AM35 -- Methods of Applied Mathematics
Brown University
Fall 2004
| Instructor: |
Professor Sigal Gottlieb |
| Email: |
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| Office Hours: |
11:45-12:00pm, 1:00-1:15pm MWF, B&H Lobby |
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| Teaching Assistant: |
Akil Narayan |
| Email: |
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| Office Hours: |
Wednesday 1-3pm, B&H Lobby |
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From BOCA: Intended primarily for students who desire a rigorous development of the mathematical foundations of the methods used, for those students considering one of the applied mathematics concentrations, and for all students in the sciences who will be taking advanced courses in applied mathematics, mathematics, physics, engineering, etc. Three hours lecture and one hour recitation.
is desirable as a corequisite. Prerequisite:
Translation: this class is about solving ordinary differential equations, and you should know differential and integral calculus to do well in it.
| Meeting Time: |
MWF 12:00pm-12:50pm lecture, B&H 158
Tuesday 12:00pm-12:50pm or 7:00pm-7:50pm recitation, B&H 158 |
| Textbook: |
"Elementary Differential Equations and Boundary Value Problems", 8th edition; William E. Boyce and Richard C. DiPrima; John Wiley & Sons, Inc. |
Course Materials
| Subject |
Homework assigned |
| Integrating Factors |
Text, pg. 39, #1-12, ignore instructions, just solve using integrating factors
Text, pp. 39-40, #13-20
Text, pg. 41, #38-42
Solutions |
| Separable Equations |
Text, pg. 48, #1-20
Solutions |
| Homogeneous Equations |
Text, pp. 49-50, #30-38 |
| Exact Equations |
Text, pp. 99-101, #1-18, #20-32 |
| Modeling First Order Equations |
Text, pp. 59-62 #1-4, 7-14, 17 |
| Population Dynamics and Autonomous Equations |
Text, pp. 88-92, #1-5, 18, 20, 22-24 |
| Euler's Method |
Text, pp. 108-109 #11-14, 20 |
| Existence and Uniqueness |
Text, pp. 117-119, #3-8, 15-18 |
| Second Order Homogeneous Constant-Coefficient ODE's |
Text, pp. 142, #1-16 |
| Fundamental Solutions |
Text, pp. 151-152, #1-6, 7-12, 21-25, 33-36 |
| The Wronskian |
Text, pp. 158, #1-6, 15-23 |
| Complex Characteristic Equation Roots |
Text, pp. 164, #7-16 |
| Reduction of Order |
Text, pp. 172, #1-10, 23-30 |
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