Test #3 Information

Important Note:  On the test, you will be given the following formulas.  These will be given exactly as they are in the book, without any of the text or explanation - just the formula.  The test will not indicate which formula is to be used for which problem:

(16) on page 605
(31) on page 613
(40) on page 616

General Information
**
Friday, Dec. 9, 11:00-11:55 in the usual classroom.
**The test will begin promptly at 11:00 and end promptly at 11:55.  If you arrive late, you may still take the test, but you must turn it in at 11:55.
**Please bring your I-card to the exam.
**No notes or books may be used on the test.
**No calculators may be used on the test.
**The exam covers Sections 9.1, 9.2, 9.3, 9.4, 9.5,  Iode Project IV, Homework Assignments #9, 10, 11
**There wil be several slightly different versions of the test to discourage any cheating.  I very much hope it won't be necessary, but if any cheating is detected, I will certainly follow through on imposing the maximum penalties allowed by the university.
**I may ask you to move your seat if it appears that you are copying or that someone is copying from you.

What will the test be like?
**If you know the material, you should be able to complete the test comfortably in 50 minutes or less.
**The test will include some very basic questions, some medium-difficulty problems, and one or two more challenging problems.
**The types of questions that may appear on the test include true/false, state the definition, give an example, explain a concept, do a proof (similar to those you've done for homework), calculational problems (similar to homework).
**Many of the problems will be quite similar to homework problems!  However I will avoid some of the very long computations which appeared on the homework and some of the difficult graphs which were time-consuming to do without a calculator.  You may be asked to outline the procedures, or to do just part of such a problem, or to do a problem of the same type in which the computations happen to be short.
**You will need to show your work on the test.
**Problems will be written in such a way that a calculator is not needed.

Definitions
Be sure you know the definitions of the following terms.  You should be able to state these definitions precisely, not necessarily with exactly the same words as the textbook, but with exactly the same mathematical meaning.  You should also be able to give examples.

  1. Fourier series
  2. Fourier coefficients
  3. piecewise continuous
  4. piecewise smooth
  5. even function
  6. odd function
  7. Fourier cosine series
  8. Fourier sine series
  9. pure resonance (as on p. 603)
  10. (one-dimensional) heat equation

Theorems
You should be able to state the following theorems, understand what they mean, and be able to use them.  Unless otherwise stated, you do not need to be able to prove them.

Theorem 1 from Section 9.2
Theorem 1 from Section 9.3

Review Problems
One of the very best ways to study for the test is to rework your old homework, especially problems that you missed or were unsure of.  Try to do them without looking at books or your notes - this is what you will be doing on the test!  Please let me know if you find any errors in the solutions I've posted.

However I will avoid some of the very long computations which appeared on the homework and some of the difficult graphs which were time-consuming to do without a calculator.  You may be asked to outline the procedures, or to do just part of such a problem, or to do a problem of the same type in which the computations happen to be short.