Numerical Methods

Garant předmětu:

Přednášející:

Cvičící:

Předmět zajišťuje:

katedra matematiky

Anotace:

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.

Požadavky:

Osnova přednášek:

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

Osnova cvičení:

1. Representation of numbers. Some recurrencies

2. Gaussian elimination

3. LU-decomposition

4. Pivoting

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

6. Conjugate gradients

7. Interpolation

8. Least Squares Method

9. Trapezoidal method, Romberg method

10. Gauss quadrature

11. Euler method, Runge-Kutta method

12. Finite difference method

13. Summary

Cíle studia:

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.

Studijní materiály:

!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, 2012. ISBN-13: 978-1133103714

!G. H. Golub, C. F. Van Loan : Matrix Computation, 2013. ISBN: 9781421407944

?A. Hohmann, P. Deufelhard : Numerical Analysis in Modern Scientific Computing, Springer, 2003, ISBN: 0387954104, 9780387954103

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Předmět je součástí následujících studijních plánů:

• Civil Engineering (povinně volitelný předmět)
• Civil Engineering (povinně volitelný předmět)