the studied second-order equations. - Syllabus
- Classification of second-order equations
- Transport equation
- Separation of variables
- Theorem of Cauchy-Kowalevskaya
- Nonlinear first-order equations, method of characteristics
- Method of Fourier's transformation
- Laplace's and Poisson's equation, harmonic functions
- Heat equation
- Wave equation
- Literature
- 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 (probably available only in Czech)
- Study Materials
The course is taught annually. - Listed among pre-requisites of other courses
- M8300 Partial differential equations
!M8110 && !NOW(M8110)
- M8300 Partial differential equations
M8110 Partial Differential Equations
Faculty of ScienceAutumn 2022
- Extent and Intensity
- 2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Taught in person. - Teacher(s)
- prof. RNDr. Roman Šimon Hilscher, DSc. (lecturer)
doc. RNDr. Michal Veselý, Ph.D. (lecturer) - Guaranteed by
- prof. RNDr. Roman Šimon Hilscher, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Tue 12:00–13:50 M4,01024
- Timetable of Seminar Groups:
- Prerequisites
- !( M8300 Part. diff. equations || NOW ( M8300 Part. diff. equations ))
Differential and integral calculus in several variables, basic methods for solving ordinary differential 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
- Geometry (programme PřF, N-MA)
- Mathematical Analysis (programme PřF, N-MA)
- Mathematical Modelling and Numeric Methods (programme PřF, N-MA)
- Course objectives
- The main aim of the course is to analyse the structure and behaviour of the four fundamental linear equations of mathematical physics (Laplace's equation, heat equation, wave equation, and transport equation).
- Learning outcomes
- At the end of the course, in particular, students will be able to:
solve first-order equations;
use the Fourier method;
formulate relevant mathematical theorems and statements and to explain methods of their proofs in the theory of the studied second-order equations;
apply problems from the theory of the studied second-order equations. - Syllabus
- Classification of second-order equations
- Transport equation
- Separation of variables
- Theorem of Cauchy-Kowalevskaya
- Nonlinear first-order equations, method of characteristics
- Method of Fourier's transformation
- Laplace's and Poisson's equation, harmonic functions
- Heat equation
- Wave equation
- Literature
- 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 (probably available only in Czech)
- The course is taught annually.
- Listed among pre-requisites of other courses
- M8300 Partial differential equations
!M8110 && !NOW(M8110)
- M8300 Partial differential equations
M8110 Partial Differential Equations
Faculty of Scienceautumn 2021
- Extent and Intensity
- 2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Taught in person. - Teacher(s)
- doc. RNDr. Michal Veselý, Ph.D. (lecturer)
- Guaranteed by
- prof. RNDr. Roman Šimon Hilscher, DSc.
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 M3,01023
- Timetable of Seminar Groups:
- Prerequisites
- !( M8300 Part. diff. equations || NOW ( M8300 Part. diff. equations ))
Differential and integral calculus in several variables, basic methods for solving ordinary differential 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
- Geometry (programme PřF, N-MA)
- Mathematical Analysis (programme PřF, N-MA)
- Mathematical Modelling and Numeric Methods (programme PřF, N-MA)
- Course objectives
- The main aim of the course is to analyse the structure and behaviour of the four fundamental linear equations of mathematical physics (Laplace's equation, heat equation, wave equation, and transport equation).
- Learning outcomes
- At the end of the course, in particular, students will be able to:
solve first-order equations;
use the Fourier method;
formulate relevant mathematical theorems and statements and to explain methods of their proofs in the theory of the studied second-order equations;
apply problems from the theory of the studied second-order equations. - Syllabus
- Classification of second-order equations
- Transport equation
- Separation of variables
- Theorem of Cauchy-Kowalevskaya
- Nonlinear first-order equations, method of characteristics
- Method of Fourier's transformation
- Laplace's and Poisson's equation, harmonic functions
- Heat equation
- Wave equation
- Literature
- 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 (probably available only in Czech)
- The course is taught annually.
- Listed among pre-requisites of other courses
- M8300 Partial differential equations
!M8110 && !NOW(M8110)
- M8300 Partial differential equations
M8110 Partial Differential Equations
Faculty of ScienceAutumn 2020
- Extent and Intensity
- 2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Taught online. - Teacher(s)
- doc. RNDr. Michal Veselý, Ph.D. (lecturer)
- Guaranteed by
- prof. RNDr. Roman Šimon Hilscher, DSc.
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
- !( M8300 Part. diff. equations || NOW ( M8300 Part. diff. equations ))
Differential and integral calculus in several variables, basic methods for solving ordinary differential 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
- Geometry (programme PřF, N-MA)
- Mathematical Analysis (programme PřF, N-MA)
- Mathematical Modelling and Numeric Methods (programme PřF, N-MA)
- Course objectives
- The main aim of the course is to analyse the structure and behaviour of the four fundamental linear equations of mathematical physics (Laplace's equation, heat equation, wave equation, and transport equation).
- Learning outcomes
- At the end of the course, in particular, students will be able to:
solve first-order equations;
use the Fourier method;
formulate relevant mathematical theorems and statements and to explain methods of their proofs in the theory of the studied second-order equations;
apply problems from the theory of the studied second-order equations. - Syllabus
- Classification of second-order equations
- Transport equation
- Separation of variables
- Theorem of Cauchy-Kowalevskaya
- Nonlinear first-order equations, method of characteristics
- Method of Fourier's transformation
- Laplace's and Poisson's equation, harmonic functions
- Heat equation
- Wave equation
- Literature
- 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 (probably available only in Czech)
- The course is taught annually.
