MATH 270C Numerical Ordinary Differential Equations

Instructor

• Prof. Melvin Leok
  Office: APM 5763
  Email: mleok@math.ucsd.edu
  Office Hours: MW 12:00pm - 12:50pm, or by appointment.

Teaching Assistant

• Shi Cheng
  Office: AP&M 5768
  Email: scheng@ucsd.edu
  Office Hours: W 2:00pm - 4:00pm, APM 5768.

Announcements

• The midterm exam will be on Friday, May 10, in class. It will cover up to Chapter 3 of Iserles (including collocation and implicit Runge-Kutta methods).
• Course Handout
• Course Notes
• Homework 1, due April 12, 2013.
• Homework 2, due April 26, 2013.
• Homework 3, due May 10, 2013.
• The resources below are password protected with the user name ma270c, and the password is the first 4 digits of:
  .

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. We will discuss this in the context of numerical methods for initial value problems and boundary value problems.

Prerequisites

• MATH 270B or consent of instructor. Programming experience in any language, e.g., C/C++, FORTRAN, MATLAB.

Textbook

• A First Course in the Numerical Analysis of Differential Equations, 2nd Edition, Cambridge Texts in Applied Mathematics
  Arieh Iserles, Cambridge University Press, 2009. ISBN: 9780521734905 [ Electronic version of First edition | Geometric Integration Chapter ]

Additional Reading

• 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%).