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Term: | Summer 2002 |
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Course: | MATH 4581 |
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Course Title: | Classical Mathematical Methods in Engineering |
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Instructor: | Gunter H. Meyer |
| School of Mathematics |
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Phone: | 404 894 5367 |
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Fax: | 404 894 4409 |
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E-mail address: |
meyer@math.gatech.edu |
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Office hours: | 2-3 PM daily. However, I generally am around and you can
talk to me whenever you find me. |
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Text: | There is no required text for this course.
Class notes for the major part of the course
dealing with the topic of separation of variables
are posted on my web site
www.math.gatech.edu/~meyer.
These notes are the product of an ongoing collaboration
with Prof. Cain; they are subject to revision but not
to major changes.
Some notes on the second topic of transform
methods for partial differential equations will be assembled
later.
A recommended (cheap) reference source is
Fourier Series and Orthogonal Functions
by Harry F. Davis,
Dover Publications, ISBN 0-486-65973-9
It and some other sources will be put on reserve
within a few days. |
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Prerequisites: | A course in ordinary differential equations
equivalent to
Mathematics 2403
(old Mathematics 3308)
and the linear algebra preceding it. |
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THESE PREREQUISITES ARE USED. IN PARTICULAR:
YOU ARE EXPECTED TO BE ABLE TO SOLVE LINEAR ORDINARY DIFFERENTIAL
EQUATIONS WITH CONSTANT COEFFICIENTS AND A SOURCE TERM.
THE METHODS OF VARIATION OF PARAMETERS AND OF UNDETERMINED
COEFFICIENTS WILL BE EMPLOYED ROUTINELY TO SOLVE SECOND ORDER
ORDINARY DIFFERENTIAL EQUATIONS.
THESE METHODS WILL NOT BE REVIEWED IN THIS COURSE.
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Grading: | Two hourly exams
 20% each |
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| Homework 20% |
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| Final 40% |
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Exams will be announced typically one week in advance.
They tend to be open book but that is not guaranteed.
Homework will be assigned regularly. You are expected
to have worked all assigned problems, and this includes
any computer assignments. However, in general, not all
homework will be collected, but answers to all homework
problems will be distributed in class (but not posted on the
web).
The exams will be written on the assumption that
you have worked and UNDERSTOOD the homework
assignments, including any computer programming
issues which may arise in the solution process.
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Outline: |
I. Linear Spaces |
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A. Functions and vectors |
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B. Linear independence, bases, dimension |
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C. Inner products |
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D. Orthogonal projections |
| II. Sturm Liouville Theorem and eigenfunctions
for ordinary differential equations |
| III. Fourier Series |
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A. Definitions and examples |
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B. Sine and cosine series |
| IV. Separation of variables for partial differential
equations in two variables with time dependent data
based on eigenfunction expansions |
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A. Heat equation |
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B. Wave equation |
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C. Potential equation |
| V. Separation of variables for partial differential
equations in more than two variables |
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A. Bessel functions |
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B. Legendre polynomials |
| VI. Application of Laplace and Fourier transforms to
partial differential equations |
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Computers:
| You are expressly asked to use the computer whenever
it can make your job easier. Often symbolic manipulation
such as differentiation, integration, and matrix algebra
with Maple, Mathematica, Matlab, etc. can be a great
shortcut. However, the course does not presume familiarity
with symbolic computation.
You will need to know how to plot functions. Matlab will
see you through nicely.
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