Numerical Methods for Computational Science and Engineering

Abstract

The course gives an introduction into fundamental techniques and algorithms that underly numerical simulations in science and technology. It discusses principles necessary for understanding modern numerical techniques. The course also involves profound instruction on implementation in MATLAB.

Objective

This course is aimed at giving s survey of fundamental numerical techniques and algorithms. It is meant to teach the principles underlying the design and analysis of numerical algorithms and it will provide mathematical tools for tackling problems in numerical analysis.

Content

1. Floating point arithmetic and rounding errors 2. Numerical solution of scalar equation 3. Numerical linear algebra 3a. Numerical solution of dense linear systems of equations 3b. Linear least squares problems 3c. Eigenvalue problems 3d. The fast Fourier Transform 4. Numerical methods for non-linear systems of equations 5. Non-linear least squares methods 6. Interpolation and approximation 6a. Polynomial interpolation 6b. Interpolation by splines 6c. Wavelets 7. Numerical quadrature 8. Initial value problems for ordinary differential equations

Resources