Numerical
Computing
MATH & CSCI 4800, Spring 2007
CLASS MEETS: MR 12:00 1:50PM, EATON 215
INSTRUCTOR: Victor Roytburd (Amos Eaton 405, Ph. 276-6889, roytbv@rpi.edu)
Office hours: Tuesday 2—4 (new time), Wednesday 6-8 (Amos Eaton 402) or by appointment.
I plan to run the
Wednesday office hours as a problem-solving seminar, devoted to homework
problems.
TIME CHANGE:
Tuesday 4/17 and Wednesday 4/18 5-7
Teaching Assistant: Banu Baydil. Office hours: Wednesday 3:30 – 5:00, Amos Eaton:
Fourth floor lobby
Topics list for the final
Final review: Monday 5/7, 2:30 –4:00 and 5:00 – ??, Lally 102 (Note new times)
WEB PAGE: http://www.rpi.edu/~roytbv/numcomp/spring07.htm
TEXTS: Scientific Computing: An Introductory Survey by M. T. Heath, Second Ed., McGraw Hill (required).
Numerical Computing with Matlab by Cleve B. Moler, SIAM ISBN-13:978-0-898715-78-1 (the book has been and will be used for the class). The author is the principal architect of Matlab. The book is available for free on line http://www.mathworks.com/moler/, but if you have any intention of using MATLAB for practical computations, I recommended buying it (the book is pretty cheap, $30 at a discount).
In any event please download the NCM Matlab
directory from the book site.
Matlab Guide by Desmond J.
Higham and Nicholas J. Higham (recommended). It is universally recognized as an
excellent reference guide. Here is a link to their webpage
Introductory Matlab Guides
- Getting Matlab on your machine
- A Practical Introduction to Matlab by Mark S. Gockenbach (pdf file; 27 pages)
- MATLAB Primer, 3d Ed. by Kermit Sigmon (pdf file; 39 pages). There is also an extended and updated version of these notes: MATLAB Primer, 7th Ed by Davis and Sigmon (about 200 pages)
The goal of the course is to learn some basic ideas
underlying numerical methods for scientific and engineering problems. Yes, students in the class will have to do some
programming, preferably in MATLAB.
OUTLINE: Here is a rough
outline of our pace through the book. The notes linked to OUTLINE are
mostly a modification of Heath’s notes. Please keep in mind that the notes are rather
incomplete.
|
Topics |
|
|
|
MATLAB tutorial. Approximation, computer arithmetic |
2 lectures |
1.1, 1.2.1-4, 1.2.6-7, 1.3.1-9 (you may skip Examples 1.13, 1.17). Notes |
|
Linear Systems |
3 lectures |
2.1, 2.2, 2.3, 2.4.1-2.4.7 (note Example 2.17), Example 2.20. Notes |
|
Nonlinear scalar equations |
2 lectures |
5.1-5.4. Notes |
|
Nonlinear Systems of Equations |
1 lecture |
5.5 (skip 5.5.5-5.5.6, 5.5.8), 5.6 (skip 5.6.3-5.6.4). Notes |
|
Test 1Test solutions (prob 5) |
Thursday 2/22 In class |
The test will cover material from Chapters 1, 2, and 5.1-5.6. There will be a review session on Wednesday 2/21 6-8 in Amos Eaton 403 |
|
Linear Least Squares |
3 lectures |
3.1, 3.2, 3.4 (skip 3.4.2), 3.5 (skip 3.5.2-3.5.4), 3.7. Notes |
|
Interpolation |
1 lecture |
7.1, 7.2, 7.3 (skip 7.3.3-7.3.4), 7.4 (skip 7.4.1). Notes |
|
Integration and Differentiation |
3 lectures |
8.1, 8.3 (skip 8.3.2, 8.3.4), 7.3.4,
8.6 (skip 8.6.2) Notes
(Chebyshev polynomials and |
|
Basics of ordinary differential equations (ODEs) |
1 lecture |
9.1, 9.2 |
|
Numerical solution of ODEs |
2 lectures |
8.7, 9.2, 9.3.1-9.3.3 Notes.
