Scientific Computing
CSC 331/431

Technical Books

• Scientific Computing, Michael Heath, McGraw Hill, 2002. The web-page contains slides and other materials, e.g. some interactive examples:
  • Rounding versus Truncation
  • Floating Point Systems
  • Rounding Rules
  • Quadratic formula
  • Condition number
  • Ill-conditioned systems
  • Polynomial fitting
  • Low rank matrix approximation
  • Bisection Method
  • Fixed Points
  • Newton's Method
  • Secant Method
  • Multivariate Newton
  • Golden Section Search
  • Successive Parabolic Interpolation
  • Newton's Method for finding local minimum
  • Steepest Descent
  • Newton's Method for local minimum in higher dimensions
  • Interpolation errors
  • Newton-Cotes Quadrature
  • Adaptive Quadrature
  • Monte Carlo Integration
  • Numerical Differentation
  • Richardson Extrapolation
  • Euler's Method
  • Error Estimation
  • Stability
  • Backward Euler Method
  • Stiff ODEs
  • Taylor Series Method
  • Runge-Kutta Methods
• Scientific Computing with Case Studies, Dianne P. O'Leary, 2009.

Articles

• What Every Computer Scientist Should Know about Floating-Point Arithmetic (by David Goldberg)
• Temperature of a Healthy Human (how we got to 98.6)

Other

• Calculus review
• Matrix Review
• Software bugs (some of them related to floating point arithmetic)
• Python
  • numpy
  • Linear Algebra in numpy (Python)
• Sage
• Automatic Differentiation Tools