640:421:04 Spring 2015 Home

640:421:04

Instructor: Professor Eugene Speer
- Hill Center 520
- 848–445–7974
- speer at math.rutgers.edu
Office hours:
- Monday, 1:40–3:00 PM, Hill Center 520
- Thursday, 10:20–11:40 AM, Hill Center 520
- Or by appointment or chance in Hill Center 520
Detailed course information and policies: As web page and as a PDF file.

The final exam in Math 421, Section 04, is scheduled for Friday, May 8, 12:00–3:00 PM, in SEC 220.

Formula sheets: You will be given the table of Laplace transforms from the first exam as well as a new formula sheet which contains all the formulas on the sheet from the second exam. No books, notes, or calculators may used during the exam.
Problem Session: We will hold a problem session on Wednesday, May 6, 10:00AM–12:00PM, in Hill Center 423. This is not a review presented by me but a chance for you to ask questions about any material in the course.

Review Problems: here is a set of problems to help you review for the exam. These problems primarily address material covered after the second midterm exam. Use the review sheet for the first exam, the review sheet for the second exam, and the exams themselves to review earlier material. Of course, homework problems are also a good source of material for review.
Extra office hours: I will not hold my normal office hours during reading or exam period. However, I will hold an extra office hour on Tuesday, May 5, 3:00–4:30 PM, and Friday, May 8, 10:00–11:00 AM, in Hill 520.

5/01/2015: Here are some notes on the Fourier transform which follow the same path that we took in class on April 28 and 30.
4/16/2015: Here is an outline of the material we will cover in the remainder of the course. I am not listing Section 13.7 because we have covered this material as we went through other PDE problems; please take a look and understand why this is true.
- April 16: Inhomogeneous PDEs, Section 13.6
- April 21: Fourier series in two variables, Section 13.8
- April 23: Separation of variables in polar coordinates, Section 14.1
- April 28, 30: Fourier integrals and Fourier transforms. In the text this material is covered in 15.3 and 15.4, but we did not follow these sections very closely. Notes on what we did do are posted here.

03/26/2015: Here is the Maple worksheet that I showed in class on Tuesday, March 24, Fourier, cosine, and sine series.

03/12/2015: Here is the Maple worksheet that I showed in class today on Fourier series.

02/09/2015: Linear Algebra. For the next few weeks we will be discussing linear algebra.
- I will be assuming some basic knowledge, which is thoroughly covered in the ODE course here (Math 244). Specifically, I will assume that you know:
  - The basic matrix algebra covered in Section 8.1 of our text;
  - The definitions of the eigenvalues and eigenvectrs of a matrix, and computational procedures needed to find the eigenvalues and eigenvectors of small matrices. all covered in Section 8,8.
  Please review these topics; the first before class on Tuesday, February 10, and the second within the following week or so.
- You should also be familiar with the topics of Gaussian elimination (in particular, the reduced row echelon form) and of the rank of a matrix, covered in Sections 8.2 and 8.3. However, these are so vital that I will spend some time on them this week. I am posting some notes on these topics; please read them.
- For the rest of the topics in our coverage of linear algebra, see the syllabus.
02/09/2015: Square wave driving. In class on Tuesday 2/05 we discussed an example of a harmonic oscillator with a square-wave driving force. Here is a PDF file reviewing what we did and continuing the calculation to extract from the solution the long-term, steady-state behavior.

The second exam will be on Tuesday, April 14.

Coverage: We will cover all our work in the course after the first exam and through Tuesday, April 7 (although we may finish up this material on Friday, April 12); this means Sections 12.1–12.3, 12.5 13.1–13.4, and Example 2 of Section 3.9. Section 13.5 will not be on the exam, despite what was said on Assignment 10.

Formula sheet: here is the formula sheet which will be provided with the exam.

Problem Session: We will have a review/problem session on Friday, April 10, 1:40-3:00 PM, in Hill Center 124. This will not be a review presented by me but a chance for you to ask questions about any material in the course.

Review Problems: here is a set of problems to help you review for the exam, and to give you something to ask questions about at the problem sessions. Some short answers are provided.
Extra office hours: I will hold office hours on Monday, April 13, 10:30–11:30 AM, in Hill 520. (This is in addition to my usual office hours.)

The first exam will be on Tuesday, March 3.

Coverage: We will cover all our work in the course through Thursday, February 26; this means all the work on the syllabus in Chapters 4, 7, and 8.

Laplace Transform Table: here is a table of Laplace transforms which will be provided with the exam. This is Table III from our text, but with the more obscure formulas—which will not be needed on the exam—omitted, and the formula for the Laplace transform of a periodic function added. There is no need to bring this table with you—you will be given a copy with your exam.

Problem Session: We will hold a problem session on Friday, February 27, from 1:40 to 3:00 PM, in Hill 124. This is not a review presented by me but a chance for you to ask questions about any material in the course.

Review Problems: here is a set of review problems to help you review for the exam, and to give you something to ask questions about at the problem session. Short answers are included for most of the problems, to help you check your work.
Extra office hour: I will hold an ofice hour on Friday, February 27, 11:00–12:00 AM, in Hill 520.
Solutions: Solutions to the exam are now posted on Sakai.