642:527
METHODS OF APPLIED MATHEMATICS
FALL 2009
Course overview, prerequisites, placement quiz
For general information on these topics please see the main
web page for Math 527.
Basic information for Fall 2008
- Instructor: Professor Eugene Speer
- Hill Center 520
- 732–445–2390 Extension 1313
- speer at math.rutgers.edu
- Office hours:
- Monday 9:00–10:00 AM, Hill 520
- Tuesday 3:20–4:40 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 final exam is scheduled for Wednesday, December
16, 8:00–11:00 AM, 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 14, 3:00–5:00 PM,
in SEC 203. Come prepared to ask questions—I won't have much
to say otherwise.
- 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.
Announcements
- Here are notes on the heat equation in a
circular disk; we covered most of this material on Novemeber 12 and will
finish it November 19.
- Here are class notes on
the lecture of November 12. I thank to Namrata Bansal for letting me
post this copy of her notes.
- 11/10/2009 We are treating material in
somewhat different order from that of the book. Below is a guide to
how the lectures and book relate.
- 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 17.3.
- We omitted section 17.5, but may come back to it briefly later.
- On Tuesday 11/3 we discussed the heat equation with homogeneous
Dirichlet and Neumann boundary conditions (covered, with other topics, in
18.3).
- On Thursday 11/04 we discussed half-range and quarter-range sine and
cosine series, Section 17.4.
- On Tuesday 11/10 we will discuss the Sturm-Liouville theory from
17.7. This material will be on the second exam.
- On Thursday 11/12 and beyond we will discuss more about Sturm-Liouville
theory, finishing 17.7 and continuing in 17.8. We will continue to
consider problems from separation of variables for PDEs as motivation. This
material will not be on the exam.
- Next we will finish some remaining material from 18.3, then move on to
the Fourier transform, sections17.9, 17.10, and 18.4.
- 11/05/2009: Here are the two Maple worksheets on Fourier series
which were shown in class on October 29 and November 5.
- 10/28/2009: Here are the notes on
expansions in inner products in PDF form. This covers the part of the
material from Sections 9.6–9.10 and 17.6 that is
essential for us.
- 10/20/2009: Here are files with some plots for systems in class
on Thursday 10/15 and Tuesday 10/20:
- 10/14/2009: Here is a file with some plots of the phase plane of the pendulum; these were shown in
class on Tuesday, 10/13.
- 10/14/2009: Here are some notes on
the geometry of the orbits for centers and foci. Your comments on these
notes, and on any errors they contain, are welcome.
- 9/14/2009:A copy of the course text (Greenberg) is now on
reserve in the Math library, Hill Center.
- 9/10/2009: Here is a summary of the
Frobenius method in PDF form. This is basically a restatement of
Theorem 4.3.1 of the text.
- 9/8/2009: Here are solutions to
the entry quiz in PDF form.
- On Tuesday, September 8, Rutgers will hold Monday
classes. Our class does not meet September 8.
Exam 2
The second exam will be held Tuesday, November 17. It will cover
all our work through Tuesday, November 10, on trajectories in the phase
plane, orthogonal expansions, Fourier series, 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.
Solutions to this assignment are posted.
- 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 2008. Of
course, the questions on this year's exam may be quite different.
- Here are the solutions for Exam 2.
Exam 1
The first exam will be held Thursday, October 8. 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 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.
- Here is most of Exam 1 from Fall 2008.
One problem has been omitted (that is why the points do not add to 100)
because it covered material that we omitted this term.
- Here are the solutions for Exam 1.