- Listed among pre-requisites of other courses
- M8300 Partial differential equations
!M8110 && !NOW(M8110)
- M8300 Partial differential equations
M8110 Partial Differential Equations
Faculty of ScienceAutumn 2019
- Extent and Intensity
- 2/2/0. 4 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
- prof. RNDr. Roman Šimon Hilscher, DSc.
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 M4,01024
- Timetable of Seminar Groups:
- Prerequisites
- !( M8300 Part. diff. equations || NOW ( M8300 Part. diff. equations ))
Differential and integral calculus in several variables, basic methods for solving ordinary differential 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
- Geometry (programme PřF, N-MA)
- Mathematical Analysis (programme PřF, N-MA)
- Mathematical Modelling and Numeric Methods (programme PřF, N-MA)
- Course objectives
- The main aim of the course is to analyse the structure and behaviour of the four fundamental linear equations of mathematical physics (Laplace's equation, heat equation, wave equation, and transport equation).
- Learning outcomes
- At the end of the course, in particular, students will be able to:
solve first-order equations;
use the Fourier method;
formulate relevant mathematical theorems and statements and to explain methods of their proofs in the theory of the studied second-order equations;
apply problems from the theory of the studied second-order equations. - Syllabus
- Classification of second-order equations
- Transport equation
- Separation of variables
- Theorem of Cauchy-Kowalevskaya
- Nonlinear first-order equations, method of characteristics
- Method of Fourier's transformation
- Laplace's and Poisson's equation, harmonic functions
- Heat equation
- Wave equation
- Literature
- 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 annually.
- Listed among pre-requisites of other courses
- M8300 Partial differential equations
!M8110 && !NOW(M8110)
- M8300 Partial differential equations
M8110 Partial Differential Equations
Faculty of ScienceAutumn 2018
- Extent and Intensity
- 2/2/0. 4 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
- prof. RNDr. Roman Šimon Hilscher, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Mon 17. 9. to Fri 14. 12. Fri 10:00–11:50 M4,01024
- Timetable of Seminar Groups:
- Prerequisites
- M5160 Ord. Differential Equations I
Differential and integral calculus in several variables, basic methods for solving ordinary differential 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
- Geometry (programme PřF, N-MA)
- Mathematical Analysis (programme PřF, N-MA)
- Mathematical Modelling and Numeric Methods (programme PřF, N-MA)
- Course objectives
- The main aim of the course is to analyse the structure and behaviour of the four fundamental linear equations of mathematical physics (Laplace's equation, heat equation, wave equation, and transport equation).
- Learning outcomes
- At the end of the course, in particular, students will be able to:
solve first-order equations;
use the Fourier method;
formulate relevant mathematical theorems and statements and to explain methods of their proofs in the theory of the studied second-order equations;
apply problems from the theory of the studied second-order equations. - Syllabus
- Classification of second-order equations
- Transport equation
- Separation of variables
- Theorem of Cauchy-Kowalevskaya
- Nonlinear first-order equations, method of characteristics
- Method of Fourier's transformation
- Laplace's and Poisson's equation, harmonic functions
- Heat equation
- Wave equation
- Literature
- 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.
- Listed among pre-requisites of other courses
- M8300 Partial differential equations
!M8110 && !NOW(M8110)
- M8300 Partial differential equations
M8110 Partial Differential Equations
Faculty of Scienceautumn 2017
- Extent and Intensity
- 2/2/0. 4 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
- prof. RNDr. Roman Šimon Hilscher, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Mon 18. 9. to Fri 15. 12. Thu 12:00–13:50 M2,01021
- Timetable of Seminar Groups:
- Prerequisites
- M5160 Ord. Differential Equations I
Differential and integral calculus in several variables, basic methods for solving ordinary differential 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
- Geometry (programme PřF, N-MA)
- Mathematical Analysis (programme PřF, N-MA)
- Mathematical Modelling and Numeric Methods (programme PřF, N-MA)
- Course objectives
- The main aim of the course is to analyse the structure and behaviour of the four fundamental linear equations of mathematical physics (Laplace's equation, heat equation, wave equation, and transport equation).
- Learning outcomes
- At the end of the course, in particular, students will be able to:
solve first-order equations;
use the Fourier method;
formulate relevant mathematical theorems and statements and to explain methods of their proofs in the theory of the studied second-order equations;
apply problems from the theory of the studied second-order equations. - Syllabus
- Classification of second-order equations
- Transport equation
- Separation of variables
- Theorem of Cauchy-Kowalevskaya
- Nonlinear first-order equations, method of characteristics
- Method of Fourier's transformation
- Laplace's and Poisson's equation, harmonic functions
- Heat equation
- Wave equation
- Literature
- 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 annually.
- Listed among pre-requisites of other courses
- M8300 Partial differential equations
!M8110 && !NOW(M8110)
- M8300 Partial differential equations
M8110 Partial Differential Equations
Faculty of ScienceAutumn 2016
- Extent and Intensity
- 2/2/0. 4 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
- prof. RNDr. Roman Šimon Hilscher, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Mon 19. 9. to Sun 18. 12. Fri 12:00–13:50 M4,01024
- Timetable of Seminar Groups:
- Prerequisites
- M5160 Ord. Differential Equations I
Differential and integral calculus in several variables, basic methods for solving ordinary differential 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
- Geometry (programme PřF, N-MA)
- Mathematical Analysis (programme PřF, N-MA)
- Mathematical Modelling and Numeric Methods (programme PřF, N-MA)
- Course objectives
- At the end of this course, students should be able to analyse the structure and behaviour of the four fundamental linear equations of mathematical physics (Laplace's equation, heat equation, wave equation and transport equation). Moreover, students will acquire the basic knowledge of Sobolev spaces which can be used to solve the linear second-order elliptic equations.
