Math 225: Scientific Computing II

A graduate course in numerical analysis

Spring 2010
TTh 10:05-11:20am
205 Physics Building


This course will develop theoretical topics and computational techniques that are fundamental in many areas of mathematics, engineering, and scienti c research applications. Topics will include approximation of functions, numerical di erentiation and integration, and solutions of initial value and boundary value problems for ordinary differential equations. If time permits, numerical partial di erential equations will be introduced. Error analysis and formulation of convergent mathematical schemes will be used to derive stable, reliable, efficient, and accurate numerical methods for large classes of problems.

  • Textbook: An Introduction to Numerical Analysis, 2nd Edition, by Kendall E. Atkinson
  • Prerequisites: Familiarity with differential equations (at the level of Math 108 or 131) and some programming experience
  • Programming: Matlab will be the main programming tool used in this course

    Course topics will include:
    • Approximation Theory
      • Discrete representation of continuous functions
      • Interpolating polynomials, Splines, Orthogonal decompositions
    • Numerical Integration and Differentiation
      • Calculus for discrete functions, Finite differences, Quadrature
      • Order of accuracy and error estimates for discretizations
    • Ordinary Differential Equations
      • Initial and Boundary Value Problems
      • Difference equations
      • Stability and convergence
      • Explicit and Implicit methods
      • Euler, Runge-Kutta, Predictor/Corrector, Deferred Corrections, Linear Multistep, Shooting, and Iterative Methods
      • Solution of systems of differential equations
      • Stability, convergence, and accuracy
      • Stiff equations
      • Finite differences, Finite elements, Spectral methods
    • Introduction to Numerical Partial Differential Equations

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