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Residential Course (in person)

Meeting Times: Tuesdays and Thursdays, 2:00-3:15
Location: CULC 152

Instructor: Edmond Chow
E-mail:


Course Description

Introduction to fundamental algorithms and analysis of numerical methods commonly used by scientists, mathematicians and engineers. Topics include numerical solutions of algebraic systems, linear least-squares, eigenvalue problems, solution of non-linear systems, interpolation, numerical integration and differentiation, initial value problems and boundary value problems for systems of ODE's.

Prerequisites

Linear and Discrete Mathematics (MATH 2602) and Differential Equations (MATH 2403/2413). Experience with Matlab. If you do not know Matlab but know another computer language and can learn Matlab on your own for the course, then taking the course is still possible. This course will be very difficult if you do not use Matlab.

Topics

  • Error analysis I: Finite precision computation and sources of error
  • Solution of nonlinear equations
  • Solution of linear systems
  • Error analysis II: stability, conditioning, and backward error
  • Numerical optimization
  • Polynomial interpolation and approximation
  • Numerical differentiation
  • Numerical integration
  • Numerical solution of ordinary differential equations
  • Numerical solution of partial differential equations

Grading

50% Assignments
20% Midterm exam (take-home)
30% Final exam (take-home)

Textbook

  • Uri M. Ascher and Chen Greif, A First Course on Numerical Methods