- Syllabus
- Classification of second-order equations
- Transport equation
- Separation of variables
- Theorem of Cauchy-Kowalevskaya
- Nonlinear first-order equations, method of characteristics
- Method of Fourier's transformation
- Laplace's and Poisson's equation, harmonic functions
- Heat equation
- Wave equation
- Sobolev spaces
- Second-order elliptic equations
- Literature
- 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 annually.
- Listed among pre-requisites of other courses
- M8300 Partial differential equations
!M8110 && !NOW(M8110)
- M8300 Partial differential equations
M8110 Partial Differential Equations
Faculty of ScienceAutumn 2015
- Extent and Intensity
- 2/2/0. 4 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
- prof. RNDr. Roman Šimon Hilscher, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Thu 14:00–15:50 M4,01024
- Timetable of Seminar Groups:
- Prerequisites
- M5160 Ord. Differential Equations I
Differential and integral calculus in several variables, basic methods for solving ordinary differential 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
- Geometry (programme PřF, N-MA)
- Mathematical Analysis (programme PřF, N-MA)
- Mathematical Modelling and Numeric Methods (programme PřF, N-MA)
- Course objectives
- At the end of this course, students should be able to analyse the structure and behaviour of the four fundamental linear equations of mathematical physics (Laplace's equation, heat equation, wave equation and transport equation). Moreover, students will acquire the basic knowledge of Sobolev spaces which can be used to solve the linear second-order elliptic equations.
- Syllabus
- Classification of second-order equations
- Transport equation
- Separation of variables
- Theorem of Cauchy-Kowalevskaya
- Nonlinear first-order equations, method of characteristics
- Method of Fourier's transformation
- Laplace's and Poisson's equation, harmonic functions
- Heat equation
- Wave equation
- Sobolev spaces
- Second-order elliptic equations
- Literature
- 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. - Listed among pre-requisites of other courses
- M8300 Partial differential equations
!M8110 && !NOW(M8110)
- M8300 Partial differential equations
M8110 Partial Differential Equations
Faculty of ScienceAutumn 2014
- Extent and Intensity
- 2/2/0. 4 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
- prof. RNDr. Roman Šimon Hilscher, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Wed 16:00–17:50 M5,01013
- Timetable of Seminar Groups:
- Prerequisites
- M5160 Ord. Differential Equations I
Differential and integral calculus in several variables, basic methods for solving ordinary differential 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
- Finance Mathematics (programme PřF, N-MA)
- Course objectives
- At the end of this course, students should be able to analyse the structure and behaviour of the four fundamental linear equations of mathematical physics (Laplace's equation, heat equation, wave equation and transport equation). Moreover, students will acquire the basic knowledge of Sobolev spaces which can be used to solve the linear second-order elliptic equations.
- Syllabus
- Classification of second-order equations
- Laplace's and Poisson's equation, harmonic functions
- Method of Fourier's transformation
- Separation of variables
- Nonlinear first-order equations, method of characteristics
- Sobolev spaces
- Second-order elliptic equations
- Literature
- 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.
- Listed among pre-requisites of other courses
- M8300 Partial differential equations
!M8110 && !NOW(M8110)
- M8300 Partial differential equations
M8110 Partial Differential Equations
Faculty of ScienceAutumn 2012
- Extent and Intensity
- 2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
- Teacher(s)
- doc. RNDr. Ladislav Adamec, CSc. (lecturer)
prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
doc. RNDr. Martin Kolář, Ph.D. (lecturer) - Guaranteed by
- doc. RNDr. Ladislav Adamec, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Tue 16:00–17:50 M3,01023
- Timetable of Seminar Groups:
- Prerequisites
- M5160 Ord. Differential Equations I
Differential and integral calculus in several veriables, basic methods for solving ordinary differential 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
- Finance Mathematics (programme PřF, N-MA)
- Course objectives
- Students will acquire techniques necessary for formulating and solving problems using partial differential equations in classical and modern setting. At the end of this course, students will be able to understand the structure and behaviour of the four fundamental linear equations of mathematical physics (Laplace's equation, Heat equation, Wave equation and transport equation) and the structure of nonlinear first order equations. Moreover students will acquire basic knowledge of Sobolev spaces and of modern technique of solution of the linear elliptic equation of second order.
- Syllabus
- Introduction
- Classification of second order equations
- Laplace's and Poisson§s equations, harmonic functions
- Fourier method
- Separation of variables
- Nonlinear first order equations - method of characteristics
- Sobolev spaces
- Second-order elliptic equations
- Literature
- Partial differential equations. Edited by Jürgen Jost. New York: Springer-Verlag, 2002, xi, 325. ISBN 0387954287. info
- RENARDY, Michael and Robert ROGERS. An introduction to partial differential equations. New York: Springer-Verlag, 1992, vii, 428. ISBN 0387979522. info
- STRAUSS, Walter A. Partial differential equations : an introduction. [New York]: John Wiley & Sons, 1992, ix, 425. ISBN 0471548685. info
- PETROVSKIJ, Ivan Georgijevič. Parciální diferenciální rovnice. 1. vyd. Praha: Přírodovědecké vydavatelství, 1952, 276 s. info
- Teaching methods
- Lectures (theoretical explanation with practical examples) and class exercises
- Assessment methods
- Oral exam.
