Numerical Methods 1

Course guarantor:

Pavel Váchal

Lecturer:

Petr Kubera

Tutor:

Petr Kubera

Supervisor:

Department of Software Engineering

Synopsis:

Requirements:

To earn credit, students must have at least 80% attendance in exercises and complete two written assignments.

The exam is oral and includes both testing theoretical knowledge and the practical creation of a short program to solve a given task. The tasks are based on exercises completed during the course.

Syllabus of lectures:

1. Numerical mathematics, method error, number representation in computers, rounding errors

2. Problem correctness and conditioning, numerical stability, numerical libraries

3. Solving systems of linear equations direct methods

4. Sparse matrices, interpolation methods for solving systems of linear equations; eigenvalues and eigenvectors

5. Interpolation and extrapolation, interpolation in multiple dimensions

6. Chebyshev approximation, Chebyshev polynomials, least squares approximation

7. Function computation; sorting

8. Finding roots of nonlinear equations and solving systems of nonlinear equations

9. Finding extrema of functions

10. Numerical integration

11. Random numbers and Monte Carlo integration

12. Ordinary differential equations initial value problems, stiff equations

13. Ordinary differential equations boundary value problems

Syllabus of tutorials:

1. Review of the basics of numerical mathematics and error analysis

2. Correctness, conditioning, and numerical stability

3. Solving linear systems and working with matrices

4. Sparse matrices, eigenvalues, and interpolation methods

5. Interpolation and function approximation

6. Function computation and data sorting

7. Finding roots and extrema of functions

8. Numerical integration

9. Random numbers and Monte Carlo methods

10. Solving ordinary differential equations

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:

• Applications of Informatics in Natural Sciences (compulsory course in the program)