Numerical Methods
Code  Completion  Credits  Range  Language 

101NMT  Z  2  1P+1C  English 
 Garant předmětu:
 Lecturer:
 Tutor:
 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.
6. Gradient methods.
7. Approximation of functions I.
8. Approximation of functions II.
9. Numerical quadrature.
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. LUdecomposition
4. Pivoting
5. Jacobi method, GaussSeidel method, S.O.R.
6. Conjugate gradients
7. Interpolation
8. Least Squares Method
9. Trapezoidal method, Romberg method
10. Gauss quadrature
11. Euler method, RungeKutta 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 ISBN13: 9780486414546
!W. Cheney, D. Kincaid : Numerical Mathematics and Computing, ISBN13: 9781133103714
!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:
 Further information:
 No timetable has been prepared for this course
 The course is a part of the following study plans:

 Civil Engineering (compulsory elective course)
 Civil Engineering (compulsory elective course)