642:527

METHODS OF APPLIED MATHEMATICS

FALL 2012

Course overview, prerequisites, diagnostic quiz

For general information on these topics please see the main web page for Math 527.

Basic information for Fall 2012

• Instructor: Professor Eugene Speer
  • Hill Center 520
  • 848–445–7974
  • speer at math.rutgers.edu
• Office hours:
  • Monday, 1:40–3:00 PM, Hill 520
  • Wednesday, 2:45–4:15 PM, Hill 520
  • Thursday, 9:00–10:00 AM, Hill 520
  • Or by appointment or chance in Hill 520
• Detailed course information and policies: As web page and as a PDF file.
• Tentative syllabus: As web page and as a PDF file.
• Homework assignments and solutions: Click here for assignments and solutions.

Final exam

• The exam is cumulative, covering everything in the course, but will probably emphasize Chapters 17, 18, and 19, and in particular material that we have covered since the last exam.
• Here is the formula sheet for the final exam. It consists of the formula sheets for exams 1 and 2, plus formulas for Sturm-Liouville problems, for the Fourier transform, and for d'Alembert's solution. You will also be given the tables in the appendices of our text for the Laplace and Fourier transforms.
• We will hold a problem session Wednesday, December 19, 3:00–5:00 PM, in SEC 212. Come prepared to ask questions—I won't have much to say otherwise.
• I will hold special office hours on reading day and during the exam period; the office hours on Monday 12/17 are primarily for students from my undergraduate class, but if none of them want to talk to me I will be happy to discuss Math 527:
  • Thursday 12/13/2012: 11:00–12:00 and 3:15–4:00, Hill 520
  • Monday, 12/17/2012: 1:45–3:00 and 3:45–4:30, Hill 520 (preference for students in Math 411)
  • Thursday, 12/17/2012: 2:00–3:00, Hill 520
• Here is the 2006 final exam for your amusement. However, I did not construct this exam and it may not completely reflect the nature of our exam. I would suggest our earlier exams and practice exams as additional review material.
• Note that an additional assignment, Assignment 13, has been posted. This will not be collected; it is for your own benefit. Solutions will posted sometime in the week of December 10.

Announcements and supplementary information

• 11/28/2012 Here are three Mapel worksheets that I showed in class: on Fourier series, the heat kernel, (which we obtained throurgh the solution of the heat equation via the Fourier transform), and solutions of the wave equation.,
• 11/28/2012 Here are some notes on the inhomogeneous heat equation for a rod, covering more or less what we did in class on Monday, 12/3.
• 11/28/2012 Here are the notes on the heat equation in a disk, a continuation of the previously posted notes on Fourier series. We will be working on this material on 11/26 and 11/28.
• 11/14/2012: Here are the slides summarizing the properties of fractional range Fourier series that I showed in class on 11/14/2012.
• 10/24/2012 Here is the first part of a set of notes on Fourier series and separation of variables. We will be working on this material on 11/07, 11/12, and 11/14. It will be covered on Exam 2.
• 10/24/2012 Here are the notes on expansions in orthonormal bases which we will be working on on 10/24 and 10/29.
• 10/24/2012: Here is a short set of notes on Orbits of Centers and Foci, explaining how one finds the rotated axes in which the orbits of a center are ellpses with their major and minor axes along the coordinate axes.
• 10/23/2012: Here are the phase plane protraits for the predator-prey model that we discussed in class on Monday 10/22. To accompany this, here is the article which found a ten-year cyclic behavior in a specific predator/prey system: lynx and hare in the arctic. Look, for example, at the graph on page 230.
• 10/23/2012: Here are the phase plane protraits for the competing species models that we discussed in class on Monday 10/22.
• 10/22/2012: Here are the phase plane protraits for the pendulum that I showed in class on Wednesday 10/17.
• 10/22/2012: Here are some phase plane portraits for the linear systems that we studied on 10/08 and 10/15.
• 9/13/2012: Here is a summary of the Frobenius method.
• 9/10/2012: Here are the solutions to the diagnostic quiz.
• 9/4/2012: Here are a set of Notes on Power Series.

Exam 2

• The exam will cover
• all our work on systems of ODEs and the phase plane;
• the posted notes on expansions in orthonormal bases and the corresponding material from Chapter 9 (some of this material is covered in Section 17.6; you might look at that section also);
• the posted notes on Fourier series and separation of variables, and the corresponding material in Greenberg: Sections 17.2, 17.3, 17.4, and parts of 18.3. The problems in Assignment 10 are a good guide to what you need to know out of Section 18.3.
• Note: In contrast to previous years, Sturm-Liouville problems (Sections 17.7, 17.8) will not be covered on the second exam.
• No calculators are to be used on the exam. I will try to make sure that all computations are simple.
• Here is the formula sheet that will be distributed with the exam. You may not use any book, or any notes or formula sheet other than the sheet that will be provided at the exam.
• Here is a set of review problems, a selection of problems from the second exams in the last two years that I taught the course. Here also is a set of brief answers (not checked carefully; be cautious).
• We will have a problem/review session on Friday, November 16 from 1:40 to 3:00 in Hill Center 124. I won't present any organized review, but I will answer any questions you may have on the review problems or anything else in the course.
• I must change my office hours for Wednesday, November 14, reverting to my original hours of 3:20-4:40 for that day only.
• Here is a set of solutions to Exam 2.

Exam 1

• No calculators are to be used on the exam. I will try to make sure that all computations are simple.
• Here is the formula sheet that will be distributed with the exam. You will also be given a copy of the table of Laplace transforms from Appendix C of our text. You may not use any book, or any notes or formula sheet other than the sheet that will be provided at the exam.
• Here is a brief set of review problems. In fact, this is essentially the first exam from Fall 2010. Here are some short answers to these problems.
• We will have a problem/review session on Tuesday, October 9, from 1:40 to 3:00 in Hill Center 124. I won't present any organized review, but I will answer any questions you may have on the review problems or anything else in the course.
• I must change my office hours for Wednesday, October 10, reverting to my original hours of 3:20-4:40 for that day only. Since I see that there is an MAE Colloquium that day I will also hold office hours
  • Wednesday, October 9, 11:00-12:00 AM, in Hill 520.
• Here is a set of solutions to Exam 1.