CS/Math 3414: Numerical Methods

Fall 2001

GTA: Li Wang, 133 MCB, liwang5@vt.edu.

Office hours: Tuesday, Thursday, 13:00-16:00.

For all labs, turn in the Mathematica scripts/commands or Fortran 90 program you used to produce the results, the output, and answers to any questions in the assignment. You must use Mathematica or Fortran 90 to do all assignments. If using Mathematica, your solution should be a functional program rather than a C-like procedural program. If using Fortran 90, you should take advantage of the power of Fortran 90 syntax and intrinsic functions, and not simply recode a C++ solution in Fortran.

Practice Problems:

• Shampine, Allen, Preuss: 3.15, 3.16, 3.21, 3.32, 5.1, 5.2
• Forsythe, Malcolm, Moler: P4-13, P5-9

Answers to most of these are in the books.

The Mathematica macros for Householder reflections and the lab notebook from the lab on Householder reflections are available.

• Syllabus: PDF , PostScript
• Lecture Notes
  1. WHY IS NUMERICAL ANALYSIS NECESSARY?: Text, Postscript
  2. FLOATING POINT ARITHMETIC: Text, Postscript
  3. LINEAR ALGEBRA: Text, Postscript (Elementary discussion, Postscript)
  4. NORMS AND INNER PRODUCTS: Text, Postscript
  5. LINEAR SYSTEMS/MATRIX DECOMPOSITION THEOREMS: Text, Postscript
  6. POLYNOMIAL INTERPOLATION: Text, Postscript
  7. CUBIC SPLINES (an elementary approach): Text, Postscript
  8. B-SPLINES (Carl deBoor): Text, Postscript, Mathematica source
  9. PIECEWISE HERMIT CUBICS: Text, Postscript
  10. FIXED POINTS and ZEROS of NONLINEAR FUNCTIONS: Text, Postscript
  11. ORTHOGONAL POLYNOMIALS: Text, Postscript
  12. NUMERICAL INTEGRATION (QUADRATURE): Text, Postscript
  13. LEAST SQUARES APPROXIMATION: Text, Postscript
  14. NUMERICAL DIFFERENTIATION: Text, Postscript
  15. ORDINARY DIFFERENTIAL EQUATIONS: Text, Postscript
• Assignments (all, PDF)
  • Lab #1: Text, Postscript due Wed 8:00, 9/5/2001. (Computer arithmetic.)
  • Lab #2: Text, Postscript due Wed 8:00, 9/12/2001. (Summation.)
  • Lab #3: Text, Postscript due Wed 8:00, 9/19/2001. (Norms, condition number.)
  • Lab #4: Text, Postscript due Fri 12:20, 9/28/2001. (Linear systems.)
  • Exam 1, Wednesday 10/3/2001.
  • Lab #5: Text, Postscript due Fri 12:20, 10/5/2001. (Polynomial interpolation.)
  • Lab #6: Text, Postscript due Wed 8:00, 10/10/2001. (Cubic splines.)
  • Lab #7: Text, Postscript due Fri 12:20, 10/19/2001. (B-splines.)
  • Lab #8: Text, Postscript due Fri 12:20, 10/26/2001. (Nonlinear equations.)
  • Lab #9: Text, Postscript due Fri 12:20, 11/2/2001. (Integration.)
  • Lab #10: Text, Postscript due Fri 12:20, 11/9/2001. (Orthogonal polynomials.)
  • Exam 2, Wednesday 11/14/2001.
  • Lab #11: Text, Postscript due Wed 8:00, 11/28/2001. (Least squares.)
  • Lab #12: Text, Postscript due Wed 8:00, 12/5/2001. (Engineering applications.)
  • Lab #13: Text, Postscript due Wed 8:00, 12/12/2001. (Two-point BVPs.)
• Final Exam: Monday, December 17, 2001 1:05-3:05
• Exams
  • Exam 1: ! Postscript
  • Exam 2: ! Postscript
  • Old Exam 1: ! Text, ! Postscript
  • Old Exam 2: ! Text, ! Postscript
• Fortran 90

  High Performance Fortran

  Fortran 77D/90D Scalable and Portable Software Modules for SIMD and MIMD Distributed Memory Parallel Computers

  IBM SP2 at HKU : High Performance Fortran

  PGI Welcome Page

  HPF courses available

  High Performance Fortran Index

  High Performance Fortran

  High Performance Fortran Textbooks

  Class 2: High Performance Fortran

  Parallel Programming Resources

  Fortran 90/95 Intel compilers for educational use

• Sample Programs: MAINF.f, MAINP.f, REAL_PRECISION.f
• Tutorial: f90.ps, f90.ps.gz