CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024
UPOZORNĚNÍ: Jsou dostupné studijní plány pro následující akademický rok.

# Numerical Methods

Code Completion Credits Range Language
101NMT Z 2 1P+1C English
Garant předmětu:
Petr Mayer
Lecturer:
Petr Mayer
Tutor:
Petr Mayer
Supervisor:
Department of Mathematics
Synopsis:

The introduction to the basic numerical methods. Great attention is paid to methods for solving systems of linear equations. Further we will study methods of approximation of functions and numerical quadrature. Finally, methods for solving ordinary and partial differential equations, will be studied.

Requirements:
Syllabus of lectures:

1. Introduction. Representation of numbers and its consequences.

2. Gaussian elimination, LU decomposition.

3. Condition number of matrix. Pivoting strategies.

4.Sparse matrix representation. Reordering.

5. Iterative methods.

7. Approximation of functions I.

8. Approximation of functions II.

10. Solution of ordinary differential equations - initial value problem.

11. Solution of ordinary differential equations - boundary value problem.

12. Solution of Partial Differential Equations.

13. Summary

Syllabus of tutorials:

1. Representation of numbers. Some recurrencies

2. Gaussian elimination

3. LU-decomposition

4. Pivoting

5. Jacobi method, Gauss-Seidel method, S.O.R.

7. Interpolation

8. Least Squares Method

9. Trapezoidal method, Romberg method

11. Euler method, Runge-Kutta method

12. Finite difference method

13. Summary

Study Objective:

The introduction to the basic numerical methods. Great attention is paid to methods for solving systems of linear equations. Further we will study methods of approximation of functions and numerical quadrature. Finally, methods for solving ordinary and partial differential equations, will be studied.

Study materials:

!Anthony Ralston, Philip Rabinowitz: A First Course in Numerical Analysis: Second Edition, Dover Publications, 2001 ISBN-13: 978-0486414546

!W. Cheney, D. Kincaid : Numerical Mathematics and Computing, ISBN-13: 978-1133103714

!G. H. Golub, C. F. Van Loan : Matrix Computation, ISBN 9781421407944

?A. Hohmann, P. Deufelhard : Numerical Analysis in Modern Scientific Computing, Springer, 2003, ISBN0387954104, 9780387954103

Note:
Time-table for winter semester 2023/2024:
Time-table is not available yet
Time-table for summer semester 2023/2024:
 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 roomTH:B-37810:00–10:50(lecture parallel1)Thákurova 7 (budova FSv)B378roomTH:B-37811:00–11:50(lecture parallel1parallel nr.101)Thákurova 7 (budova FSv)B378
The course is a part of the following study plans:
Data valid to 2024-05-25
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