CMSC/AMSC/MAPL 460 Computational Methods
Office Hours: Monday 10-11:30 and Thursday 3:30-4:30 and by appointment, in AVW 3365.
Instructor: Ramani Duraiswami E-mail: ramani AT umiacs.umd.edu;
Teaching Assistant: Abdel-Hameed Abdel-Salam Badawy, E-mail: absalam AT Glue.umd.edu
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.
The university has site licenses to this software and you will need to figure
out how you can access this. Registered students should receive email by
January 26. 2007 with details on class accounts.
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%
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DATE |
LECTURE |
CONTENTS |
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01/25, 2007 (Thursday) |
|
Introduction to the course. Rules. Introduction to MATLAB |
|
01/30, 2007 (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 |
|
02/01, 2007 (Thursday)
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Lecture 3 | Recap of the floating point representation; examples of how representation errors can cause problems during calculations; forward and backward error analysis |
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02/06, 2007 (Tuesday) |
Lecture 4
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Matrices, vectors,
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02/08,2007 (Thursday)
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Lecture 5 | Matrices, vectors, Linear systems of equations, Gauss elimination, LU decomposition |
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02/13, 2007 (Tuesday) |
Lecture 6 | LU decomposition, pivoting, error analysis |
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02/15, 2007 (Thursday)
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Lecture 7 | Interpolation, polynomials, polynomial interpolation |
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02/20, 2007 (Tuesday) |
Lecture 8
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Lagrange and Newton forms, divided differences. instability of polynomial interpolation, piecewise linear interpolation |
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02/22, 2007 (Thursday)
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Lecture 9 | piecewise cubic interpolation |
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02/27, 2007 (Tuesday) |
Lecture 10
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Finding zeros of functions: Bisection, Modified Secant; Secant and Newton methods |
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03/01, 2007 (Thursday)
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Lecture 11
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Inverse Quadratic Interpolation, Optimization, Golden Search, multidimensional optimization |
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03/06, 2007 (Tuesday) |
Lecture 12
|
Least Squares: Linear models, parameter estimation via least squares; the "normal" equations
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03/08, 2007 (Thursday)
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Lecture 13
|
Least Squares: Null space; Orthogonal Matrices; QR
decomposition;
Homework 5: Do the following problems from the text: 5.5, 5.7, 5.8, 5.12 Due first class after spring break
|
|
03/13, 2007 (Tuesday) |
Lecture 14 |
Least Squares: Givens and Householder transformations. Wrap
up Review of material for mid-term Some optional reading: John Kerl, The Householder transformation in numerical linear algebra |
|
03/15, 2007 (Thursday)
|
Exam. |
Sample
exam
Solutions You are allowed to bring 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. |
|
03/20, 2007 (Tuesday) |
No Class, Spring Break
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03/22, 2007 (Thursday) |
No Class, Spring Break |
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03/27, 2007 (Tuesday) |
Lecture 15 | Exam Review. Numerical Integration: Newton-Cotes Rules |
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03/29, 2007 (Thursday)
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Lecture 16 | Numerical Integration: Gaussian quadrature |
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04/03, 2007 (Tuesday) |
Lecture 17
|
Numerical integration: error bounds, adaptive quadrature wrap up |
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04/05, 2007 (Thursday)
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Lecture 18 | Ordinary differential equations; initial value problems, standard form, Euler method, modified Euler Method |
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04/10, 2007 (Tuesday) |
Lecture 19 |
Runge Kutta Methods; introduction to multistep methods matlab: volteratest.m rabfox.m |
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04/12, 2007 (Thursday)
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Lecture 20
|
multistep methods; implicit methods; Adams-Bashforth and Adams Moulton; notions of stability and stiffness matlab: stiff_ode.m |
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04/17, 2007 (Tuesday) |
Lecture 21 |
wrapup of ODEs;
Eigenvalue problems |
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04/19, 2007 (Thursday)
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Lecture 22 | Eigen value problems |
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04/24, 2007 (Tuesday) |
Lecture 23
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04/26, 2007 (Thursday)
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Lecture 24 | Fourier Methods |
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05/01, 2007 (Tuesday) |
Lecture 25 | Partial differential equations |
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05/03, 2007 (Thursday)
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Lecture 26 | Partial differential equations |
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05/08, 2007 (Tuesday) |
Lecture 27 | Review |
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05/10, 2007 (Thursday) |
Lecture 28 |
Review Last day of classes |
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05/17, 2007 (Thursday) |
FINAL EXAM |
Thursday, May 17 1:30-3:30 pm in the same classroom Material: Lectures 13-26 inclusive. You are allowed to bring 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. |
Useful Links
Previous versions of 460 offered.
Prof. O'Leary: Fall 2002 (some of my material is adapted from this course)
Prof. Elman:
MATLAB resources:
Introductory Tutorials
Slightly more advanced Tutorials
More complete references/tutorials/FAQs