CMSC/AMSC/MAPL 460 Computational Methods


Office Hours: Monday 10-11:30 and Thursday 3:30-4:30 and by appointment, in AVW 3365.


Instructor: Ramani Duraiswami  E-mail: ramani AT;

Teaching Assistant: Abdel-Hameed Abdel-Salam Badawy, E-mail: absalam AT


Textbook (Required)Numerical Computing with MATLAB, by Cleve Moler, ISBN 0-89871-560-1

Individual Chapters may be downloaded from the author's web site at             

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

Grading: Homework 40%, Mid-Term 25%, Final 35%

 Previous versions of this course: (for reference) Fall-2005




01/25, 2007


Lecture 1


Introduction to the course.

Rules. Introduction to MATLAB

Chapter 1

01/30, 2007


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



Lecture 3

Homework 1

Recap of the floating point representation; examples of how representation errors can cause problems during calculations; forward and backward error analysis

02/06, 2007


Lecture 4


Matrices, vectors,


Accessing MATLAB on GRACE from a PC




Lecture 5

Homework 2

Matrices, vectors, Linear systems of equations, Gauss elimination, LU decomposition

02/13, 2007


Lecture 6 LU decomposition, pivoting, error analysis

02/15, 2007



Lecture 7 Interpolation, polynomials, polynomial interpolation

02/20, 2007


Lecture 8


Homework 3

Lagrange and Newton forms, divided differences. instability of polynomial interpolation, piecewise linear interpolation

02/22, 2007



Lecture 9 piecewise cubic interpolation

02/27, 2007


Lecture 10



Finding zeros of functions: Bisection, Modified Secant; Secant and Newton methods

03/01, 2007



Lecture 11

Homework 4


Inverse Quadratic Interpolation, Optimization, Golden Search, multidimensional optimization

03/06, 2007


Lecture 12


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


03/08, 2007



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


Lecture 14 Least Squares: Givens and Householder transformations. Wrap up

Review of material for mid-term

Some optional reading: John Kerl, The Householder transformation in numerical linear algebra

03/15, 2007



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


  No Class,

Spring Break


03/22, 2007


  No Class,

Spring Break

03/27, 2007


Lecture 15 Exam Review. Numerical Integration: Newton-Cotes Rules

03/29, 2007



Lecture 16 Numerical Integration: Gaussian quadrature

04/03, 2007


Lecture 17


Homework 6

Numerical integration: error bounds, adaptive quadrature wrap up

04/05, 2007



Lecture 18 Ordinary differential equations; initial value problems, standard form, Euler method, modified Euler Method

04/10, 2007


Lecture 19 Runge Kutta Methods; introduction to multistep methods

matlab: volteratest.m  rabfox.m

04/12, 2007



Lecture 20


Homework 7

multistep methods; implicit methods; Adams-Bashforth and Adams Moulton;

notions of stability and stiffness

matlab: stiff_ode.m

04/17, 2007


Lecture 21 wrapup of ODEs;

Eigenvalue problems

04/19, 2007



Lecture 22 Eigen value problems

04/24, 2007


Lecture 23



04/26, 2007



Lecture 24

Homework 8

Fourier Methods

05/01, 2007


Lecture 25 Partial differential equations

05/03, 2007



Lecture 26 Partial differential equations

05/08, 2007


Lecture 27 Review

Sample final

05/10, 2007


Lecture 28 Review

Last day of classes

05/17, 2007


FINAL EXAM Thursday, May 17 1:30-3:30 pm in the same classroom

Material: Lectures 13-26 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

MATLAB tutorial from University of Utah

MATLAB tutorial from Carnegie Mellon University

MATLAB tutorial from Indiana University

  Slightly more advanced Tutorials

  More complete references/tutorials/FAQs