S17: Introduction to Numerical Methods

Lectures

1. Introduction, numerical aspects of computing
2. Solving non-linear equations (Maple worksheet with algorithms)
3. Curve fitting
4. Matrix algebra
5. Eigensystems
6. Numerical integration
7. Fourier series
8. Ordinary differential equations
9. Partial differential equations
10. Monte Carlo methods
11. Monte Carlo integration
12. Homework and revision
    • "Bread and butter" numerical methods summary (pdf)

Homework problems by week

• Week 1
  • Last year's set 1, problems for Taylor Series and Determination of Roots
• Week 2
  • Last year's set 4, problems for Linear Algebra, Eigenvalues (problem 1), and Fourier Series and Transforms
• Week 3
  • Last year's set 1, problems for Quadrature
  • Last year's set 2, problems for First order ODE's
  • Last year's set 3, problems for Second (and Higher order) and coupled ODE's, Elliptical PDE's, Parabolic and Hyperbolic PDE's
• Week 4
  • Last year's set 2, problems for Monte Carlo Integration

Texts

• RL Burden, JD Faires, Numerical Methods, 3rd ed., Boston: Prindle, Weber & Schmidt, 1985.
• SD Conte, Carl de Boor, Elementary Numerical Analysis: An Algorithmic Approach, New York: McGraw-Hill, 1980.
• Koonin and Meredith, Computational Physics.
• Kalos and Whitlock, Monte Carlo Methods, vol. 1.
• Veterling, Numerical Recipes.
• Luc Devroye, Non-Uniform Random Variate Generation, see below.

Links

• Resources from the practical labs (including last year's lecture notes)
• Luc Devroye, Non-Uniform Random Variate Generation. The book is out of print, but the content can be found on the web.
• Interactive Educational Modules in Computational Science. This website features a number of interactive Java applications which illustrate numerical techniques.

Past Exams

S17 has been a short option since 2005, and can be found in the Part A or Part B short option paper set.

J Tseng
Updated 23 April 2008