CMSC/AMSC/MAPL 460 Computational Methods
Class: TuTh......12:30pm- 1:45pm (CSI 1122)
Instructor: Ramani Duraiswami E-mail: 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; E-mail: yluo1 AT umd.edu
Office Hours: 2:30-4:00 p.m. Thursdays, 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 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 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
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DATE |
LECTURE |
CONTENTS |
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01/26, 2010 (Tuesday) |
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Introduction to the course. Rules. Introduction to MATLAB
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01/28, 2010 (Thursday) |
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Representing numbers on a computer, unsigned integers, signed integers, floating point numbers |
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02/02, 2010 (Tuesday) |
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Examples of computations sensitive to error; forward and backward error analysis; well-posed problems |
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Due 02/09, at the beginning of class |
Homework 1
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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
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02/04, 2010 (Thursday) |
Vectors, Matrices; Matlab |
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02/09,2010 (Tuesday) |
No Class |
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02/11, 2010 (Thursday) |
No Class |
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02/16, 2010 (Tuesday) |
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Diagonal solve, Triangular solves, Permutation Matrices, Gaussian Elimination, LU decomposition |
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02/18, 2010 (Thursday) |
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Coding the LU decomposition; solving a linear system via LU; the Matlab backslash operatior
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Due 02/25 |
Homework 2 |
2.7, 2.8, 2.11, 2.16, 2.18
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02/23, 2010 (Tuesday) |
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Wrap up of LU: Examples where not pivoting causes problems; Error analysis; relation between residual and error; Condition number; Wrap up |
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02/25, 2010 (Thursday) |
Polynomial Interpolation; Monomial Interpolation and Vandermonde Matrices; Lagrange Interpolation
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03/02, 2010 (Tuesday) |
Lagrange Interpolation, Newton Interpolation, piecewise linear interpolation |
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03/04, 2010 (Thursday) |
Cubic spline interpolation. End conditions. |
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Due 03/11, 2010 |
Homework 3
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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. |
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03/09, 2010 (Tuesday) |
Finding zeros of functions. Bisection. Modified secant method. Newton method, Secant Method |
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03/11, 2010 (Thursday) |
Inverse Quadratic Interpolation. Optimization. Golden search. Multi-dimensional Newton. Least Squares |
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Due 03/25 |
Homework 4 |
Problems 4.3, 4.8, 4.9, 4.15, 4.18 |
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03/16, 2010 (Tuesday) |
NO CLASS |
Spring Break
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03/18, 2010 (Thursday) |
NO CLASS |
Spring Break. March madness --- GO TERPS! |
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03/23, 2010 (Tuesday) |
Least Squares: The normal equations |
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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. |
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03/30
(Tuesday) |
Least Squares: The QR decomposition |
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04/01, 2010 (Thursday) |
Least Squares: Householder and Givens, SVD, Wrap up |
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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.
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04/06, 2010 (Tuesday) |
Integration: Trapezoid, Simpson formulae; Open and Closed formulae; Composite Rules; Adaptive Quadrature |
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04/08, 2010 (Thursday) |
Adaptive Quadrature, Romberg Integration, Gaussian Integration |
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Due 04/20 |
Homework 6 |
Problems 6.1, 6.3, 6.6 |
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04/13, 2010 (Thursday) |
Ordinary differential equations: Introduction. Standard form. Eulers Method |
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04/15, 2010 (Tuesday) |
Euler’s Method, Runge Kutta, Adam’s-Bashforth |
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04/20, 2010 (Thursday) |
Lecture 21
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See lectures above and below |
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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) |
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04/20, 2010 (Tuesday) |
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Implicit Methods, Stability |
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04/22, 2010 (Thursday) |
ODE Wrap up.
Eigenvalues and Eigenvectors. Shifts. Similar Matrices. |
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04/27, 2010 (Tuesday) |
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Power Method, QR Algorithm |
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04/29, 2010 (Thursday) |
QR Algorithm, Shifts, SVD |
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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? |
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05/04, 2010 (Tuesday) |
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Fourier Series and the Discrete Fourier Transform |
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05/06/2010 |
Fast Fourier Transform |
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05/11/2010 |
Lecture 28 |
Review Grades |
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05/18, 2010 (Tuesday) |
FINAL EXAM
GRADES |
Tuesday, May 18: 1:30pm-3:30pm 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
- 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