Description:

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.

Contents:

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

Seminar contents:

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

Recommended literature:

!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, ISBN 0387954104, 9780387954103

Abbreviations used:

Semester:

• W ... winter semester (usually October - February)
• S ... spring semester (usually March - June)
• W,S ... both semesters

Mode of completion of the course:

• A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
• GA ... Graded Assessment (a grade is awarded for this course)
• EX ... Examination (a grade is awarded for this course)
• A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)

Weekly load (hours per week):

• P ... lecture
• C ... seminar
• L ... laboratory
• R ... proseminar
• S ... seminar