Notes on stability have been added, pages D11A-E. |
|
Test 2. Review Session:
Eaton 216, 5-7, Friday 3/23. You are allowed
one sheet of notes for this test. |
Monday 3/26 |
The test will cover material from Chapters 3, 7, 8, and 9.1, 9.3.1-2. |
|
Numerical solution of ODEs: RK, stiffness |
1 lecture |
9.3 (skip 9.3.5, 9.3.7, 9.3.9). Notes. I recommend you to play with Moler’s examples (http://www.mathworks.com/moler/ Chap. 7, p.14-ff). The Lorenz equation is especially cool. |
|
Fast Fourier Transform |
2 days |
12.1, 12.2
(you can skip the general algorithm, Algorithm 12.1), 12.3. Notes. |
|
Eigenvalue Problems and SVD I |
2 days |
|
|
Eigenvalue Problems and SVD II |
2 days |
Moler: 10.6-10.8; Heath: 4.4, 4.5.1 - 4.5.3 |
|
Test 2 Review |
4/19 |
|
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Test 3 |
Monday 4/23 |
|
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Computation of
Eigenvalues |
4/26 |
Heath: 4.4, 4.5.1 - 4.5.3 |
|
Final Review |
May 7 |
|
|
Final Exam: May
8, 11:30 – 2:30 |
|
SAGE 5101 |
4.1,
4.2 (skip 4.2.5), 4.7.
Homework: There will be homework assignments that will be collected and graded. As a rule, homework assignments are due on Thursday by 4:00 pm, every week except exam weeks. Late homework is not accepted.
Tests: There will be 3 midterms and a final exam. The first midterm will be given on 2/22. The tentative dates of other midterms 3/26, and 4/23
Grading: The course grade will be determined by your performance: Homework (24%), three exams (17% each), the final exam (25%).
STATEMENT
OF ACADEMIC INTEGRITY:
The guiding
principle is that work that you present for grading as your own should in fact BE
your own. With respect to exams, this means that no assistance or collaboration
of any kind is permitted. With respect to homework, you are free to seek
assistance from any person, or book. But before working together on the
homework, it is in your best interest to think over the problems on your own.
You must write up your solutions on your own. You are not allowed to just copy
from a shared (or someone else's) set of notes.
HOMEWORK ASSIGNMENTS may
be either submitted in class, or deposited in my mailbox in AE 301, or under my
door AE 405 by 4:00 pm on the due day.
The TA insists on
getting hard copies of your papers, it is in your best interests to comply.
Homework
#1, due Thursday January 25; Homework solutions
Homework
#2, due Thursday February 1; Homework
solutions
Homework
#3, due Thursday February 8; Homework solutions
Homework
#4, due Thursday February 15; Homework solutions
Homework
#5, due Thursday March 1.
If you wish you can replace the original computer problem by
the following shorter problem
Homework #5 solutions
Homework #6, due Thursday March 15. Homework solutions
Homework
#7, due Thursday March 22; Homework solutions
Homework #8, due Thursday April 5 Hint; Homework solutions
Homework
#9, due Thursday April 12;
Homework solutions
Homework
#10, due Thursday April 19;
Homework solutions
Final review: Monday 5/7, 2:30 –4:00 and 5:00 – ??, Lally 102 (Note new times)
Topics list for the final
TESTS: Problems will be similar to homework
problems. Just to give you some idea of the format and level of difficulty
here are tests given by Professor Kapila a few years ago: test1 and test2
MY OLD TESTS: Here is a declassified file of my old exams. Please
keep in mind that this semester I will give three tests and the final (in contrast with the two tests for the prior year). Also the
order of the material is a bit different, so you will have to do some creative
work to figure out which problems are relevant for your tests. Here are the
solutions to old tests: Test 1 and Test 2
Last updated 5/04/07
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