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Winter 2006 Math 411

What, When, and Where:

Course Description:

Numerical Methods for Differential Equations: root-finding, optimization, interpolation, numerical differentiation and integration, Monte Carlo simulation, initial-value methods for ODE, boundary-value methods for ODE, finite-difference methods for PDE, finite-element methods for PDE.

Text:

Title: Numerical Analysis (download freely)
Author: Levy

Title: Finite Difference and Spectral Methods (download freely)
Author: Trefethen

Matlab Texts

Title: Introduction to Matlab (download freely)
Author: Spencer

Title: Computational Physics (download freely)
Author: Spencer

Title: Mastering Matlab 7 (purchase)
Author: Hanselman and Littlefield

Lectures:

MWF 8:00-8:50 135 TMCB (classroom)
MWF 8:00-8:50 150 TMCB (computer room)

Office Hours:

MWF 9:00-9:50 306 TMCB

Grading Scheme:

50% Homework
50% Term Project

Course Schedule: (subject to change)

Jan 09 Introduction, Expectations
Jan 11 1-D Bisection, Newton, Secant Methods
Jan 13 Matlab Exploration
Jan 18 Multi-D Newton and Quasi-Newton Methods
Jan 20 Matlab Exploration
Jan 23 Interpolation, Lagrange Polynomials
Jan 25 Vandermonde Matrix and Newton Interpolation
Jan 27 Matlab Exploration
Jan 30 Divided Differences
Feb 01 Splines
Feb 03 Matlab Exploration
Feb 06 Cubic Splines
Feb 08 Bernstein Polynomials
Feb 10 Matlab Exploration
Feb 13 Bezier Curves I
Feb 15 Bezier Curves II
Feb 17 Matlab Exploration
Feb 20 Difference Algebra
Feb 22 Numerical Differentiation
Feb 24 Matlab Exploration
Feb 27 Numerical Integration I
Mar 01 Numerical Integration II
Mar 03 Matlab Exploration
Mar 06 Simpson's Rule
Mar 08 Gaussian Quadrature
Mar 10 LaTeX sample file
Mar 13 Gaussian Quadrature II
Mar 15 Gaussian Quadrature III
Mar 17 Matlab Exploration
Mar 20 Euler Method
Mar 22 Runge Kutta
Mar 24 Matlab Exploration
Mar 27 Finite Difference Method
Mar 29 Galerkin Method
Mar 31 Matlab Exploration
Apr 03 Explicit Method
Apr 05 Implicit Method
Apr 07 Matlab Exploration
Apr 10 Crank Nicolson Method
Apr 12 Discrete Fourier Transform
Apr 14 Matlab Exploration
Apr 16 FFT and IFFT

Assignments:

Assignment #1 (Due 01/23/06)
(pdf) (notes)

Assignment #2 (Due 02/01/06)
(pdf)

Assignment #3 (Due 02/13/06)
(pdf)

Assignment #4 (Due 02/27/06)
(pdf) (notes)

Assignment #5 (Due 03/24/06)
(pdf)

Assignment #6 (Due 04/10/06)
(pdf) (notes)

Assignment #7 (Due 04/17/06)
(pdf)