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Exploring Numerical Methods: Solving Complex Problems in Computing

Learn the reasons to study numerical methods in computing and explore topics like finding roots of equations, curve fitting, matrix algebra, eigensystems, and more. Gain familiarity with common algorithms and understand how numerical methods play a crucial role in solving problems with no analytic solution. Discover the complexities, improvements, and potential failures of these methods. Join us in this introduction to the numerical aspects of computing and enhance your problem-solving skills.

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Exploring Numerical Methods: Solving Complex Problems in Computing

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  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 shouldn’t be used blindly

  3. 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 Course outline

  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/s17/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/NumericalMethods/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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