Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

MAT 226C: Numerical Methods: Ordinary Differential Equations
Approved: 2008-06-01, Roland Freund

Units/Lecture:

Spring, alt years; 1st LEC 3.0 hrs/wk; 2nd T-D 1.0 hrs/wk

Suggested Textbook: (actual textbook varies by instructor; check your instructor)

Prerequisites:

22B or equivalent, or consent of instructor; familiarity with some programming language.

Course Description:

Numerical methods for the solution of ordinary differential equations, including methods for initial-value problems and two-point boundary-value problems, theory of and methods for differential algebraic equations, dimension reduction of large-scale dynamical systems.

Suggested Schedule:

- Initial Value Problems
          o One-step methods
          o Multistep methods
          o Runge-Kutta methods
          o Stiff equations
- Two-Point Boundary Value Problems
          o Shooting methods
          o Collocation methods
- Differential Algebraic Equations
          o Index-1 systems
          o General systems
- Linear Dynamical Systems
          o Time-invariant systems
          o Dimension reduction of large-scale systems

Additional Notes:

No required textbook. Optional references:
  • A. Iserles, A First Course in the Numerical Analysis of Differential Equations, Cambridge University Press, 1996
  • J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, 3rd Ed., Springer-Verlag, 2002

Assessment:

Homework assignments, covering both theory and computational problems: 50%. Final project and report: 50%