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MATH 270C Numerical Ordinary Differential Equations
MWF 12:00-12:50pm, APM 2402.
Instructor
- Prof. Melvin Leok
Office: APM 5763
Email: mleok@math.ucsd.edu
Office Hours: MW 3:00pm-4:00pm, or by appointment.
Teaching Assistant
Announcements
- Course
Handout
- Course Notes
- The resources below are password protected with the user name ma270c,
and the password is the first 4 digits of:
.
- Homework 1, [ PDF ], Due
April 15, 2011.
- Homework 2, [ PDF ], Due
April 22, 2011.
- Homework 3, Question 3.4, 3.5, 3.7 and 3.8 from the first edition of
Iserles (see link below), Due April 29, 2011.
- Homework 4, Question 4.1, 4.4, 4.5, 4.6b, 4.8 from the first edition
of Iserles (see link below), Due May 11, 2011.
- Homework 5, Question 5.3(a,b), 5.4 from the first edition
of Iserles (see link below), will not be collected. Please also
familiarize yourself with the tableau representation of Embedded RK
methods (see page 84).
Course Description
- This course will focus on the mathematical analysis and derivation of
numerical methods for the solution of ordinary differential equations.
Issues include order of accuracy, convergence, stability, adaptivity, and
structure-preservation. Time permitting, we will also introduce methods
for elliptic PDEs based on finite-difference, finite-element, and spectral
discretizations.
Prerequisites
- MATH 270B or consent of instructor. Programming experience in any
language, e.g., C/C++, FORTRAN, MATLAB.
Textbook
Additional Reading
These additional references address advanced topics in the numerical
analysis of differential equations.
- Numerical
Methods for Ordinary Differential Equations, 2nd
Edition
John Butcher. John-Wiley, 2008. ISBN: 0470723351
[ Electronic Version ]
- Solving
Ordinary Differential Equations I: Nonstiff
Problems, 2nd Revised Edition
Hairer, Norsett, Wanner. Springer-Verlag 2010. ISBN: 3642051634
[ Electronic Version ]
- Solving
Ordinary Differential Equations II: Stiff and
Differential-Algebraic Equations, 2nd Revised Edition
Hairer, Wanner. Springer-Verlag 2010. ISBN: 9783642052200
[ Electronic Version ]
- Geometric
Numerical Integration, 2nd Edition, Springer Series in Computational
Mathematics
Hairer, Lubich, Wanner. Springer-Verlag, 2006. ISBN:
3540306633
[ Electronic Version ]
- Simulating
Hamiltonian Dynamics, Cambridge Monographs on Applied and
Computational Mathematics
Leimkuhler, Reich, Cambridge University Press, 2005. ISBN: 0521772907
[ Electronic Version ]
Grading
- Your grade in the course is based on homework (25%), a midterm exam
(25%), and a final exam (50%).