- Language of instruction
- Czech
- Follow-Up Courses
- Further Comments
- Study Materials
The course is taught once in two years. - Listed among pre-requisites of other courses
- M8300 Partial differential equations
!M8110 && !NOW(M8110)
- M8300 Partial differential equations
M8110 Partial Differential Equations
Faculty of ScienceAutumn 2010
- Extent and Intensity
- 2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
- Teacher(s)
- doc. RNDr. Ladislav Adamec, CSc. (lecturer)
- Guaranteed by
- prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Tue 16:00–17:50 M3,01023
- Timetable of Seminar Groups:
- Prerequisites
- M5160 Ord. Differential Equations I
Differential and integral calculus in several veriables, basic methods for solving ordinary differential 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
- Finance Mathematics (programme PřF, N-AM)
- Mathematics (programme PřF, N-MA)
- Course objectives
- Students will acquire techniques necessary for formulating and solving problems using partial differential equations in classical and modern setting. At the end of this course, students will be able to understand the structure and behaviour of the four fundamental linear equations of mathematical physics (Laplace's equation, Heat equation, Wave equation and transport equation) and the structure of nonlinear first order equations. Moreover students will acquire basic knowledge of Sobolev spaces and of modern technique of solution of the linear elliptic equation of second order.
- Syllabus
- Introduction
- Classification of second order equations
- Laplace's and Poisson§s equations, harmonic functions
- Fourier method
- Separation of variables
- Nonlinear first order equations - method of characteristics
- Sobolev spaces
- Second-order elliptic equations
- Literature
- Teaching methods
- Lectures (theoretical explanation with practical examples) and class exercises
- Assessment methods
- Oral exam.
- Language of instruction
- Czech
- Follow-Up Courses
- Further Comments
- The course is taught once in two years.
- Listed among pre-requisites of other courses
- M8300 Partial differential equations
!M8110 && !NOW(M8110)
- M8300 Partial differential equations
M8110 Partial Differential Equations - Classical Methods
Faculty of ScienceAutumn 2009
- Extent and Intensity
- 2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
- Teacher(s)
- doc. RNDr. Ladislav Adamec, CSc. (lecturer)
- Guaranteed by
- prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Mon 16:00–17:50 M2,01021
- Timetable of Seminar Groups:
- Prerequisites
- M5160 Differential Eqs.&Cont. Models
Differential and integral calculus in several veriables, basic methods for solving ordinary differential 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
- Finance Mathematics (programme PřF, N-AM)
- Mathematics (programme PřF, M-MA)
- Mathematics (programme PřF, N-MA)
- Course objectives
- Students will acquire techniques necessary for formulating and solving problems using partial differential equations in classical setting. At the end of this course, students will be able to understand the structure and behaviour of the four fundamental linear equations of mathematical physics (Laplace's equation, Heat equation, Wave equation and transport equation) and the structure of nonlinear first order equations.
- Syllabus
- Introduction
- Tranport equation
- Laplace's equation
- Heat equation
- Wave equation
- Nonlinear first order equations - Method of characteristics
- Classification of second order equations
- Separation of variables
- Integral transformations
- Literature
- Teaching methods
- Lectures (theoretical explanation with practical examples) and class exercises
- Assessment methods
- Oral exam.
- Language of instruction
- Czech
- Follow-Up Courses
- Further Comments
- Study Materials
The course is taught annually. - Listed among pre-requisites of other courses
- M8300 Partial differential equations
!M8110 && !NOW(M8110)
- M8300 Partial differential equations
M8110 Partial Differential Equations I
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)
- doc. RNDr. Ladislav Adamec, CSc. (lecturer)
- Guaranteed by
- doc. RNDr. Martin Kolář, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Mon 8:00–9:50 MS1,01016
- Timetable of Seminar Groups:
- Prerequisites
- M5160 Differential Eqs.&Cont. Models
Differential and integral calculus in several veriables, basic methods for solving ordinary differential 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
- Finance Mathematics (programme PřF, N-AM)
- Mathematics (programme PřF, M-MA)
- Mathematics (programme PřF, N-MA)
- Course objectives
- The aim of the course is to aquire techniques necessary for formulating and solving problems using partial differential equations in classical setting.
- Syllabus
- Introduction
- Tranport equation
- Laplace's equation
- Heat equation
- Wave equation
- Nonlinear first order equations - Method of characteristics
- Classification of second order equations
- Separation of variables
- Integral transformations
- Literature
- Assessment methods
- lectures and class exercises,
oral exam. - Language of instruction
- Czech
- Follow-Up Courses
- Further Comments
- The course is taught annually.
- Listed among pre-requisites of other courses
- M8300 Partial differential equations
!M8110 && !NOW(M8110)
- M8300 Partial differential equations
M8110 Partial Differential Equations I
Faculty of ScienceAutumn 2007
- Extent and Intensity
- 2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
- Teacher(s)
- doc. RNDr. Ladislav Adamec, CSc. (lecturer)
- Guaranteed by
- doc. RNDr. Martin Kolář, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Thu 17:00–18:50 UP2
- Timetable of Seminar Groups:
- Prerequisites
- M5160 Differential Eqs.&Cont. Models
Differential and integral calculus in several veriables, basic methods for solving ordinary differential 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)
- Mathematics (programme PřF, N-MA)
- Course objectives
- The aim of the course is to aquire techniques necessary for formulating and solving problems using partial differential equations. The first part contains a theory for first order equations, solutions using power series, local existence and uniqueness, classification of second order linear equations. the second part contains analysis of the fundamental equations of mathematical physics - the heat equation, wave equation and Laplace equation. Techniques for solving appropriate initial and boundary value problems are discussed - Separation of variables, integral transformations, use of characteristics, Green's function, maximum principles and uniqueness of solutions.
