642:527
METHODS OF APPLIED MATHEMATICS
FALL 2016
Course overview and prerequisites
For general information on these topics please see the main web page for Math
527.
Basic information for Fall 2016
- Instructor: Professor Eugene Speer
- Hill Center 520
- 848–445–7974
- speer at math.rutgers.edu
- Office hours:
- Monday, 10:30–11:30 AM, 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 Monday, December 19, 4:00–7:00
PM, in SEC 208. Note the change of room from our usual classrooms.
- 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.
- 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.
- Here is a set of review problems. Here
are brief answers to the review problems;
these have not been checked carefully and may contain errors.
- We will hold a problem session Thursday, December 15, 10:00–11:30
AM, in SEC 216. Come prepared to ask questions—I won't
have much to say otherwise.
- I will not hold my usual office hours once classes are over.
However, I will hold a special office hour on Monday 12/19,
10:00–11:00 AM, in Hill 520.
- Note that an additional assignment, Assignment 14, has been posted.
This will not be collected; it is for your own benefit. Solutions will
posted sometime in the week of December 12.
Announcements and supplementary information
- 12/213/2016: Here are notes
on the Fourier transform, which we
will discuss during the last week of the course.
- 11/29/2016: Here are notes on
inhomogeneous partial differential equations, which we will
discuss today.
- 11/29/2016: Here are notes on
the the heat equation in a disk, which we
discussed Wednesday, November 16.
- 11/15/2016: Here are some slides summarizing
the properties of fractional range Fourier
series.
- 11/14/2016 I am making a change in the coverage of Exam 2.
In addition to the originally announced material, the exam will cover the
material discussed in class on Monday, November 14; this is the
material of Section 17.7.
A full description of the exam coverage, and a selection of problems
on the material of Section 17.7, will be posted by Wednesday, November 16.
- 11/01/2016 Here is the first part
of a set of notes on Fourier series and
PDE's.
- 10/26/2016 Here are the notes on
expansions in orthonormal bases which we will be working on on 10/26
and 10/31.
- 10/26/2016: Here are the phase plane
protraits for the predator-prey model that we discussed in class on
Monday 10/24. 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.
- 10/26/2016: Here are the phase plane
protraits for the competing species models that we discussed in class
on Wednesday 10/19 and Monday 10/24.
- 10/26/2016: Here are the phase plane
protraits for the pendulum that I showed in class on Wednesday
10/19.
- 10/18/2016: Here are some phase plane
portraits for the linear systems that we studied on 10/12 and 10/17;
these were shown in lecture on 10/17.
- 9/12/2016: Here is a continuation of the Notes on Power Series, covering series
solutions of ordinary differential equations
- 9/11/2016: Here is a copy of
the exercises from Sections 4.2 and 4.3 of our text by Greenberg.
- 9/7/2016: Here is a set of Notes on
Power Series.
Exam 2
The second exam will be held Monday, November 21. It will cover
our work through Monday, November 14, 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.
- Here are some old slides summarizing the
properties of fractional range Fourier series; I hope they may help
you in organizing this material.
- Solutions for Exam 2 are now posted as Resources on
Sakai.
Exam 1
The first exam will be held Monday, October 10. 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 5,
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,
(based on previous exams).
Here are some short answers to these
problems.
- We will have a problem/review session on Friday, October 7,
from 1:40 to 3:00 in SEC 212. 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.
- Solutions for Exam 1 are now posted as Resources on
Sakai.