CMSC/AMSC/MAPL 460 Computational Methods
Fall 2005, Tuesdays and Thursdays,
2:00pm 3:15pm (CSI
2107)
Office Hours: Monday 1011:30 and Thursday 3:304:30 and by appointment, in AVW 3365.
Instructor:
Ramani Duraiswami
Email: ramani AT umiacs.umd.edu;
Textbook (Required): Numerical Computing with MATLAB, by Cleve Moler, ISBN 0898715601
Individual Chapters may be downloaded from the author's web site at http://www.mathworks.com/moler/chapters.html
The book may be purchased from the bookstore, or from the web.
Software (required):
MATLAB.
The university has site licenses to this software and you will need to figure
out how you can access this. Registered students should have received email
with details on class accounts.
Prerequisites: Programming, advanced calculus, linear algebra.
Description in the catalog: Basic computational methods for interpolation, least squares, approximation, numerical quadrature, numerical solution of polynomial and transcendental equations, systems of linear equations and initial value problems for ordinary differential equations. Emphasis on methods and their computational properties rather than their analytical aspects.
Homework will be given out periodically, and will be due one week from the date handed out. No late homework, without prior arrangement. Homework will be posted on this web page. You are responsible for checking this page.
Policy: Honor code http://www.studenthonorcouncil.umd.edu/code.html
Grading: Homework 40%, MidTerm 25%, Final 35%
DATE 
LECTURE 
CONTENTS 
09/1, 2005 (Thursday) 

Introduction to the course. Rules. Introduction to MATLAB 
09/6, 2005 (Tuesday) 

Types of error. Fixed point and floating point representations. Consequences.

09/8, 2005 (Thursday)

Vectors. Matrices. Storage. Access. Norms. 

09/13, 2005 (Tuesday) 

Norms, Cramer’s rule, Gauss Elimination, Triangular and permutation matrices, LU decomposition 
09/15,2005 (Thursday)


LU decomposition. The need for pivoting. Condition numbers and sensitivity. 
09/20, 2005 (Tuesday) 
Polynomial Interpolation 

09/22, 2005 (Thursday)


Piecewise polynomial interpolation 
09/27, 2005 (Tuesday) 
Finding zeros/solving nonlinear equations 

09/29, 2005 (Thursday)


Nonlinear Equations 
10/4, 2005 (Tuesday) 
Least Squares 

10/6, 2005 (Thursday)

Least Squares/QR/SVD 

10/11, 2005 (Tuesday) 
Numerical Integration 

10/13, 2005 (Thursday)

Lecture 13 
Review of material 
10/18, 2005 (Tuesday) 
Lecture 14 
Mid Term 
10/20, 2005 (Thursday)

Numerical integration: Romberg integration 

10/25, 2005 (Tuesday) 
Gaussian quadrature 

10/27, 2005 (Thursday) 
No class 

11/1, 2005 (Tuesday) 
Ordinary Differential Equations 

11/3, 2005 (Thursday)

Ordinary Differential Equations 

11/8, 2005 (Tuesday) 
Ordinary Differential Equations 

11/10, 2005 (Thursday)

Fast Fourier Transforms 

11/15, 2005 (Tuesday) 

Fast Fourier Transforms 
11/17, 2005 (Thursday)

FFT wrapup. Eigenvalues and Eigenvectors 

11/22, 2005 (Tuesday) 
Eigenvalues and Eigenvectors 

11/24, 2005 (Thursday)

No Class (Thanksgiving) 

11/29, 2005 (Tuesday) 
Eigenvalue decomposition and SCD 

12/1, 2005 (Thursday)

Lecture 26 
Review 
12/6, 2005 (Tuesday) 
Lecture 27 
No class 
12/8, 2005 (Thursday)

Lecture 28 
No class 
12/13, 2005 (Tuesday) 
Lecture 29 
Review 
12/19, 2005 (Monday) 
Final Exam 10:30am12:30pm 
Tentative (subject to change) 
Useful Links
Previous versions of 460 offered.
Prof. Elman:
MATLAB resources:
Introductory Tutorials
Slightly more advanced Tutorials
More complete references/tutorials/FAQs