Numerical Mathematics and Modeling

Course guarantor:

Petr Mayer

Lecturer:

Petr Mayer

Tutor:

Petr Mayer

Supervisor:

Department of Mathematics

Synopsis:

An overview of some numerical methods and their use in solving real problems.

Requirements:

Basic knowledge of mathematics in the scope of the first three semesters. Basic knowledge of programming.

Syllabus of lectures:

1. Representation of numbers, meaning of calculation error estimation

2. Solving systems of linear equations - direct methods

3. Approximation of functions

4. Numerical quadrature

5. Roots of functions

6. The method of least squares

7. Finite element method

8. Solving ordinary differential equations - initial problem

9. Solving partial differential equations

10. Systems of linear equations - iteration methods

11. Equation of heat conduction

12. Markov chains - introduction, stationary probability distribution

13. Markov chains - other characteristics

Syllabus of tutorials:

1. Representation of numbers, meaning of calculation error estimation

2. Solving systems of linear equations, GEM

3. Approximation of functions, Lagrange interpolation

4. Numerical quadrature, Gaussian quadrature

5. Roots of functions, Newton's method, method of secants

6. Method of least squares, implementation in 1D

7. Finite element method, implementation in 1D

8. Solving ordinary differential equations - initial problem

9. Solving partial differential equations

10. Systems of linear equations - iteration methods. PCG, SD, GMRES.

11. Equation of heat conduction

12. Markov chains - introduction, stationary probability distribution

13. Markov chains - other characteristics, matrix of mean times of the first transition

Study Objective:

The goal is to gain an overview of the possibilities of numerical calculations and their use in solving real problems.

Study materials:

Povinná literatura:

Anthony Ralston, Philip Rabinowitz: A First Course in Numerical Analysis: Second Edition, Dover Publications, 2001

W. Cheney, D. Kincaid : Numerical Mathematics and Computing

G. H. Golub, C. F. Van Loan : Matrix Computation

Doporučená literatura:

A. Hohmann, P. Deufelhard : Numerical Analysis in Modern Scientific Computing, Springer, 2003

Note:

Time-table for winter semester 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans: