CMSC/AMSC/MAPL 460 Computational Methods
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;
Teaching Assistant: AbdelHameed AbdelSalam Badawy, Email: absalam AT Glue.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 receive email by
January 26. 2007 with details on class accounts.
Printing: Most homework will call for printing material (graphs, programs and the like off Matlab) and submitting it. Emailed homework is NOT acceptable.
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 on the first class in the following week from the date handed out. No late homework, without prior arrangement. Homework will be posted on this web page.
Collaboration Policy: You may study together and discuss problems and methods of solution with each other to improve your understanding. You are welcome to discuss assignments in a general way among yourselves, but you may not use other students' written work or programs. Use of external references for your work should be cited. Clear similarities between your work and others will result in a grade reduction for all parties. Flagrant violations will be referred to appropriate university authorities.
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 
01/25, 2007 (Thursday) 

Introduction to the course. Rules. Introduction to MATLAB 
01/30, 2007 (Tuesday) 
Lecture 2 
Errors. Well posed problems. Floating point representation.
Keywords: fixed point, floating point, Mantissa, significand, exponent, sign, overflow, underflow, zero, Inf, NaN, float (single precision), double (double precision), IEEE 754 
02/01, 2007 (Thursday)

Lecture 3  Recap of the floating point representation; examples of how representation errors can cause problems during calculations; forward and backward error analysis 
02/06, 2007 (Tuesday) 
Lecture 4

Matrices, vectors,

02/08,2007 (Thursday)

Lecture 5  Matrices, vectors, Linear systems of equations, Gauss elimination, LU decomposition 
02/13, 2007 (Tuesday) 
Lecture 6  LU decomposition, pivoting, error analysis 
02/15, 2007 (Thursday)

Lecture 7  Interpolation, polynomials, polynomial interpolation 
02/20, 2007 (Tuesday) 
Lecture 8

Lagrange and Newton forms, divided differences. instability of polynomial interpolation, piecewise linear interpolation 
02/22, 2007 (Thursday)

Lecture 9  piecewise cubic interpolation 
02/27, 2007 (Tuesday) 
Lecture 10

Finding zeros of functions: Bisection, Modified Secant; Secant and Newton methods 
03/01, 2007 (Thursday)

Lecture 11

Inverse Quadratic Interpolation, Optimization, Golden Search, multidimensional optimization 
03/06, 2007 (Tuesday) 
Lecture 12

Least Squares: Linear models, parameter estimation via least squares; the "normal" equations

03/08, 2007 (Thursday)

Lecture 13

Least Squares: Null space; Orthogonal Matrices; QR
decomposition;
Homework 5: Do the following problems from the text: 5.5, 5.7, 5.8, 5.12 Due first class after spring break

03/13, 2007 (Tuesday) 
Lecture 14 
Least Squares: Givens and Householder transformations. Wrap
up Review of material for midterm Some optional reading: John Kerl, The Householder transformation in numerical linear algebra 
03/15, 2007 (Thursday)

Exam. 
Sample
exam
Solutions You are allowed to bring a single sheet of paper to the exam with any information you want on it. However, you should prepare the material on the sheet yourself, and submit it with the exam. 
03/20, 2007 (Tuesday) 
No Class, Spring Break


03/22, 2007 (Thursday) 
No Class, Spring Break 

03/27, 2007 (Tuesday) 
Lecture 15  Exam Review. Numerical Integration: NewtonCotes Rules 
03/29, 2007 (Thursday)

Lecture 16  Numerical Integration: Gaussian quadrature 
04/03, 2007 (Tuesday) 
Lecture 17

Numerical integration: error bounds, adaptive quadrature wrap up 
04/05, 2007 (Thursday)

Lecture 18  Ordinary differential equations; initial value problems, standard form, Euler method, modified Euler Method 
04/10, 2007 (Tuesday) 
Lecture 19 
Runge Kutta Methods; introduction to multistep methods matlab: volteratest.m rabfox.m 
04/12, 2007 (Thursday)

Lecture 20

multistep methods; implicit methods; AdamsBashforth and Adams Moulton; notions of stability and stiffness matlab: stiff_ode.m 
04/17, 2007 (Tuesday) 
Lecture 21 
wrapup of ODEs;
Eigenvalue problems 
04/19, 2007 (Thursday)

Lecture 22  Eigen value problems 
04/24, 2007 (Tuesday) 
Lecture 23


04/26, 2007 (Thursday)

Lecture 24  Fourier Methods 
05/01, 2007 (Tuesday) 
Lecture 25  Partial differential equations 
05/03, 2007 (Thursday)

Lecture 26  Partial differential equations 
05/08, 2007 (Tuesday) 
Lecture 27  Review 
05/10, 2007 (Thursday) 
Lecture 28 
Review Last day of classes 
05/17, 2007 (Thursday) 
FINAL EXAM 
Thursday, May 17 1:303:30 pm in the same classroom Material: Lectures 1326 inclusive. You are allowed to bring a single sheet of paper to the exam with any information you want on it. However, you should prepare the material on the sheet yourself, and submit it with the exam. 
Useful Links
Previous versions of 460 offered.
Prof. O'Leary: Fall 2002 (some of my material is adapted from this course)
Prof. Elman:
MATLAB resources:
Introductory Tutorials
Slightly more advanced Tutorials
More complete references/tutorials/FAQs