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%