Math 463 Scientific Computing

Course Description

(3-0) 3 credits. Prerequisite: MATH 373 or CSC 372 or permission of instructor. This course is an introduction to the elements of numerical analysis and modern scientific computing. The primary focus will be on the mathematical analysis of computational methods and the effective use of scientific computation as it relates to the needs of engineering and science. Topics will include: machine arithmetic and error analysis, the approximation of eigenvalues, and numerical solutions of ordinary differential equations. Additional topics in numerical analysis will be included as time permits.

Couse Learning Outcomes

A student who successfully completes this course should be able to:

  1. implement the use of machine arithmetic method, for example, IEEE standardized floating point number system
  2. identify sources of approximation and error in scientific computation including modeling, measurement, truncation, discretization, and rounding
  3. describe well-posed vs. ill-posed and/or well-conditioned vs. ill-conditioned. Students will also be able to describe the notions of stability of an algorithm and accuracy of a solution as well as the relationships between conditioning, stability and accuracy
  4. implement the use of scientific computation on standard probelms, for example, linear least squares, eigenvalue approximation, nonlinear equations, initial value and/or boundary value problems for ordinary differential equations