CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024
UPOZORNĚNÍ: Jsou dostupné studijní plány pro následující akademický rok.

Mathematics 4

The course is not on the list Without time-table
Code Completion Credits Range Language
101MAT4 Z,ZK 5 2P+2C English
Garant předmětu:
Ondřej Zindulka
Lecturer:
Yuliya Namlyeyeva, Ondřej Zindulka
Tutor:
Yuliya Namlyeyeva, Ondřej Zindulka
Supervisor:
Department of Mathematics
Synopsis:

1. Matrices, eigenvalues and eigenvectors, spectrum.

2. Norm, norms of matrices, condition number, Gershgorin Theorem.

3. Symmetric matrices, positive definite matrices.

4. Cholesky decomposition. Variational principle.

5. Iterative methods. Sparse matrices. Conditioning.

6. Ordinary linear differential equations - basic properties.

7. Boundary value problems for second order differential equations; eigenvalues and eigenfunctions.

8. Function spaces, dot product of functions. Eigenspaces.

7. Solvability of boundary value problems for second order linear differential equations.

8. Differential operators, operator equations, eigenvalues and eigenfunctions. Solvability of operator equations.

9. Variational principle. Stable and unstable solutions.

10. Variational methods (Ritz, finite elements).

11. Laplace and Poisson Equation.

12. Wave equation.

13. Backup.

Requirements:

https://mat.fsv.cvut.cz/kucera/

Syllabus of lectures:

https://mat.fsv.cvut.cz/kucera/

Syllabus of tutorials:

https://mat.fsv.cvut.cz/kucera/

Study Objective:

https://mat.fsv.cvut.cz/kucera/

Study materials:

!F. Bubeník: Mathematics for Engineers. CVUT, 2014, ISBN 978-80-01-03792-8.

!F. Bubeník: Problems to Mathematics for Engineers, CVUT 2014, ISBN 978-80-01-05621-9

?K. Rektorys: Solving Ordinary and Partial Boundary Value Problems in Science and Engineering (Applied and Computational Mechanics), CRC Press; 1 edition (1998), ISBN 978-0849325526

?Sherman Stein, Anthony Barcellos, Calculus and Analytic Geometry 5th ed., Mcgraw-Hill 1992, ISBN 978-0070611757

Note:
Further information:
https://mat.fsv.cvut.cz/kucera/
No time-table has been prepared for this course
The course is a part of the following study plans:
Data valid to 2024-05-16
Aktualizace výše uvedených informací naleznete na adrese https://bilakniha.cvut.cz/en/predmet148205.html