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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2024/2025

Applied Mathematics

The course is not on the list Without time-table
Code Completion Credits Range Language
101APM Z,ZK 3 1P+1C Czech
Garant předmětu:
Lecturer:
Tutor:
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
No time-table has been prepared for this course
The course is a part of the following study plans:
Data valid to 2024-03-28
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