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 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.
  • The Fourier series of a square wave, with an application to a square-wave driven damped oscillator.
  • The various types of Fourier series of the function f(x) = x on [0,1].
• 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:
  • the phase planes of two competing species models,
  • the phase plane and solutions plots of the predator-prey model,
  • the the phase plane of the Van der Pol oscillator. This is a new version of the slide that I showed in class on 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

• 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

• 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.