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## S17: Introduction to Numerical Methods

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Title: S17: Introduction to Numerical Methods

1
S17 Introduction toNumerical Methods
• TT 2008
• Lecture 1
• Numerical aspects of computing

2
Reasons to study
• Solve problems with no analytic solution
• Non-linear equations
• Complex behaviors
• Understand these methods
• Gain familiarity with common algorithms
• Computing realities and calculations in principle
• How they can be improved
• How they can fail
• Numerical methods shouldnt be used blindly

3
Course outline
• Introduction, numerical aspects of computing
• Finding roots of equations
• Curve fitting
• Matrix algebra
• Eigensystems
• Numerical integration
• Fourier series
• Ordinary differential equations
• Partial differential equations
• Monte Carlo methods
• Monte Carlo integration
• Homework and revision

4
Lectures
• Week 1 W Th F 2pm
• Week 2 W Th F 2pm
• Week 3 no lectures
• Week 4 Th F 2pm (no Wednesday)
• Week 5 W Th F 2pm

5
Resources
• http//www-pnp.physics.ox.ac.uk/tseng/teaching/s1
7/index.html
• My main resource R.L. Burden, J.D. Faires,
Numerical Methods, 3rd ed., Boston Prindle,
Weber Schmidt, 1985.
• More mathematical S.D. 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
• Devroye, Non-Uniform Random Variate Generation
http//cg.scs.carleton.ca/luc/rnbookindex.html
• http//www-teaching.physics.ox.ac.uk/computing/Num
ericalMethods/nummethods.html
• Lecture notes from 2005
• Online courses
• Problem sets (will be augmented occasionally)

6
Next lecture
• Thursday 2pm, same location
• Solving non-linear equations