| Session: Spring 2009 | Instructor: Barry McQuarrie | Office Hours: | ||
| Meeting Time TBA | Office: Science 1380 | M--F 12:00-1:30pm | ||
| Location: Sci 1380 | Phone: 589-6302 (I do not use voicemail) | |||
| mcquarrb@morris.umn.edu | drop in (if my door is open we can talk, if it is closed I am not available) | |||
| http://cda.morris.umn.edu/~mcquarrb/ | other times via email appointment |
Introduction
This page was prepared for a 2cr course (Math 3993 Directed Study) for Spring 2009. If you would like to take this as a directed study come and talk to me. You can sign up for directed studies at any point in the semester.
Course Prerequisites
Prerequisites: Multivariable Calculus, Ordinary Differential Equations, Mathematica experience, a willingness to work hard, and most importantly an ability to work on your own.
Recommended: Linear Algebra. A smattering of Analysis would not hurt in parts either.
Textbook
Partial Differential Equations and Boundary Value Problems, Nakhle Asmar (first or second edition). Fabulous book, in my opinion.
Nakhle Asmar homepage with information related to his textbooks.
Course Components
Meetings. We will meet once a week to talk about what you have been working on. There will be no formal lectures. The meeting time will be determined based on the schedules of whoever is taking the course. This course should be thought of as an independent study, where you will work on material at your own pace throughout the semester. I will keep you on track and assist as needed (and, of course, provide the general outline of what you should focus on).
Assignments. The questions listed below will be turned in for grading. Each week turn in what you have completed so far. We can adjust as we go.
Final Paper. You will write a final paper based on either:
- Chapter 5 (Partial Differential Equations in Spherical Coordinates), or
- Chapter 6 (Sturm-Liouville Theory with Engineering Applications), or
- Chapter 8 (The Laplace and Hankel Transforms with Applications), or
- Chapter 9 (Finite Difference Numerical Methods), or
- Chapter 10 (Sampliing and Discrete Fourier Analysis with Application to PDEs), or
- Chapter 11 (An Introduction to Quantum Mechanics).
The paper should contain a summary of the concepts studied, and some example problems. It may contain some Mathematica, and if it does the Mathematica should be seamlessly integrated into the flow of the paper. The paper should be typed up using Word or LaTeX, or be written with exceedingly legible handwriting.
Grading
Here is the University-wide uniform grading policy.
- A: Represents achievement that is outstanding relative to the level necessary to meet course requirements.
- B: Represents achievement that is significantly above the level necessary to meet course requirements.
- C: Represents achievement that meets the course requirements in every respect.
- D: Represents achievement that is worthy of credit even though it fails to fully meet the course requirements.
- F: Represents failure and indicates that the coursework was completed but at a level unworthy of credit, or was not completed and there was no agreement between the instructor and student that the student would be temporarily given an incomplete.
- I: See the catalog.
The grade for the course will be calculated by the following formula:
| Assignments | 80% |
| Paper | 20% |
Your numerical grades will be converted to letter grades and finally Grade Points via the following cutoffs (see the UMM Catalog for more on Grades and Grading Policy):
| Numerical | 95% | 90% | 87% | 83% | 80% | 77% | 73% | 70% | 65% | 60% | Below 60% |
| Letter | A | A- | B+ | B | B- | C+ | C | C- | D+ | D | F |
| Grade Point | 4.00 | 3.67 | 3.33 | 3.00 | 2.67 | 2.33 | 2.00 | 1.67 | 1.33 | 1.00 | 0.00 |
Course Calendar
| # | Date | Lecture Topic | Homework | Resources | |
|---|---|---|---|---|---|
| 1 | Jan 25 | Course Introduction | |||
| 2 | Jan 27 | 2.1 Periodic Functions | Periodic Functions (MMA) | ||
| 3 | Jan 29 | 2.2 Fourier Series | 7, 24 | Fourier Series (MMA) Gibbs Phenomenon Applet |
|
| 4 | Feb 1 | 2.3 Fourier Series and Functions with Arbitrary Periods | Fourier Series for Functions with arbitrary period (MMA) | ||
| 5 | Feb 3 | 2.4 Half-Range Expansions: The Cosine and Sine Series | 17 | ||
| 6 | Feb 5 | 2.5 Mean Square Approximation and Parseval's Identity | 18 | ||
| 7 | Feb 8 | 2.6 Complex Form of Fourier Series | |||
| 8 | Feb 10 | 2.7 Uniform Convergence of Sequences and Series of Functions | |||
| 9 | Feb 12 | 2.8 Dirichlet Test and Convergence of Fourier Series | |||
| 10 | Feb 15 | 3.1 Partial Differential Equations in Physics and Engineering | Method of Characteristics: Notes | Mathematica | ||
| 11 | Feb 17 | 3.2 Modeling: Vibrating Strings and the Wave Equation | 6 | ||
| 12 | Feb 19 | 3.3 Solution of the 1D Wave Equation: Separation of Variables | 12 | ||
| 13 | Feb 22 | 3.4 D'Alembert's Method | 17 | ||
| 14 | Feb 24 | 3.5 The One Dimensional Heat Equation | |||
| 15 | Feb 26 | 3.6 Heat Conduction in Bars: Varying the Boundary Condition | 19, 20 | ||
| 16 | Mar 1 | 3.7 The Two Dimensional Wave and Heat Equations | 17 | ||
| 17 | Mar 3 | 3.8 Laplace's Equation in Rectangular Coordinates | |||
| 18 | Mar 5 | 4.2 Vibrations of a Circular Membrane: Symmetric Case | 10 | Symmetric Vibrating Drumhead (MMA file) General Vibrating Drumhead (MMA file) (based on 4.3) |
|
| 19 | Mar 8 | 5.2 Dirichlet Problems with Symmetry | 12 | ||
| 20 | Mar 10 | 6.1 Orthogonal Functions | |||
| 21 | Mar 12 | 6.2 Sturm-Liouville Theory | 35 | Hanging Chain with Kick (MMA file) (based on 6.3) | |
| Mar 15--19: Spring Break | |||||
| 22 | Mar 22 | 7.1 The Fourier Integral Representation | 23, 24 | ||
| 23 | Mar 25 | 7.2 The Fourier Transform | 1 | ||
| 24 | Mar 27 | 7.3 The Fourier Transform Method | 23, 24 | ||