Teaching / Course archive
Math 170C: Spring 2007
Numerical analysis of ODE
Course Record
Overview
Numerical ordinary differential equations course at UCSD covering numerical differentiation and integration, numerical ODE solvers, stability, difference equations, and boundary value problems.
MATLAB was the official mathematical software and programming tool.
Schedule and Topics
| Date | Topic |
|---|---|
| Apr 2 | Finite difference formulas for approximate differentiation. |
| Apr 9 | Newton-Cotes formulas: trapezoid, midpoint, Simpson, open and composite formulas. |
| Apr 18 | Gauss-Legendre quadrature. |
| Apr 20 | Initial value problems, existence and uniqueness, and Euler's method. |
| Apr 27 | Systems of ordinary differential equations, higher order equations, and the physical pendulum. |
| May 2 | Runge-Kutta methods and the Hodgkin-Huxley neuron. |
| May 16 | Multistep methods: Adams-Bashforth, Adams-Moulton, and predictor-corrector methods. |
| May 21 | Boundary value problems and shooting methods. |
| May 23 | Finite difference methods for linear boundary value problems. |
| Jun 4 | Galerkin method and finite elements. |
| Jun 15 | Final exam. |
Topic List
- Finite difference formulas for differentiation and rounding error
- Newton-Cotes formulas, Romberg integration, adaptive quadrature, and Gauss-Legendre quadrature
- Initial value problems, Euler's method, Heun's method, midpoint method, and Runge-Kutta methods
- Systems of ODEs, orbital mechanics, Lorenz equations, and variable step-size methods
- Implicit methods, stiff equations, multistep methods, and predictor-corrector methods
- Boundary value problems, shooting methods, finite difference methods, collocation, Galerkin method, and finite elements
Books and Related Pages
Books
- Timothy Sauer, Numerical Analysis. Pearson, 2006.
- Eugene Isaacson and Herbert B. Keller, Analysis of Numerical Methods.
Assignments and Projects
Assignments and Exams
- Nine homework assignments, mixing analytical exercises and computer problems.
- Midterm exam on numerical differentiation, quadrature, and initial value problem methods.
- Cumulative final exam.
Archive Note
The recovered page listed many MATLAB file names; the files themselves are not present in the local public archive.