CMSC/AMSC/MAPL 460 Computational Methods

 

Class:  T, Th......12:30pm-1:45 pm (CSI 2107)

 

Instructor: Ramani Duraiswami E-mail: ramani AT umiacs.umd.edu;

Office Hours:  Wednesdays 1:30 p.m. - 3:00, in AVW 3361. (you must confirm I am there before coming by emailing me)

 

TA: Ross Adelman; E-mail: rna AT umd.edu

Office Hours: 1:00 PM to 2:30 PM on Fridays, in AVW 3368

 

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 http://www.mathworks.com/moler/chapters.html

The book may be purchased from the bookstore, or from the web.

Textbook (other): A useful reference is Ascher & Greif

 

Software (required): MATLAB.

You will need reliable access to MATLAB and a printer for doing homework in this course.

If you 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. Moreover, the system tends to be slow.


 

PIAZZA for peer-to-peer 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 30%, Mid-Term 25%, Final 35%, Participation 10%

Previous versions of this course: (for reference) Fall-2005 Spring-2007 Fall 2008  Spring 2010 

LECTURE

CONTENTS

1/24/2013

(Thursday)

Lecture 1

 

Chapter 1

Introduction to the course. Why study Computational Methods?

Rules. Syllabus

 

1/29/2013

(Tuesday)
Lecture 2

Matlab
 Introduction to MATLAB. Ways to implement a matrix vector product 
1/31/2013

(Thursday)
Lecture 3

Representing numbers on a computer

Overflow and conversion errors
02/05/2013

(Tuesday)
Lecture 4 IEEE-754 floating point
Homework 1See Piazza
02/07/2013

(Thursday)
Lecture 5Matrices vectors

Book
02/12/2013

(Tuesday)
Lecture 6Gaussian Elimination
02/14/2013

(Thursday)
Lecture 7LU
Homework 2See Piazza
02/19/2013

(Tuesday)
Lecture 8LU wrapup
02/21/2013

(Thursday)
Lecture 9 LU

Lecture 9 Interp
Homework Discussion (LU). Polynomial interplation
02/26/2013

(Tuesday)
Lecture 10Polynomial interplation (Newton and Lagrange forms)

Book
02/28/2013

(Thursday)
Lecture 11Newton form and error analysis of polynomial interpolation
03/05/2013

(Tuesday)
Lecture 12

Matlab
Errors in high order polynomial interpolation

Local interpolation, linear splines
03/07/2013

(Thursday)
Lecture 13Cubic Spline Interpolation
03/12/2013

(Tuesday)
Review
03/14/2013

(Thursday)
ExamSee Piazza for solution
03/19/2013

(Tuesday)
Spring Break
03/21/2013

(Thursday)
Spring Break
03/26/2013
\
(Tuesday)
Lecture 14Bisection, Newton and Secant

Book
03/28/2013

(Thursday)
Lecture 15Convergence, golden search
04/02/2013

(Tuesday)
Lecture 16Wrap up of Lecture 15. Begin Least Squares. Normal Equations

Book
04/04/2013

(Thursday)
Lecture 17Least Squares via QR decomposition
04/09/2013

(Tuesday)
Lecture 18

Matlab
Computing the QR decomposition via Givens Rotations
04/11/2013

(Thursday)
Review 
04/16/2013

(Tuesday)
Exam
04/18/2013

(Thursday)
Lecture 20

Matlab
Householder transforms
 Course EvalCourse evaluation
04/23/2013

(Tuesday)
Lecture 21Eigenvalues and Eigenvectors

Book
04/25/2013

(Thursday)
Lecture 22

Matlab
Algorithms to compute Eigenvalues and Eigenvectors
04/30/2013

(Tuesday)
Lecture 23

Matlab
The Singular Value Decomposition
05/02/2013

(Thursday)
Lecture 24Quadrature: Newton Rules, Error

Book
05/07/2013

(Tuesday)
Lecture 25Quadrature: Romberg integration, Gaussian quadrature
05/09/2013

(Thursday)
Lecture 26Last Day of Classes!
Review
05/16/2013

(Thursday)
Final Exam

1:30 - 3:30 p.m.
 In class