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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:

*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**- 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.

- Enrolment Statistics (recent)

- Permalink: https://is.muni.cz/course/sci/autumn2018/M8110