CS590C: Introduction to Computational Science

Fall 1996

Week 1

• Introduction to Computational Science
• Evolution of Hardware / Software
• Elementary Linear Algebra
  
  Study Material
  • Lecture1: Scope and nature of computational science. (postscript slides)
  • Lecture2: Evolution of hardware. (postscript slides)
  • Lecture3: Basic Linear Algebra. (postscript slides)
  • Introduction to Computer Architectures (the CSEP Book)
  • Introduction to Linear Algebra, by Gilbert Strang, Wellesley-Cambridge Press 1993, (Chapters 1-3).

Week 2

• Introduction to Mathematical Tools
• Symbollic Computation: MAXIMA
• Matlab
  
  Study Material
  • Lecture 4,5,6: Tools for Symbollic Math and Presentations. (postscript slides)
  • Assignment 1: Gnuplot and MAXIMA. (postscript)
  • User Guide to MAXIMA (ps).
  • MAXIMA: Examples and Internals (ps).
  • MAXIMA: Online Tutorial.

Week 3

• Using Matlab.
  
  Study Material
  • Lecture 7,8: Using Matlab.
  • Matlab Tutorial (ps).
  • Matlab: Online Tutorial.
  • User Guide to Mathematica (ps).
  • Mathematica: Online Tutorial.

Week 4

• Mathematica.
• Libraries for linear algebra: BLAS, LAPACK, LINPACK, EISPACK Study Material
  • Lecture 9: Using Mathematica.
  • Lecture 10: Using Tcl/Tk.
  • Lecture 11: Software sources on the net.
  • Assignment 2: Matlab and Tcl/Tk. (postscript)
  • Supplementary programming material for lec. 10
  • User Guide to Mathematica (ps).
  • Mathematica: Online Tutorial.

Week 5

• Sparse Linear Algebra.
• • Lecture 12: Dense Linear System Solvers
  • Lecture 13: Sparse Matrix Methods (Representation, Factorization)
  • Lecture 14: Sparse Matrix Factorization. (Orderings, Row Cholesky, Column Cholesky, Frontal Methods)

Week 6

• Sparse Linear Algebra.
• • Lecture 15: Incomplete LU factorization preconditioners. (Chapter 10 of Iterative Methods for Sparse Linear Systems by Y. Saad).

Week 7

• Lecture 18: Iterative methods (Jacobi, Gauss-Siedel, SOR)
• Lecture 19,20: Semi direct methods (Lanczos Method, Conjugate Gradient)

Week 8

• Lecture 21: Mid-semester break.
• Lecture 21: Preconditioning for iterative and semi direct methods. Online text on iterative methods (Chapter on preconditioning)
• Lecture 22: Preconditioning (continued), Fast Poisson Solvers (FFTs) Lecture Notes of Jim Demel's CS267 Lecture at Berkeley

Week 9

• Lecture 23: N-body methods. Lecture Notes of Jim Demel's CS267 Lecture at Berkeley (part 1)
  Lecture Notes of Jim Demel's CS267 Lecture at Berkeley (part 2)
  

Week 10

• Assignment 3: Iterative Methods. (postscript)
• Assignment 4: Parallel Computing. (postscript)