640:421:06

Advanced Calculus for Engineering

SPRING 2012

Basic information

• Instructor: Professor Eugene Speer
  • Hill Center 520
  • 732–445–2390 Extension 1313
  • speer at math.rutgers.edu

• Office hours:
  • Tuesday, 3:20–4:40 PM, Hill 520
  • Thursday, 10:20–11:40 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.

Final exam

• Coverage: The exam will cover all our work in the course.
• 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. Note: the formula for the solution ot Euler's equation on the posted formula sheet has been corrected.
• Problem Session: We will hold a problem session on Wednesday, May 2, 1:30–3:30, in SEC 212. 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. (The review sheet for exam 2 now posted includes some corrections to the answers as well as a correction in problem 7.)

• Extra office hours: I will not hold my normal office hours during reading or exam period. However, I will hold extra office hours on Monday May 7, 1:00–2:00 PM and Tuesday May 8, 10:00–11:00 AM, in Hill 520.

Announcements and supplementary material

• Here are pdf files with notes on Bessel functions. There are two versions: a version with plots in color, good for viewing on the screen, and a version with plots in black and white, probably best for printing. For completeness, here are the plots that I showed in class, but these are also included in thenotes.
• 04/03/2012: Here are Maple worksheets on solutions of the heat equation and solutions of the wave equation that I showed in class March 27 and March 30.
• 03/06/2012: Here is the Maple worksheet on Fourier series that I showed in class today.
• 02/13/2012: Here are some notes on linear algebra. These are mainly concerned with the solution of linear equations, with some additional material on linear independence of vectors. Most of the material is in the text in some form (Sections 8.2, 8.3, and some of 8.6), but the notes are closer to the way I approached it in class.

• 02/02/2012: I must change my office hours on Thursday, 2/09. That day my office hours will be 9:30–10:20 and 11:20–11:50.

• 02/02/2012: In class on Friday 2/03 we worked out the connection between the Laplace transform and linear algebra approaches to a first order linear homogeneous system of ODE's. I have written this up as a pdf file. I did make a small change in notation: in the written notes I use λ₁ and λ₂ consistently for the eigenvalues of the matrix A.

• 02/02/2012: In class on Tuesday 1/31 we worked an example of a harmonic oscillator with a square-wave driving force; we got the solution but did not show how to extract the long-term, steady-state behavior. Here is a PDF file showing how to complete the problem.

• 01/31/2012: Beginning with Assignment 3, homework assignments will be due on Fridays.

Exam 2

• Coverage: We will cover all our work in the course after the first exam and through Tuesday, April 3 (although we may finish up this material on Friday, April 6); this means Sections 12.1–12.5, 13.1–13.5, and Example 2 of Section 3.9.
• Formula sheet: here is the formula sheet which will be provided with the exam.
• Problem Session: There are now two scheduled review sessions for Exam 2 in Math 640:06:
  • Sunday April 8, 2:30-4:00 PM, SEC 212
  • Monday April 9, 8:40-10:00 AM, Hill 525
  These will not be reviews 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: Office hours Monday, April 9, 10:20-11:40 AM are now BY APPOINTMENT ONLY. If you have a genuine conflict with the 8:40 AM review session, you may email me by 6:00 PM Sunday for an appointment. A "genuine conflict" is a scheduled class or some other equally compelling commitment; no version of "8:40 is too early for me" is considered a genuine conflict.

Exam 1

• Coverage: We will cover all our work in the course through Friday, February 24; 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.
• Problem Session: We will hold a problem session on Sunday, February 26, 3:00–4:30, in SEC 212. 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 to help you review for the exam, and to give you something to ask questions about at the problem session.
  And here are some short answers to the review pro blems. In problem 6(c) I forgot to specify an initial condition for y(t}; in the short answers I solved with y(0)=2.
  There is an error on the review problem sheet; in problem 4 the left hand side should read y'' - 4y' + 4y. You can in fact solve the problem as it is given, but in preparing the answer sheet I used the left hand side given here.
• Extra office hours: I will hold ofice hours on Monday, February 27, 10:20–11:40 AM, in Hill 520.