Syllabus Detail

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
    • One-step methods
    • Multistep methods
    • Runge-Kutta methods
    • Stiff equations
  • Two-Point Boundary Value Problems
    • Shooting methods
    • Collocation methods
  • Differential Algebraic Equations
    • Index-1 systems
    • General systems
  • Linear Dynamical Systems
    • Time-invariant systems
    • 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%