Lecture 1

CMSC/AMSC/MAPL 460 Computational Methods

Class: TuTh......12:30pm- 1:45pm (CSI 1121)

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

Instructor: Ramani Duraiswami E-mail: ramani AT umiacs.umd.edu;
Office Hours: Monday 10-11:30 and by appointment, in AVW 3365.

Teaching Assistant: Alison Teoh; E-mail: alison.lk.teoh AT gmail.com
Office Hours: 1:45 to 3:45 pm on Wednesdays.

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.

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 a 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.

Registered students should receive email with details on class accounts on the Grace computers.

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%, Mid-Term 25%, Final 35%

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

DATE

LECTURE

CONTENTS

09/02, 2009

(Tuesday)

Lecture 0

Chapter 1

Accessing MATLAB on GRACE from a PC

09/04, 2008

(Thursday)

Lecture 1

Introduction to the course.

Rules. Introduction to MATLAB

09/09, 2008

(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

Homework 1

Due 09/18

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

09/11, 2008

(Thursday)

Lecture 3

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

09/16,2008

(Tuesday)

Lecture 4

Matrices, vectors,

Homework 2

Due 09/25

Do the following problems in the text: 2.7, 2.8, 2.11, 2.16, 2.18

Also for a small extra-credit of one point register for the class forum and post something

09/18, 2008

(Thursday)

Lecture 5

Solving diagonal and triangular systems

Gaussian elimination

LU decomposition

09/23, 2008

(Tuesday)

Lecture 6

LU decomposition

Permutation Matrices

Matlab tricks, Wrap -up

09/25, 2008

(Thursday)

Lecture 7

Matlab

Polynomial Interpolation

Monomials & Vandermonde matrices

Lagrange & Newton forms

Instability of polynomial interpolation

Due 10/07

Homework 3

hand

1. Do the following problems 3.3, 3.4, 3.7, 3.9

2. Read section 3.4 of the book, and summarize the shape-preserving 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.

09/30, 2008

(Tuesday)

Lecture 8

Error analysis of Polynomial interpolation

Piecewise Linear Interpolation

10/02, 2008

(Thursday)

Lecture 9

Cubic spline interpolation. Tridiagonal system solution.

Horner’s rule.

10/07, 2008

(Tuesday)

Lecture 10

Matlab

Zero finding, bisection. Secant method. Newton method.

Due 10/14

Homework 4

1. Do the following problems: 4.3, 4.8, 4.9, 4.15, 4.18

10/09, 2008

(Thursday)

Lecture 11 opt

Lecture 11

Wrap up of zero finding and optimization

Least squares – normal equations

10/14, 2008

(Tuesday)

Lecture 12

Least Square – QR algorithm. Givens Rotations

10/16, 2008

(Thursday)

Lecture 13

Least squares. QR via the Householder transform

Reference: John Kerl’s article on Householder transforms. (local copy)

Due 10/23

Homework 5

Least squares: Do the following problems from the text:

5.5, 5.7, 5.8, 5.12

10/21, 2008

(Tuesday)

Exam.

Sample exam Solutions

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.

10/23, 2008

(Thursday)

Lecture 14

Numerical Integration, Newton-Cotes Formulae

10/28, 2008

(Tuesday)

Lecture 15

(notes above)

Adaptive Integration, Richardson extrapolation, Romberg integration

10/30, 2008

(Thursday)

Lecture 16

(notes above)

Gaussian Integration

Due

Thursday

11/11/2008

Homework 6

1. Problems 6.1, 6.3, 6.6

2. Derive error bounds for the approximation of the integral below via the Simpson 1/3 rule of integration in terms of the size of the domain of integration and derivatives of the function f(t):