AMS 147 - Winter 2008
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
- Numerical differentiation and integration
- Runge-Kutta methods for solving differential equations
- Estimating error from two numerical solutions
- Cubic spline interpolation (fitting to exact data)
- Least square fitting (fitting to data with noise)
- Fast Fourier transform
- Conjugate gradient method for solving sparse linear systems