CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024

Applied Mathematics

Code Completion Credits Range Language
101APM Z,ZK 3 1P+1C Czech
Garant předmětu:
Petr Kučera, Zdeněk Skalák
Lecturer:
Zdeněk Skalák
Tutor:
Zdeněk Skalák
Supervisor:
Department of Mathematics
Synopsis:

basic concepts of differential and integral calculus of functions of one and more real variables, basic concepts from linear algebra, solutions of systems of liner algebraic equations, boundary problems for ordinary and partial differential equations (ODE,PDE), concept of classical solution, weak formulations of boundary problems, weak solutions, Lax-Milgram lemma, existence of weak solution, boundary problems for linear ODE of second order with mixed boundary conditions, relation between classial and weak solution, regularity of weak solutions, finite difference method, finite element method for solutions of boundary problems, solution of Laplace's and Poisson's equations by finite difference method, solution of heat equation by finite difference method, one-dimensional case, solution of heat equation by finite difference method, two-dimensional case, solution of heat equation by finite element method, one-dimensional case.

Requirements:

https://mat.fsv.cvut.cz/vyuka/magistri/zs/apm

Syllabus of lectures:

1) Repetition: differentiation and integration of functions of one real variable, functions of more variables, partial derivatives, multiple integrals.

2) Repetition: basic concepts from linear algebra, solutions of systems of liner algebraic equations.

3) ordinary differential equations (ODE), classical solution, examples.

4) boundary problems for ODE of second order with mixed boundary conditions, discussion of solvability.

5) weak formulation of boundary problems, weak solution, Lax-Milgram lemma, existence of weak solution.

6) relation between classical and weak solution, regularity of weak solutions.

7) finite difference method for solutions of boundary problems.

8) finite element method for solutions of boundary problems.

9) partial differential equations (PDE), classical solutions, examples.

10) boundary problems for PDE solution of Laplace's and Poisson's equations by finite difference method.

11) solution of heat equation by finite difference method, one-dimensional case.

12) solution of heat equation by finite difference method, two-dimensional case.

13) solution of heat equation by finite element method, one-dimensional case.

Syllabus of tutorials:

corresponds with syllabus of lectures

Study Objective:

https://mat.fsv.cvut.cz/vyuka/magistri/zs/apm

Study materials:

TBA

Note:
Further information:
https://mat.fsv.cvut.cz/vyuka/magistri/zs/apm
Time-table for winter semester 2023/2024:
 06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00 roomTH:A-43413:00–13:50(lecture parallel1)Thákurova 7 (budova FSv)A434 roomTH:B-37510:00–11:50EVEN WEEK(lecture parallel1parallel nr.103)Thákurova 7 (budova FSv)B375roomTH:B-68612:00–13:50EVEN WEEK(lecture parallel1parallel nr.101)Thákurova 7 (budova FSv)B686
Time-table for summer semester 2023/2024:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2024-07-17
Aktualizace výše uvedených informací naleznete na adrese https://bilakniha.cvut.cz/en/predmet6867806.html