714-0925/03 – Classical Methods of Solution of Partial Differential Equations (PDR)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 10 |
| Subject guarantor | doc. RNDr. Jarmila Doležalová, CSc. | Subject version guarantor | doc. RNDr. Jarmila Doležalová, CSc. |
| Study level | postgraduate | | |
| | Study language | Czech |
| Year of introduction | 2013/2014 | Year of cancellation | 2019/2020 |
| Intended for the faculties | FBI, USP, HGF, FAST, FEI, FMT, FS | Intended for study types | Doctoral |
Subject aims expressed by acquired skills and competences
Main study goals:
(i) to be acquainted with actual progress in this mathematical discipline,
(ii) to extend needed theoretical knowledge with emphasized orientation to its applicability,
(iii) to increase communication ability of specialists in different branches.
With regard to professional orientation of students learning themes modification is offered to fulfill presented aims.
Teaching methods
Lectures
Individual consultations
Tutorials
Project work
Summary
Fourier series: orthogonal functions, Fourier coefficients, even and odd
functions, convergence of the Fourier series, complex form, solution of second
order linear differential equations.
Partial differential equations: general discussion, first-order and second-
order
partial differential equations (initial and boundary conditions, methods of
solution), second-order linear partial differential equations (method of the
characteristics, method of separation of variables), the wave equation, the
heat-conduction equation, the Laplace equation, Maxwell's equations.
Compulsory literature:
Recommended literature:
Way of continuous check of knowledge in the course of semester
Each student makes project.
In a test student solves 3 examples, in a theoretical part defends succesfully the project.
E-learning
Other requirements
Each student must develop:
a) examples,
b) project.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Syllabus of lecture
1. Fourier series: periodic functions, Fourier coefficients, functions of the period 2, function of the period T, even and odd functions
2. Even and odd functions, half - range cosine and sine series, convergence of Fourier series
3. Solution of 2nd order linear differential equations with constant coefficients by Fourier series
4. Partial differential equations: general discussion
5. Methods of solutions of partial differential equations of the first order
6. Methods of solutions of partial differential equations of the second order
7. Fourier´s method of separation
8. 2nd order partial linear differential equations
9. Canonical form of 2nd order partial linear differential equations
10. Laplace equation: separated solutions, boundary conditions
11. Solution of the one-dimensional wave equation: d’Alembert solution, method of the
separation of variables,
12. Solution of a boundary problem
13. Solution of the heat-conduction: one dimensional heat conduction equation, separation method.
14. Reserve
Conditions for subject completion
Conditions for completion are defined only for particular subject version and form of study
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.