- Syllabus
- I. Introduction Tranport equation Laplace's equation Heat equation Wave equation Nonlinear first order equations - Method of characteristics Classification of second order equations Separation of variables Integral transformations
- Literature
- Assessment methods (in Czech)
- Výuka : přednáška a cvičení, Zkouška : ústní
- Language of instruction
- Czech
- Follow-Up Courses
- Further Comments
- The course is taught annually.
- Listed among pre-requisites of other courses
- M8300 Partial differential equations
!M8110 && !NOW(M8110)
- M8300 Partial differential equations
M8110 Partial Differential Equations I
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)
- doc. RNDr. Ladislav Adamec, CSc. (lecturer)
- Guaranteed by
- doc. RNDr. Martin Kolář, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Ladislav Adamec, CSc. - Timetable
- Thu 17:00–18:50 UP1
- Timetable of Seminar Groups:
- Prerequisites
- M5160 Differential Eqs.&Cont. Models
Differential and integral calculus in several veriables, basic methods for solving ordinary differential 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)
- Mathematics (programme PřF, N-MA)
- Course objectives
- The aim of the course is to aquire techniques necessary for formulating and solving problems using partial differential equations. The first part contains a theory for first order equations, solutions using power series, local existence and uniqueness, classification of second order linear equations. the second part contains analysis of the fundamental equations of mathematical physics - the heat equation, wave equation and Laplace equation. Techniques for solving appropriate initial and boundary value problems are discussed - Separation of variables, integral transformations, use of characteristics, Green's function, maximum principles and uniqueness of solutions.
- Syllabus
- I. Introduction First order equations Cauchy problem for k-th order equations Classification of second order equations and canonical forms Derivation of the basic equations of mathematical physics and initial and boundary conditions II Classical methods Method of characteristics Separation of variables Integral transformations Maximum principles, harmonic functions and uniqueness of solutions
- Literature
- Assessment methods (in Czech)
- Výuka : přednáška a cvičení, Zkouška : ústní
- Language of instruction
- Czech
- Follow-Up Courses
- Further Comments
- The course is taught annually.
- Listed among pre-requisites of other courses
- M8300 Partial differential equations
!M8110 && !NOW(M8110)
- M8300 Partial differential equations
M8110 Partial Differential Equations I
Faculty of ScienceAutumn 2005
- Extent and Intensity
- 2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
- Teacher(s)
- doc. RNDr. Ladislav Adamec, CSc. (lecturer)
- Guaranteed by
- doc. RNDr. Martin Kolář, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Ladislav Adamec, CSc. - Timetable
- Tue 17:00–18:50 UM
- Timetable of Seminar Groups:
- Prerequisites
- M5160 Differential Eqs.&Cont. Models
Differential and integral calculus in several veriables, basic methods for solving ordinary differential 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)
- Mathematics (programme PřF, N-MA)
- Course objectives
- The aim of the course is to aquire techniques necessary for formulating and solving problems using partial differential equations. The first part contains a theory for first order equations, solutions using power series, local existence and uniqueness, classification of second order linear equations. the second part contains analysis of the fundamental equations of mathematical physics - the heat equation, wave equation and Laplace equation. Techniques for solving appropriate initial and boundary value problems are discussed - Separation of variables, integral transformations, use of characteristics, Green's function, maximum principles and uniqueness of solutions.
- Syllabus
- I. Introduction First order equations Cauchy problem for k-th order equations Classification of second order equations and canonical forms Derivation of the basic equations of mathematical physics and initial and boundary conditions II Classical methods Method of characteristics Separation of variables Integral transformations Maximum principles, harmonic functions and uniqueness of solutions
- Literature
- Assessment methods (in Czech)
- Výuka : přednáška a cvičení, Zkouška : ústní
- Language of instruction
- Czech
- Follow-Up Courses
- Further Comments
- The course is taught annually.
- Listed among pre-requisites of other courses
- M8300 Partial differential equations
!M8110 && !NOW(M8110)
- M8300 Partial differential equations
M8110 Partial Differential Equations I
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)
- doc. RNDr. Ladislav Adamec, CSc. (lecturer)
- Guaranteed by
- doc. RNDr. Martin Kolář, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Ladislav Adamec, CSc. - Timetable
- Wed 8:00–9:50 UM
- Timetable of Seminar Groups:
- Prerequisites
- M5160 Differential Eqs.&Cont. Models
Differential and integral calculus in several veriables, basic methods for solving ordinary differential 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)
- Mathematics (programme PřF, N-MA)
- Course objectives
- The aim of the course is to aquire techniques necessary for formulating and solving problems using partial differential equations. The first part contains a theory for first order equations, solutions using power series, local existence and uniqueness, classification of second order linear equations. the second part contains analysis of the fundamental equations of mathematical physics - the heat equation, wave equation and Laplace equation. Techniques for solving appropriate initial and boundary value problems are discussed - Separation of variables, integral transformations, use of characteristics, Green's function, maximum principles and uniqueness of solutions.
- Syllabus
- I. Introduction First order equations Cauchy problem for k-th order equations Classification of second order equations and canonical forms Derivation of the basic equations of mathematical physics and initial and boundary conditions II Classical methods Method of characteristics Separation of variables Integral transformations Green's function Maximum principles, harmonic functions and uniqueness of solutions
- Literature
- ARSENIN, Vasilij Jakovlevič. Metody matematičeskoj fiziki i special'nyje funkcii. 2. perer. i dop. izd. Moskva: Nauka, 1984, 382 s. info
- Assessment methods (in Czech)
- Výuka : přednáška a cvičení, Zkouška : ústní
- Language of instruction
- Czech
- Follow-Up Courses
- Further Comments
- The course is taught annually.
