Mathematics for Applications+Numerical Methods 1

Course guarantor:

Petr Mayer

Lecturer:

Petr Mayer

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

Numerical methods of numerical linear algebra and analysis.

Requirements:

Syllabus of lectures:

1. Computations, rounding errors, numerical stability

2. Roots of systems of nonlinear equations

3. Iterative method, Aitken's acceleration

4. Newton's method and modified Newton's method

5. Systems of linear algebraic equations

6. Eliminations techniques of Gauss type, Choleski decompostion

7. Systems with banded matrices, systems with positive definite matrices, systems with tridiagonal matrices

8. Simplex method

9. Numerical quadrature, computation of Fourier coeficients

10. Iterative methods for linear systems

11. Jacobi, Gauss-Seidel and SOR methods

12. PCG and GMRES methods

13. Eigenvalue problem

14. Power method, Kellogg's proccess

15. Numerical methods for initial value problem for ODE's and systems of ODE's

Syllabus of tutorials:

Study Objective:

Study materials:

Note:

Time-table for winter semester 2025/2026:

Time-table is not available yet

Time-table for summer semester 2025/2026:

Time-table is not available yet

The course is a part of the following study plans: