Credits -- 4 (4-0-0)
Term Offered -- Fall
Prerequisite -- M561 or similar, and preparedness to do programming in
a standard language
- Text
-- - There are many possible
texts. One of them is: Stoer J. and Bulirsch, R., Introduction to
Numerical Analysis, 1980, Springer. Another possible text is:
Atkinson, K. E., An Introduction to Numerical Analysis,
1989, John Wiley and Sons, second edition
- Course Objective
-- - To provide our
graduate students with a broad overview on basic topics in Numerical
Analysis. Problem solving is emphasized.
Course Content --
- Interpolation
(a) Polynomial Interpolation
(b) Divided Differences
(c) Hermite Interpolation
(d) Cubic Splines
(e) Trigonometric Interpolation
(f) Fast Fourier Transform
- Approximation
(a) Minimax Problems
(b) Least Squares Problems
(c) Newton-like Methods
(d) Unconstrained Optimization
- Quadrature
(a) Integration by Interpolation
(b) Adaptive Integration
(c) Gauss Quadrature
(d) Integration by Extrapolation
- Initial Value Problems
(a) Runge-Kutta Methods
(b) Predictor-Corrector Methods
(c) Extrapolation Based on the Midpoint Rule
(d) Stability and Convergence
(e) Stiffness
- Boundary Value Problems
(a) Shooting Method
(b) Finite Difference Methods
(c) Finite Element Methods