Course Catalogue PřF:M8110 Partial Diff. Equations - Course Information # PřF:M8110 Partial Diff. Equations - Course Information

## M8110 Partial Differential Equations

Faculty of Science
Autumn 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)
Supervisor
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:
M8110/01: Mon 17. 9. to Fri 14. 12. Fri 12:00–13:50 M4,01024, M. Veselý
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 the course is directly associated with
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
recommended literature
• Partial differential equations. Edited by Jürgen Jost. New York: Springer-Verlag, 2002. xi, 325. ISBN 0387954287. info
• STRAUSS, Walter A. Partial differential equations : an introduction. [New York]: John Wiley & Sons, 1992. ix, 425. ISBN 0471548685. info
not specified
• RENARDY, Michael and Robert ROGERS. An introduction to partial differential equations. New York: Springer-Verlag, 1992. vii, 428. ISBN 0387979522. info
• PETROVSKIJ, Ivan Georgijevič. Parciální diferenciální rovnice. 1. vyd. Praha: Přírodovědecké vydavatelství, 1952. 276 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