COURSE OUTLINE

AMSC 460 / CMSC 460 Computational Methods Section 0101
Fall 2007

  • Introduction, Computer Arithmetic and Errors (Notes)
    (approx. 4 lectures)
  • course survey
  • introduction to Matlab
  • machine arithmetic
  • error analysis
  • stability and conditioning
  • Interpolation (Chapters 2-3)
    (approx. 5 lectures)
  • polynomial interpolation in two bases
  • piecewise polynomial interpolation
  • spline interpolation
  • Integration (Chapter 4)
    (approx. 3 lectures)
  • elementary integration formulas (midpoint, trapezoid, etc.)
  • compound and adaptive integration formulas
  • Matrix Computations (Chapter 5)
    (approx. 3 lectures)
  • Solving Linear Systems of Equations (Chapter 6)
    (approx. 4 lectures)
  • Gaussian elimination
  • well-conditioning vs. ill-conditioning, matrix and vector norms
  • sparse systems: direct and iterative methods
  • Solving Linear Least Squares Problems (Chapter 7)
    (approx. 3 lectures)
  • data-fitting and least squares
  • QR factorization
  • Solving Nonlinear Systems of Equations (Chapter 8)
    (approx. 3 lectures)
  • bisection, Newton's method, and secant method
  • methods for systems of equations
  • Ordinary Differential Equations (Chapter 9)
    (approx. 4 lectures)
  • ordinary differential equations and Euler's method
  • adaptive methods for ordinary differential equations
  • methods for stiff systems
    • Chapter references are to: Introduction to Scientific Computing by Charles F. van Loan, Prentice Hall.