Numerical Mathematics and Modeling
Code  Completion  Credits  Range  Language 

101XNMM  Z  1  1P+1C  Czech 
 Garant předmětu:
 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:
 Timetable for winter semester 2023/2024:
 Timetable is not available yet
 Timetable for summer semester 2023/2024:
 Timetable is not available yet
 The course is a part of the following study plans: