642:527 Fall 2014 Home

642:527

METHODS OF APPLIED MATHEMATICS

FALL 2014

Course overview, prerequisites, diagnostic quiz

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

Basic information for Fall 2014

Instructor: Professor Eugene Speer
- Hill Center 520
- 848–445–7974
- speer at math.rutgers.edu
Office hours:
- Monday, 3:30–4:30 PM, Hill 520
- Wednesday, 1:40–3:00 PM, Hill 520
- Thursday, 10:30–11:30 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 final exam is scheduled for Tuesday, December 16, 8:00–11:00 AM, in LCB 110, our usual classroom.

The exam is cumulative, covering everything in the course, but will probably emphasize Chapters 17, 18, 19, and 20, and in particular material that we have covered since the last exam. As is clear from the homework assignments, we are covering roughly 17.1–17.8, 17.10, 18.1–18.4, 19.2, 19.4, and 20.2.
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 Friday, December 12, 1:30–3:30 PM, in SEC 210. Come prepared to ask questions—I won't have much to say otherwise.
I will not observe my usual office hours after the end of classes, but will hold special office hours Monday, December 15, 10:00–11:00 AM and 1:00–2:00 PM.
Here is a set of practice problems for your amusement. I would suggest our earlier exams and practice exams, as well as homework, as additional review material. Here are brief answers to the probems.
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 8.

Announcements and supplementary information

10/31/2012 Here are the notes on inhomogeneous boundary value problems.
10/31/2012 Here are the notes on Fourier series which we will be working on for the next few weeks.
10/22/2012 Here are the notes on expansions in orthonormal bases which we will be working on on 10/22 and 10/27. NOTE: a preliminary version of these notes was posted by error on Wednesday, 10/22. For the current version, page 11 was changed. If you downloaded the earlier version, please download a fresh copy of at least page 11.
10/22/2014: Here are the phase plane protraits for the predator-prey model that we discussed in class on Monday 10/20. 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.
10/22/2014: Here are the phase plane protraits for the competing species models that we discussed in class on Wednesday 10/15 and Monday 10/20.
10/20/2014: Here are the phase plane protraits for the pendulum that I showed in class on Wednesday 10/15.
10/14/2014: Here are some phase plane portraits for the linear systems that we studied on 10/08 and 10/13.
9/17/2014: Here are a set of Notes on Solution of ODEs by Power Series. These are written as a continuation of the notes on power series posted below.
9/8/2014: Here is a set of solutions to the diagnostic quiz.
9/3/2014: Here are a set of Notes on Power Series.

Exam 2

The second exam will be held Monday, November 17. It will cover our work through Monday, November 10, on trajectories in the phase plane, orthogonal expansions, Fourier series, regular Sturm-Liouville problems, and the one-dimensional heat equation with homogeneous Dirichlet and/or Neumann boundary conditions.

I have posted homework Assignment 11, but it is only for your use in studying; it will not be collected.
No calculators are to be used on the exam. I will try to make sure that all computations are simple.
Here is formula sheet that will be distributed with the exam.
Here is a set of review problems, taken from previous exams. Here are brief answers to the review problems; these have not been checked and may contain errors.

Exam 1

The first exam will be held Monday, October 6. It will cover all our work on power series solutions of differential equations, including Legendre's and Bessel's equations, and Laplace transforms. There is a homework "Assignment," Assignment 5, for the week of October 6, but it is only for your use in studying; it will not be collected.

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. (Both problem 7 and its answer were revised 10/3/2014.)
We will hold a problem/review session on Friday, October 3, 1:40–3:00 P.M., in SEC 210. 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.

A set of solutions to Exam 1 has been posted on Sakai.