CMSC/AMSC/MAPL 460 Computational Methods
Class: TuTh......12:30pm 1:45pm (CSI 1122)
Instructor: Ramani Duraiswami Email: ramani AT umiacs.umd.edu;
Office Hours: Fridays 10:30 a.m.  noon, in AVW 3365. (confirm I am there before coming by emailing me)
Teaching Assistant: Yuancheng [mike] Luo; Email: yluo1 AT umd.edu
Office Hours: 2:304:00 p.m. Thursdays, AVW 3368.
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.
You will need reliable access to MATLAB and a printer for doing homework in this course.
If you already do not have access to Matlab and have a PC, the best option would be to buy the student edition from the bookstore.
You can also get by without buying this copy and using the software which should be accessible from University computers. However, this requires a degree of computer savviness, and your are responsible for figuring this out ASAP.
Registered students should receive email with details on class accounts on the Grace computers.
Class Forum: for peertopeer discussions/assistance.
NO LAPTOPS IN CLASS
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%
Previous versions of this course: (for reference) Fall2005 Spring2007 Fall 2008
DATE 
LECTURE 
CONTENTS 
01/26, 2010 (Tuesday) 

Introduction to the course. Rules. Introduction to MATLAB

01/28, 2010 (Thursday) 

Representing numbers on a computer, unsigned integers, signed integers, floating point numbers 
02/02, 2010 (Tuesday) 

Examples of computations sensitive to error; forward and backward error analysis; wellposed problems 
Due 02/09, at the beginning of class 
Homework 1

Matlab: do the following problems in the text: 1.5, 1.6., 1.7, and 1.20 Floating point representation: 1.34, 1.35, 1.38, 1.39

02/04, 2010 (Thursday) 
Vectors, Matrices; Matlab 

02/09,2010 (Tuesday) 
No Class 

02/11, 2010 (Thursday) 
No Class 

02/16, 2010 (Tuesday) 

Diagonal solve, Triangular solves, Permutation Matrices, Gaussian Elimination, LU decomposition 
02/18, 2010 (Thursday) 

Coding the LU decomposition; solving a linear system via LU; the Matlab backslash operatior

Due 02/25 
Homework 2 
2.7, 2.8, 2.11, 2.16, 2.18

02/23, 2010 (Tuesday) 

Wrap up of LU: Examples where not pivoting causes problems; Error analysis; relation between residual and error; Condition number; Wrap up 
02/25, 2010 (Thursday) 
Polynomial Interpolation; Monomial Interpolation and Vandermonde Matrices; Lagrange Interpolation


03/02, 2010 (Tuesday) 
Lagrange Interpolation, Newton Interpolation, piecewise linear interpolation 

03/04, 2010 (Thursday) 
Cubic spline interpolation. End conditions. 

Due 03/11, 2010 
Homework 3

1. Do the following problems: 3.3, 3.4, 3.7, 3.9 2. Read section 3.4 of the book, and summarize the shapepreserving piecewise cubic spline algorithm. How would a program to interpolate a spline using this algorithm differ from one using the cubic spline algorithm discussed in class. 
03/09, 2010 (Tuesday) 
Finding zeros of functions. Bisection. Modified secant method. Newton method, Secant Method 

03/11, 2010 (Thursday) 
Inverse Quadratic Interpolation. Optimization. Golden search. Multidimensional Newton. Least Squares 

Due 03/25 
Homework 4 
Problems 4.3, 4.8, 4.9, 4.15, 4.18 
03/16, 2010 (Tuesday) 
NO CLASS 
Spring Break

03/18, 2010 (Thursday) 
NO CLASS 
Spring Break. March madness  GO TERPS! 
03/23, 2010 (Tuesday) 
Least Squares: The normal equations 

03/25, 2010 (Thursday) 
Lecture 14 MID TERM EXAM 
You are allowed to bring a calculator and 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. 
03/30
(Tuesday) 
Least Squares: The QR decomposition 

04/01, 2010 (Thursday) 
Least Squares: Householder and Givens, SVD, Wrap up 

Due 04/13 
Homework 5 
Do the following problems from the text: 5.5, 5.7, 5.8, 5.12. Also in 5.5 (a) do the same via a sequence of Givens rotations.

04/06, 2010 (Tuesday) 
Integration: Trapezoid, Simpson formulae; Open and Closed formulae; Composite Rules; Adaptive Quadrature 

04/08, 2010 (Thursday) 
Adaptive Quadrature, Romberg Integration, Gaussian Integration 

Due 04/20 
Homework 6 
Problems 6.1, 6.3, 6.6 
04/13, 2010 (Thursday) 
Ordinary differential equations: Introduction. Standard form. Eulers Method 

04/15, 2010 (Tuesday) 
Euler’s Method, Runge Kutta, Adam’sBashforth 

04/20, 2010 (Thursday) 
Lecture 21

See lectures above and below 
Due 04/29 
Homework 8 
1. Do the following problems 7.2, 7.3, 7.12, 7.13 /__ __ 0 __ _ 1_ 2. Let y(0)=1 . Convert to standard form. Is the problem stable or unstable at t=0? 3. Apply three steps of the Euler and the modified Euler methods, with a step size of 0.1 for the above problem, and compute approximations for y(0.1), y(0.2) and y(0.3) 
04/20, 2010 (Tuesday) 

Implicit Methods, Stability 
04/22, 2010 (Thursday) 
ODE Wrap up.
Eigenvalues and Eigenvectors. Shifts. Similar Matrices. 

04/27, 2010 (Tuesday) 

Power Method, QR Algorithm 
04/29, 2010 (Thursday) 
QR Algorithm, Shifts, SVD 

Due 05/11 
Using the function eigshow provided with the book, answer the following questions for the different 2x2 matrices that are displayed in the drop down box Which matrices are singular? Which matrices have complex eigenvalues? Which matrices have double eigenvalues? In each case answer why, and comment on the graphical picture the function produces? 

05/04, 2010 (Tuesday) 

Fourier Series and the Discrete Fourier Transform 
05/06/2010 
Fast Fourier Transform 

05/11/2010 
Lecture 28 
Review Grades 
05/18, 2010 (Tuesday) 
FINAL EXAM
GRADES 
Tuesday, May 18: 1:30pm3:30pm in the same classroom Material: things covered after the mid term, plus basic concepts from throughout the course. You are allowed to bring two sheets of paper to the exam with any information you want on them. 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)
MATLAB resources (Most links are somewhat dated  your book has a very good introduction):
Introductory Tutorials
Slightly more advanced Tutorials
More complete references/tutorials/FAQs