The module gives an introduction to practical techniques for carrying out numerical computations on a range of mathematical problems. We will rely on your existing acquaintance with Matlab and further develop your programming skills to implement, test and evaluate a number of fundamental numerical methods. We will combine theoretical analysis of numerical algorithms and hands-on experience of developing and using them.
Syllabus to include topics such as:
0. An introduction to practical computations
- Algorithms
- Simple examples
- Pitfalls
1. Solving single nonlinear equations
- Bisection method
- Newton-Raphson method
2. Numerical solution of ordinary differential equations
- Euler method
- Runge-Kutta methods
- Linear multi-step methods
3. Interpolation
- Polynomial interpolation
- Optimal interpolation points
- Fourier and trigonometric series
4. Numerical linear algebra
- Gaussian elimination
- Partial pivoting
- Iterative methods
On completion of the module students should be able to:
- appreciate the processes and pitfalls of mathematical approximation
- demonstrate knowledge and understanding of mathematical computing
- motivate and describe the derivation of the numerical algorithms covered in the module
- carry out simple numerical processes "by hand"
- implement and execute algorithms in Matlab
- evaluate, contrast and reflect upon the numerical results arising from different algorithms.
- Module Supervisor: Dmitry Savostyanov