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S17: Introduction to Numerical Methods

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Numerical methods shouldn't be used blindly. Course outline ... More mathematical: S.D. Conte, Carl de Boor, Elementary Numerical Analysis: An ... – PowerPoint PPT presentation

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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
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