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Mathematical
Methods for Engineers (10.539/24.539)
Detailed Course Syllabus
The tables below represent a working course syllabus that lists
the primary subjects to be treated and the associated homework
assignment that covers the material on a particular topic. Generally,
it represents a rough road map for the entire course, and it directly
follows your Math Methods Lecture Notes (indicated chapters refer
to the Lecture Notes). This syllabus is tentative and it will
be modified as required to meet the needs of this particular class.
There will be roughly nine homework sets and two or three projects,
which averages to about one assignment per week (times allocated
may be adjusted slightly to account for the difficulty or length
of the particular assignment). The specific problems for each
assignment will be given in class and posted on the web as they
become available, and the due dates for the assignments will be
announced in class.
Solution
of ODEs |
Chapter |
Topic |
HW
Assignment |
1
- 3 |
Review
of Introductory Differential Equations and Linear Algebra |
HW
#1 |
4 |
General
Solution to IVPs (analytical and numerical solution to 1st
order systems) |
HW
#2 |
|
Project
#1 -- Some Typical IVPs |
|
5 |
General
Solution to BVPs (numerical solution via the Shooting and
FD methods) |
HW
#3 |
6 |
Numerical
Solution of Algebraic Equations |
--- |
|
Project
#2 -- Some Typical BVPs |
|
Appendix
I |
Introduction
to COMSOL
Multiphysics
(with focus on solution of ODEs) |
HW
#4 |
Advanced
Analysis Techniques |
Chapter |
Topic |
HW
Assignment |
7 |
Power
Series Solution Method |
HW
#5 |
8 |
Special
Functions and Orthogonality |
HW
#6
|
9 |
Sturm-Liouville
Theory and Generalized Fourier Series |
Solution
of PDEs |
Chapter |
Topic |
HW
Assignment |
10 |
Analytical
Solution of PDEs (Separation of Variables and Integral Transform
Methods) |
HW
#7 |
11 |
Numerical
Solution of PDEs via the FD Method |
HW
#8 |
Appendix
I |
Introduction
to COMSOL Multiphysics (with focus on solution of PDEs) |
HW
#9 |
|
Project
#3 -- Some Typical PDEs |
|
Last
updated by Prof. John R. White (Sept. 2007)
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