Welcome to MATH 8600 Introduction to Scientific Computing (Fall 2014)

1. This site: http://www.math.clemson.edu/~heister/math8600-fall2014/
2. Blackboard: http://bb.clemson.edu
3. Syllabus

This course is designed to introduce students to the appropriate numerical methods for approximating solutions to scientific problems.

Topical Outline:

1. Computer representation of number and floating point arithmetic,
2. Solution of non-linear equations,
3. Solution of linear systems
4. Least squares solution to equations,
5. Interpolation and curve fitting,
6. Numerical integration and differentiation,
7. Numerical approximation of Initial Value Problems.

Prerequisites:

• CP SC 110, MATHSC 208, 311

See http://www.registrar.clemson.edu/pdf/academicCalendar2014.pdf and http://www.registrar.clemson.edu/html/examSched.htm for important dates.

Schedule:

• 08/21:
  • Introduction, Overview, Syllabus
  • Chapter 1: numerical method, errors, convergence orders
• 08/26:
  • Chapter 2: binary numbers, 64bit floating point format, roundoff
• 08/28:
  • Nonlinear scalar equations
  • Bisection
  • Convergence rate/order
• 09/02:
  • Fixed Point iteration
  • Newton's method
  • Secant method
• 09/04:
  • Minimization
  • Linear systems
  • Back Substitution
  • Gauss Elimination
• 09/09:
  • flops Gauss Elimination
  • LU decomposition
  • pivoting
• 09/11:
  • Cholesky decomposition
  • sparse matrices, storage formats
  • banded matrices
  • vector norms