Logo ČVUT
CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

Mathematics 4

Login to KOS for course enrollment Display time-table
Code Completion Credits Range Language
101MAT4 Z,ZK 5 2P+2C
Lecturer:
Ondřej Zindulka (guarantor)
Tutor:
Ondřej Zindulka (guarantor)
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:
Syllabus of lectures:
Syllabus of tutorials:
Study Objective:
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:
Time-table for winter semester 2019/2020:
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
Mon
Tue
Fri
roomTH:B-975

13:00–14:50
(lecture parallel1)
Thákurova 7 (FSv-budova A)
B975
roomTH:B-975

15:00–16:50
(lecture parallel1
parallel nr.101)

Thákurova 7 (FSv-budova A)
B975
Thu
Fri
Time-table for summer semester 2019/2020:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2020-04-08
For updated information see http://bilakniha.cvut.cz/en/predmet148205.html