- Listed among pre-requisites of other courses
- M8300 Partial differential equations
!M8110 && !NOW(M8110)
- M8300 Partial differential equations
M8110 Partial Differential Equations I
Faculty of ScienceSpring 2004
- Extent and Intensity
- 2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
- Teacher(s)
- doc. RNDr. Martin Kolář, Ph.D. (lecturer)
- Guaranteed by
- doc. RNDr. Martin Kolář, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Martin Kolář, Ph.D. - Timetable
- Wed 15:00–16:50 U1
- Timetable of Seminar Groups:
- Prerequisites
- M5160 Differential Eqs.&Cont. Models
Differential and integral calculus in several veriables, basic methods for solving ordinary differential 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)
- Mathematics (programme PřF, N-MA)
- Course objectives
- The aim of the course is to aquire techniques necessary for formulating and solving problems using partial differential equations. The first part contains a theory for first order equations, solutions using power series, local existence and uniqueness, classification of second order linear equations. the second part contains analysis of the fundamental equations of mathematical physics - the heat equation, wave equation and Laplace equation. Techniques for solving appropriate initial and boundary value problems are discussed - Separation of variables, integral transformations, use of characteristics, Green's function, maximum principles and uniqueness of solutions.
- Syllabus
- I. Introduction First order equations Cauchy problem for k-th order equations Classification of second order equations and canonical forms Derivation of the basic equations of mathematical physics and initial and boundary conditions II Classical methods Method of characteristics Separation of variables Integral transformations Green's function Maximum principles, harmonic functions and uniqueness of solutions
- Literature
- ARSENIN, Vasilij Jakovlevič. Metody matematičeskoj fiziki i special'nyje funkcii. 2. perer. i dop. izd. Moskva: Nauka, 1984, 382 s. info
- Assessment methods (in Czech)
- Výuka : přednáška a cvičení, Zkouška : ústní
- Language of instruction
- Czech
- Further Comments
- The course is taught annually.
- Listed among pre-requisites of other courses
- M8300 Partial differential equations
!M8110 && !NOW(M8110)
- M8300 Partial differential equations
M8110 Partial Differential Equations I
Faculty of ScienceSpring 2003
- Extent and Intensity
- 2/1/0. 3 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
- Teacher(s)
- doc. RNDr. Martin Kolář, Ph.D. (lecturer)
- Guaranteed by
- doc. RNDr. Martin Kolář, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Martin Kolář, Ph.D. - Timetable of Seminar Groups
- M8110/01: No timetable has been entered into IS. M. Kolář
- Prerequisites
- M5160 Differential Eqs.&Cont. Models
Differential and integral calculus in several veriables, basic methods for solving ordinary differential 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)
- Mathematics (programme PřF, N-MA)
- Course objectives
- The aim of the course is to aquire techniques necessary for formulating and solving problems using partial differential equations. The first part contains a theory for first order equations, solutions using power series, local existence and uniqueness, classification of second order linear equations. the second part contains analysis of the fundamental equations of mathematical physics - the heat equation, wave equation and Laplace equation. Techniques for solving appropriate initial and boundary value problems are discussed - Separation of variables, integral transformations, use of characteristics, Green's function, maximum principles and uniqueness of solutions.
- Syllabus
- I. Introduction First order equations Cauchy problem for k-th order equations Classification of second order equations and canonical forms Derivation of the basic equations of mathematical physics and initial and boundary conditions II Classical methods Method of characteristics Separation of variables Integral transformations Green's function Maximum principles, harmonic functions and uniqueness of solutions
- Literature
- ARSENIN, Vasilij Jakovlevič. Metody matematičeskoj fiziki i special'nyje funkcii. 2. perer. i dop. izd. Moskva: Nauka, 1984, 382 s. info
- Assessment methods (in Czech)
- Výuka : přednáška a cvičení, Zkouška : ústní
- Language of instruction
- Czech
- Further Comments
- The course is taught annually.
- Listed among pre-requisites of other courses
- M8300 Partial differential equations
!M8110 && !NOW(M8110)
- M8300 Partial differential equations
M8110 Partial Differential Equations I
Faculty of ScienceSpring 2002
- Extent and Intensity
- 2/1/0. 4 credit(s). Type of Completion: zk (examination).
- Teacher(s)
- doc. RNDr. Martin Kolář, Ph.D. (lecturer)
- Guaranteed by
- doc. RNDr. Martin Kolář, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Martin Kolář, Ph.D. - 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)
- Mathematics (programme PřF, N-MA)
- Course objectives
- I. Introduction First order equations Cauchy problem for k-th order equations Classification of second order equations and canonical forms Derivation of the basic equations of mathematical physics and initial and boundary conditions II Classical methods Method of characteristics Separation of variables Integral transformations Green's function Maximum principles, harmonic functions and uniqueness of solutions
- Literature
- ARSENIN, Vasilij Jakovlevič. Metody matematičeskoj fiziki i special'nyje funkcii. 2. perer. i dop. izd. Moskva: Nauka, 1984, 382 s. info
- Language of instruction
- Czech
- Further Comments
- The course is taught annually.
The course is taught: every week. - Listed among pre-requisites of other courses
- M8300 Partial differential equations
!M8110 && !NOW(M8110)
- M8300 Partial differential equations
M8110 Partial Differential Equations I
Faculty of ScienceSpring 2001
- Extent and Intensity
- 2/1/0. 4 credit(s). Type of Completion: zk (examination).
