Course description of AMS 147

In this class, we discuss the numerical methods for solving problems in sciences and engineerings. We will learn how they work (and why they fail sometimes). We will learn how to implement these numerical methods using Matlab. The topics include

Iterative methods for solving non-linear equations

Golden search method for optimization

Floating point representation of real numbers, round-off error, loss of accuracy due to numerical cancellation

Numerical differentiation and integration, optimal step size in numerical differentiation

Runge-Kutta methods for solving differential equations

Stiff problems and implicit methods

Estimating error from two numerical solutions

Numerical interpolation, Gibbs phenomenon, cubic spline

Least squares fitting

Fast Fourier transform and its application in image compression

Solving linear systems: LU decomposition, condition number, error propagation

Solving sparse linear systems: conjugate gradient method