Math 371:   Numerical Algorithms
Development and application of fundamental algorithms for finding roots of equations, solving systems of linear equations, interpolating, fitting data using least-squares, differentiation, integration, and solving ordinary differential equations.
Prereq: A high level programming language (e.g., Math171 or Computer Science 102),
      231, 241 (or 247), and basic matrix algebra (e.g., 200 or 251 or 257).
3 credits

______________________ Contents Outline ______________________

• Introduction:
  • scientific computing as a tool for computational science
  • calculus review, Taylor expansion
  • errors in computation
  • machine arithmetic
  • conditioning
• Fundamental Algorithms for:
  • Solving equations (finding roots)
  • Solving linear systems
  • Interpolation
  • Numerical Differentiation and Integration
  • Numerical methods for ODEs
  • Curve fitting
  • Approximation - FFT
  • Optimization

______________________ Some Web Resources ______________________

Numerical Methods Course Notes by Steven E. Pav, 2005   nice set of notes
  also available on FreeScience,   can download .pdf

Numerical Methods Online Course/Slides by Aaron Naiman, 2003   nice viewgraphs

Mathematics Source Library C & ASM brief description of core num. methods (and C codes) ...excellent

Numerical Recipes in Fortran 90, 2nd Ed. 1996

Numerical Methods on Wolfram MathWorld

______________________ Some Relevant Books _____________________

Burden-Faires, Numerical Analysis, Brooks/Cole,   any edition, good book, recommended
  (google it, 7th and 8th ed. seem to be freely available...)

Steven Chapra Applied Numerical Methods with Matlab, 2nd ed., McGraw-Hill 2008
  compare prices looks very good, recommended

W.Cheney - D.Kincaid, Numerical Mathematics and Computing, 6th ed., Brooks/Cole, 2008
  available on ichapters.com by echapter!

J.Epperson, Introduction to Numerical Methods and Analysis, Wiley, 2002

C.F.Gerald - P.O.Wheatley, Applied Numerical Analysis, 7th ed., Addison-Wesley, 2003

M.T.Heath, Scientific Computing, McGraw-Hill, 2002

D.Kahaner - C.Moler - S.Nash,Numerical Methods and Software, 1989

C.Pozrikidis, Numerical Computation in Science & Engineering, Oxford U. Press, 1998

(useful only for Matlab)  C.Moler, Numerical Computing with Matlab , SIAM 2004 , book chapters (free!)