- Teacher(s)
- doc. RNDr. Martin Kolář, Ph.D. (lecturer)
- Guaranteed by
- doc. RNDr. Martin Kolář, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Martin Kolář, Ph.D. - 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)
- Mathematics (programme PřF, N-MA)
- Course objectives
- I. Introduction First order equations Cauchy problem for k-th order equations Classification of second order equations and canonical forms Derivation of the basic equations of mathematical physics and initial and boundary conditions II Classical methods Method of characteristics Separation of variables Integral transformations Green's function Maximum principles, harmonic functions and uniqueness of solutions
- Literature
- ARSENIN, Vasilij Jakovlevič. Metody matematičeskoj fiziki i special'nyje funkcii. 2. perer. i dop. izd. Moskva: Nauka, 1984, 382 s. info
- Language of instruction
- Czech
- Further Comments
- The course is taught annually.
The course is taught: every week. - Listed among pre-requisites of other courses
- M8300 Partial differential equations
!M8110 && !NOW(M8110)
- M8300 Partial differential equations
M8110 Partial Differential Equations I
Faculty of ScienceSpring 2000
- Extent and Intensity
- 2/1/0. 4 credit(s). Type of Completion: zk (examination).
- Teacher(s)
- doc. RNDr. Martin Kolář, Ph.D. (lecturer)
- Guaranteed by
- doc. RNDr. Martin Kolář, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Martin Kolář, Ph.D. - 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)
- Mathematics (programme PřF, N-MA)
- Syllabus
- I. Introduction First order equations Cauchy problem for k-th order equations Classification of second order equations and canonical forms Derivation of the basic equations of mathematical physics and initial and boundary conditions II Classical methods Method of characteristics Separation of variables Integral transformations Green's function Maximum principles, harmonic functions and uniqueness of solutions
- Literature
- ARSENIN, Vasilij Jakovlevič. Metody matematičeskoj fiziki i special'nyje funkcii. 2. perer. i dop. izd. Moskva: Nauka, 1984, 382 s. info
- Language of instruction
- Czech
- Further Comments
- The course is taught annually.
The course is taught: every week. - Listed among pre-requisites of other courses
- M8300 Partial differential equations
!M8110 && !NOW(M8110)
- M8300 Partial differential equations
M8110 Partial Differential Equations
Faculty of ScienceAutumn 2013
The course is not taught in Autumn 2013
- Extent and Intensity
- 2/2/0. 4 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
- prof. RNDr. Roman Šimon Hilscher, DSc.
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
Differential and integral calculus in several variables, basic methods for solving ordinary differential 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
- Finance Mathematics (programme PřF, N-MA)
- Course objectives
- At the end of this course, students should be able to analyse the structure and behaviour of the four fundamental linear equations of mathematical physics (Laplace's equation, heat equation, wave equation and transport equation). Moreover, students will acquire the basic knowledge of Sobolev spaces which can be used to solve the linear second-order elliptic equations.
- Syllabus
- Classification of second-order equations
- Laplace's and Poisson's equation, harmonic functions
- Method of Fourier's transformation
- Separation of variables
- Nonlinear first-order equations, method of characteristics
- Sobolev spaces
- Second-order elliptic equations
- Literature
- Teaching methods
- Lectures, seminars
- Assessment methods
- Oral exam
- Language of instruction
- Czech
- Further Comments
- The course is taught once in two years.
The course is taught: every week. - Listed among pre-requisites of other courses
- M8300 Partial differential equations
!M8110 && !NOW(M8110)
- M8300 Partial differential equations
M8110 Partial Differential Equations
Faculty of ScienceAutumn 2011
The course is not taught in Autumn 2011
- Extent and Intensity
- 2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
- Teacher(s)
- doc. RNDr. Ladislav Adamec, CSc. (lecturer)
- Guaranteed by
- prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science - Prerequisites
- M5160 Ord. Differential Equations I
Differential and integral calculus in several veriables, basic methods for solving ordinary differential 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
- Finance Mathematics (programme PřF, N-AM)
- Finance Mathematics (programme PřF, N-MA)
- Mathematics (programme PřF, N-MA)
- Course objectives
- Students will acquire techniques necessary for formulating and solving problems using partial differential equations in classical and modern setting. At the end of this course, students will be able to understand the structure and behaviour of the four fundamental linear equations of mathematical physics (Laplace's equation, Heat equation, Wave equation and transport equation) and the structure of nonlinear first order equations. Moreover students will acquire basic knowledge of Sobolev spaces and of modern technique of solution of the linear elliptic equation of second order.
- Syllabus
- Introduction
- Classification of second order equations
- Laplace's and Poisson§s equations, harmonic functions
- Fourier method
- Separation of variables
- Nonlinear first order equations - method of characteristics
- Sobolev spaces
- Second-order elliptic equations
- Literature
- Partial differential equations. Edited by Jürgen Jost. New York: Springer-Verlag, 2002, xi, 325. ISBN 0387954287. info
- RENARDY, Michael and Robert ROGERS. An introduction to partial differential equations. New York: Springer-Verlag, 1992, vii, 428. ISBN 0387979522. info
- STRAUSS, Walter A. Partial differential equations : an introduction. [New York]: John Wiley & Sons, 1992, ix, 425. ISBN 0471548685. info
- PETROVSKIJ, Ivan Georgijevič. Parciální diferenciální rovnice. 1. vyd. Praha: Přírodovědecké vydavatelství, 1952, 276 s. info
- Teaching methods
- Lectures (theoretical explanation with practical examples) and class exercises
- Assessment methods
- Oral exam.
- Language of instruction
- Czech
- Follow-Up Courses
- Further Comments
- The course is taught once in two years.
