Numerical Methods

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Lecturer:

Tutor:

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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. 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

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:

Further information:

No time-table 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)