642:527
METHODS OF APPLIED MATHEMATICS
FALL 2010
Course overview, prerequisites, placement quiz
For general information on these topics please see the main
web page for Math 527.
Basic information for Fall 2010
- Instructor: Professor Eugene Speer
- Hill Center 520
- 732–445–2390 Extension 1313
- speer at math.rutgers.edu
- Office hours:
- Tuesday and Friday, 9:00–9:40 AM, Murray 114
- Tuesday, 3:20–4:40 PM, 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 Wednesday, December 22, 12:00–3:00
PM, in SEC 203.
- 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 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 Monday, December 20, 4:00–5:30
PM, in HILL 120. Come prepared to ask questions—I won't
have much to say otherwise.
- I will hold office hours Wednesday, December 22, 10:00–11:00
AM. I expect to be at Rutgers on the second day of reading period,
Wednesday, December 15, and you could make an appointment (by email) to see
me that day.
- 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.
- Solutions to Assignment 14 have been posted.
Announcements and supplementary information
11/24/2010 Here are notes on the heat equation
in a disk. These are a continuation of the notes posted 11/2/2010.
11/11/2010 We are treating material in
somewhat different order from that of the book. Below is a guide to
how what parts of the book we have covered and will cover later.
- We have covered parts of sections 9.6, 9.9, 9.10, and 17.6. You should
look over these, particularly 17.6. The essential points are summarized in
the lecture notes on expansions in inner products, posted below.
- We have covered 17.2, 17.3, and 17.4, as well as the heat equation with
{\it homogeneous} Dirichlet and Neumann boundary conditions (covered, with
other topics, in 18.3). This material is in the second set of notes posted
below.
- We omitted section 17.5; you should take a look at it, but it will not appear on exams.
- On Thursday 11/4 and Tuesday 11/09 we discussed the part of the
Sturm-Liouville theory covered in 17.7. This material will be on the
second exam.
- On Thursday 11/11 and beyond we will discuss more about Sturm-Liouville
theory, continuing in 17.8. We will continue to consider problems from
separation of variables for PDEs as motivation. This material will not be
on Exam 2.
- Next we will discuss inhomogeneous initial/boundary value problems
(Section 18.3), then move on to the Fourier transform: sections 17.9, 17.10,
and 18.4.
11/7/2010 Here are notes Fourier series,
separation of variables, and half and quarter range series. These are a
continuation of the notes posted 10/21.
10/21/2010 Here are notes on expansions in
orthonormal bases.
10/20/2010 Here are the various slides shown in class on
October 14 and October 19:
Finally, here is the article which found a ten-year cyclic behavior in a specific predator/prey system: lynx and hare in the arctic.
10/13/2010 Here are notes on the phase
plane of centers and foci, showing how to determine the axes of the
elliptical trajectories of a center in the phase plane.
9/9/2010 Here is a summary of the
Frobenius method in PDF form. This is basically a restatement of
Theorem 4.3.1 of the text.
9/09/2010 Here are the solutions solutions to the entrance quiz given Tuesday 9/07/10.
9/02/2010 Here are a set of Notes on
Power Series.
Exam 2
The second exam will be held Thursday, November 18. It will cover
our work through Tuesday, November 11, 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. See the guide posted
11/10/02 below for the relation between lectures, text, and notes. There
is a homework "Assignment" for the week of November 17 (Assignment 10), 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 Exam 2 from Fall 2009. Of
course, the questions on this year's exam may be quite different.
Exam 1
The first exam will be held Thursday, October 7. 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" for the week of October 4, 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.
- Here is a brief set of review problems. In
fact, this is essentially the first exam from Fall 2009, together with one
extra problem.
- We will have a review session on Wednesday, October 6, from
1:40 to 3:00 in SEC 203. More precisely, 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.
- Here are the solutions
for Exam 1.