S17: Introduction to Numerical Methods TT 2008 Lecture 1 Numerical aspects of computing

Reasons to study “Solve” problems with no analytic solution “Solve” problems with no analytic solution Non-linear equations Non-linear equations Complex behaviors Complex behaviors Understand these methods Understand these methods Gain familiarity with common algorithms Gain familiarity with common algorithms Computing realities and calculations in principle Computing realities and calculations in principle How they can be improved How they can be improved How they can fail How they can fail Numerical methods shouldn’t be used blindly Numerical methods shouldn’t be used blindly

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

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

Resources My main resource: R.L. Burden, J.D. Faires, Numerical Methods, 3 rd ed., Boston: Prindle, Weber & Schmidt, My main resource: R.L. Burden, J.D. Faires, Numerical Methods, 3 rd ed., Boston: Prindle, Weber & Schmidt, More mathematical: S.D. Conte, Carl de Boor, Elementary Numerical Analysis: An Algorithmic Approach, New York: McGraw-Hill, More mathematical: S.D. Conte, Carl de Boor, Elementary Numerical Analysis: An Algorithmic Approach, New York: McGraw-Hill, Koonin and Meredith, Computational Physics Koonin and Meredith, Computational Physics Kalos and Whitlock, Monte Carlo Methods, vol. 1. Kalos and Whitlock, Monte Carlo Methods, vol. 1. Veterling, Numerical Recipes Veterling, Numerical Recipes Devroye, Non-Uniform Random Variate Generation Devroye, Non-Uniform Random Variate Generation teaching.physics.ox.ac.uk/computing/NumericalMethods/nummethods.html teaching.physics.ox.ac.uk/computing/NumericalMethods/nummethods.html teaching.physics.ox.ac.uk/computing/NumericalMethods/nummethods.html teaching.physics.ox.ac.uk/computing/NumericalMethods/nummethods.html Lecture notes from 2005 Lecture notes from 2005 Online courses Online courses Problem sets (will be augmented occasionally) Problem sets (will be augmented occasionally)

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