The course is taught: every week. - Listed among pre-requisites of other courses
- M8300 Partial differential equations
!M8110 && !NOW(M8110)
- M8300 Partial differential equations
M8110 Partial Differential Equations
Faculty of ScienceAutumn 2011 - acreditation
The information about the term Autumn 2011 - acreditation is not made public
- Extent and Intensity
- 2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
- Teacher(s)
- doc. RNDr. Ladislav Adamec, CSc. (lecturer)
- Guaranteed by
- prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science - Prerequisites
- M5160 Ord. Differential Equations I
Differential and integral calculus in several veriables, basic methods for solving ordinary differential 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
- Finance Mathematics (programme PřF, N-AM)
- Mathematics (programme PřF, N-MA)
- Course objectives
- Students will acquire techniques necessary for formulating and solving problems using partial differential equations in classical and modern setting. At the end of this course, students will be able to understand the structure and behaviour of the four fundamental linear equations of mathematical physics (Laplace's equation, Heat equation, Wave equation and transport equation) and the structure of nonlinear first order equations. Moreover students will acquire basic knowledge of Sobolev spaces and of modern technique of solution of the linear elliptic equation of second order.
- Syllabus
- Introduction
- Classification of second order equations
- Laplace's and Poisson§s equations, harmonic functions
- Fourier method
- Separation of variables
- Nonlinear first order equations - method of characteristics
- Sobolev spaces
- Second-order elliptic equations
- Literature
- Partial differential equations. Edited by Jürgen Jost. New York: Springer-Verlag, 2002, xi, 325. ISBN 0387954287. info
- RENARDY, Michael and Robert ROGERS. An introduction to partial differential equations. New York: Springer-Verlag, 1992, vii, 428. ISBN 0387979522. info
- STRAUSS, Walter A. Partial differential equations : an introduction. [New York]: John Wiley & Sons, 1992, ix, 425. ISBN 0471548685. info
- PETROVSKIJ, Ivan Georgijevič. Parciální diferenciální rovnice. 1. vyd. Praha: Přírodovědecké vydavatelství, 1952, 276 s. info
- Teaching methods
- Lectures (theoretical explanation with practical examples) and class exercises
- Assessment methods
- Oral exam.
- Language of instruction
- Czech
- Follow-Up Courses
- Further Comments
- The course is taught once in two years.
The course is taught: every week. - Listed among pre-requisites of other courses
- M8300 Partial differential equations
!M8110 && !NOW(M8110)
- M8300 Partial differential equations
M8110 Partial Differential Equations
Faculty of ScienceAutumn 2010 - only for the accreditation
- Extent and Intensity
- 2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
- Teacher(s)
- doc. RNDr. Ladislav Adamec, CSc. (lecturer)
- Guaranteed by
- prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science - Prerequisites
- M5160 Ord. Differential Equations I
Differential and integral calculus in several veriables, basic methods for solving ordinary differential 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
- Finance Mathematics (programme PřF, N-AM)
- Mathematics (programme PřF, M-MA)
- Mathematics (programme PřF, N-MA)
- Course objectives
- Students will acquire techniques necessary for formulating and solving problems using partial differential equations in classical and modern setting. At the end of this course, students will be able to understand the structure and behaviour of the four fundamental linear equations of mathematical physics (Laplace's equation, Heat equation, Wave equation and transport equation) and the structure of nonlinear first order equations.
- Syllabus
- Introduction
- Classification of second order equations
- Laplace's and Poisson§s equations, harmonic functions
- Fourier method
- Separation of variables
- Nonlinear first order equations - method of characteristics
- Sobolev spaces
- Second-order elliptic equations
- Literature
- Teaching methods
- Lectures (theoretical explanation with practical examples) and class exercises
- Assessment methods
- Oral exam.
- Language of instruction
- Czech
- Follow-Up Courses
- Further Comments
- The course is taught annually.
The course is taught: every week. - Listed among pre-requisites of other courses
- M8300 Partial differential equations
!M8110 && !NOW(M8110)
- M8300 Partial differential equations
M8110 Partial Differential Equations I
Faculty of ScienceAutumn 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)
- doc. RNDr. Ladislav Adamec, CSc. (lecturer)
- Guaranteed by
- doc. RNDr. Martin Kolář, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Ladislav Adamec, CSc. - Prerequisites
- M5160 Differential Eqs.&Cont. Models
Differential and integral calculus in several veriables, basic methods for solving ordinary differential 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)
- Mathematics (programme PřF, N-MA)
- Course objectives
- The aim of the course is to aquire techniques necessary for formulating and solving problems using partial differential equations. The first part contains a theory for first order equations, solutions using power series, local existence and uniqueness, classification of second order linear equations. the second part contains analysis of the fundamental equations of mathematical physics - the heat equation, wave equation and Laplace equation. Techniques for solving appropriate initial and boundary value problems are discussed - Separation of variables, integral transformations, use of characteristics, Green's function, maximum principles and uniqueness of solutions.
- Syllabus
- I. Introduction First order equations Cauchy problem for k-th order equations Classification of second order equations and canonical forms Derivation of the basic equations of mathematical physics and initial and boundary conditions II Classical methods Method of characteristics Separation of variables Integral transformations Maximum principles, harmonic functions and uniqueness of solutions
- Literature
- Assessment methods (in Czech)
- Výuka : přednáška a cvičení, Zkouška : ústní
- Language of instruction
- Czech
- Follow-Up Courses
- Further Comments
- The course is taught annually.
The course is taught: every week. - Listed among pre-requisites of other courses
- M8300 Partial differential equations
!M8110 && !NOW(M8110)
- M8300 Partial differential equations
- Enrolment Statistics (recent)