An introduction to Applied Mathematics
From the course description....
Introduction to ideas and techniques used in solving problems
arising in a variety of physical settings. Stability of
nonlinear systems of ODE's. Sturm-Liouville problems and
Green's functions. The wave, heat and Laplace equations.
Elementary analysis of some nonlinear PDE's. Elementary
perturbation theory.
Schedule
| Week |
Lecture |
Description |
Section |
Exam |
Recommended
problems |
|
| 1 |
09/02 |
F |
Presentation |
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| 2 |
09/07 |
W |
1.
Dimension, dimensionless variables and Buckingham's Pi
Theorem |
1.1 |
(Section 1.1.2)
1, 2, 5 & 6 |
|
| 09/09 |
F |
(Section 1.1.4)
1, 4, 5, 6 & 7 |
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| 3 |
09/12 |
M |
2.
Scaling |
1.2 |
(Section 1.2) 1, 2, 4, 5,
6, 7 & 8 |
|
| 09/14 |
W |
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| 09/16 |
F |
Work
and quiz day (Topics 1 and 2) |
Quiz
1 |
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| 4 |
09/19 |
M |
3. Landau symbols
and asymptotic series |
2.1.4 |
(Section 2.1) 3
& 5 |
|
| 09/21 |
W |
4. Regular
perturbation, including the Poincare-Linstedt method |
2.1 |
(Section 2.1) 1, 2, 4, 6, 8, 10, 11 & 14 |
||
| 09/23 |
F |
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| 5 |
09/26 |
M |
(Topic 4 continues) |
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| 09/28 |
W |
5. Singular perturbation and two-scale phenomena | 2.2 | (Section
2.2) 1 & 2 |
||
| 09/30 |
F |
Work
and quiz day (Topics 3 and 4) |
Quiz
2 |
|||
| 6 | 10/03 |
M |
(Topic 5 continues) |
2.3 & 2.4
|
(Section 2.3) 1(a,b,c,d), 2, 5 & 6 |
|
| 10/05 |
W |
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| 10/07 |
F |
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| 7 | 10/10 |
M |
(Topic
5 ends) |
(Section 2.4) 1,3, 6 & 7 | ||
| 10/12 |
W |
6. Open sets and test functions | ||||
| 10/14 |
F |
Exam
1, Part 1 (Topics 1 through 5). In-class. Part 2 (take
home) |
Exam
1 |
|||
| 8 | 10/17 |
M |
(Topic 6 continues) |
Worksheet |
||
| 10/19 |
W |
7. Calculus
of variations |
3.1 & 3.2
|
|||
| 10/21 |
F |
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| 9 | 10/24 |
M |
(Topic 7 continues) |
3.2 & 3.3
|
(Section 3.2) 1,
3, 4, 5 & 7 |
|
| 10/26 |
W |
|||||
| 10/28 |
F |
Work
and quiz day (Topics 6 and 7) |
Quiz
3 |
|||
| 10 | 10/31 |
M |
{TIME FOR REVIEW} |
|||
| 11/02 |
W |
(Topic 7 ends) |
3.3 & 3.4
|
(Section 3.3) 3, 4, 6, 11 & 14 (Section 3.4) 1, 3, 5 & 6 |
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| 11/04 |
F |
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| 11 | 11/07 |
M |
8.
Weak derivatives of functions of one variable |
4.5 |
(Section 4.5) 1, 2, 3, 5, 8
& 11 |
|
| 11/09 |
W |
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| 11/11 |
F |
9. The Laplace transform | ||||
| 12 | 11/14 |
M |
Work and quiz day (Topics 7 and 8) | Quiz 4 | ||
| 11/16 |
W |
(Topic 9 continues) |
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| 11/18 |
F |
|||||
| 13 | 11/21 |
M |
10. More advanced
topics on the Laplace transform |
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| Thanksgiving
Weekend (no lectures Wednesday and Friday) |
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| 14 | 11/28 |
M |
(Topic 10 continues) |
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| 11/30 |
W |
|||||
| 12/02 |
F |
Exam 2, Part 3 (Topics
1-8.) Parts 1 and 2 are take-home. |
Exam 2 |
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| 15 | 12/05 |
M |
(Topic
10 ends) |
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| 12/07 |
W |
Preview
of MATH617 |
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