CMSC/AMSC/MAPL 460 Computational Methods
Class: M,W,F......12:00pm-12:50 pm (EGR 1108)
Instructor: Ramani Duraiswami E-mail: ramani AT umiacs.umd.edu;
Office Hours: Mondays 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: 11:00 AM to 1:00 PM on Tuesdays, 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.
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.
Registered students should receive email with details on class accounts on the Grace computers.
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 40%, Mid-Term 25%, Final 35%
Previous versions of this course: (for reference) Fall-2005 Spring-2007 Fall 2008 Spring 2010
|
DATE |
LECTURE |
CONTENTS |
|
01/25 2012 (Wednesday) |
|
Introduction to the course. Why study Computational Methods? Rules. Syllabus
|
01/27 2012 (Friday) |
Lecture 2 | Syllabus. Introduction to MATLAB. |
01/30 2012 (Monday) |
Lecture 3 |
Representing numbers on a computer Overflow and conversion errors |
02/01 2012 (Wednesday) |
Lecture 4 | Floating Point numbers |
| Due 02/10 | 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 |
| 02/03 2012 (Friday) | Lecture 5 | Errors in computation |
| 02/06 2012 (Monday) | Lecture 6 | Vectors, Matrices, Organization on a computer |
| 02/08 2012 (Wednesday) | Lecture 7 Chapter 2 | Matrix products, Diagonal and Triangular systems |
| 02/10 2012 (Friday) | Lecture 8 | LU decomposition |
| 02/13 2012 (Monday) | Lecture 9 | Wrap up LU decomposition, use in solving a linear system, examples showing the need for pivoring. |
| Due 02/20 | Homework 2 | Problems 2.1, 2.7, 2.8, 2.11, 2.19 |
| 02/15 2012 (Wednesday) | Lecture 10 | Polynomial Interpolation |
| 02/17 2012 (Friday) | Lecture 11 Chapter 3 | Polynomial Interpolation, Lagrange and Newton forms |
| 02/20 2012 (Monday) | Lecture 12 Matlab | Piecewise polynomial interpolation |
| 02/22 2012 (Wednesday) | Exam 1 | In class |
| 02/24 2012 (Friday) | Lecture 13 Chapter 4 | Wrapup of interpolation Begin root finding: Bisection |
| Due 03/02/2012 |
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 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. |
| 02/27 2012 (Monday) | Lecture 14 | Bisection, Secant, Newton |
| 02/29 2012 Leap Day! (Wednesday) | Lecture 15 Chapter 5 | Least squares. Straight Line regression Normal Equations |
| 03/02 2012 (Friday) | Lecture 16 | QR Decomposition |
| Due 03/09/2012 | Homework 4 | Problems 4.3, 4.8, 4.9, 4.15, 4.18 |
| 03/05/2012 (Monday) | Lecture 17 | Least Squares via QR; Givens; Householder |
| 03/07/2012 (Wednesday) | Lecture 18 | Wrap up QR, Least Squares; Solve example |
| 03/09/2012 (Friday) | Lecture 19 Chapter 6 | Numerical Integration |
| Due 03/16/2012 | Homework 5 | Do the following problems from the text: 5.5, 5.7, 5.8, 5.12.
|
| 03/12/2012 (Monday) | Lecture 20 | Numerical Integration |
| 03/14/2012 (Wednesday) | Lecture 21 Chapter 7 | ODEs, Standard Form rabfox.m |
Due 03/28/2012 | Homework 6 | Problems 6.1, 6.3, 6.6 |
| 03/16/2012 (Friday) | Lecture 22 | Euler Method, Runge Kutta volteratest.m |
| 03/19-03/23 | No Classes | SPRING BREAK |
| 03/26/2012 (Monday) | Lecture 23 | Runge Kutta, Adams |
| 03/28/2012 (Wednesday) | Lecture 24 | Implicit methods |
| 03/30/2012 (Friday) | Lecture 25 | Stability stiff_ode.m |
| Due 04/09/12 | Homework 7 | 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 method, 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) |
| 04/02/2012 (Monday) | Lecture 26 Chapter 8 | Eigenvalues & Eigenvectors, Eigen Value Decomposition, Shifts, Similar Matrices |
| 04/04/2012 (Wednesday) | Lecture 27 | Power iteration |
| 04/06/2012 (Friday) | Lecture 28 | QR Algorithm |
| 04/09/2012 (Monday) | Lecture 29 | SVD |
| Due 04/20/12 |
Homework 8 |
see Piazza |
| 04/11/2012 (Wednesday) | Lecture 30 | http://amath.colorado.edu/pub/matlab/music/ |
| 04/13/2012 (Friday) | Lecture 31 | Complex representation, roots of unity, symmetry |
| 04/16/2012 (Monday) | Lecture 32 | Danielson Lanczos lemma, FFT |
| 04/18/2012 (Wednesday) | Lecture 33 | Review |
| 04/20/2012 (Friday) | Lecture 34 | Matlab Review |
| 04/23/2012 (Monday) | Lecture 35 | QR Algorithm convergence Review |
| 04/25/2012 (Wednesday) | Lecture 36 | Review |
| 04/27/2012 (Friday) | No Class | Course Evaluations! |
| 04/30/2012 (Monday) | Exam 2 | In Class |
| 05/02/2012 (Wednesday) | Lecture 37 | Random Numbers |
| 05/04/2012 (Friday) | Lecture 39 | Random Numbers |
| 05/07/2012 (Monday) | Lecture 40 | Wrap up random numbers. Review |
| 05/09/2012 (Wednesday) | Lecture 41 | Review |
| 05/17/2012 (Thursday) | Final Exam | Comprehensive Final 8:00 a.m. - 10:00 a.m., In Class |
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
- MATLAB tutorial from University of New Hampshire
- MATLAB tutorial/reference from University of Florida
- MATLAB tutorial from Michigan Technological University
More complete references/tutorials/FAQs