Test #1 Information

General Information
**Friday, Sept. 30, 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 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 2.1, 2.2, 2.4, 2.5, Iode Labs I and II, Iode Projects I and II, Homework Assignments #1, 2, 3, 4
**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!
**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.

  1. ordinary differential equation
  2. solution of a differential equation
  3. order of a differential equation
  4. initial value problem
  5. general solution of a differential equation
  6. particular solution of a differential equation
  7. slope field (also known as direction field)
  8. separable differential equation
  9. linear first-order differential equation
  10. integrating factor
  11. homogeneous first-order differential equation
  12. Bernoulli equation
  13. exact differential equation
  14. logistic equation
  15. autonomous differential equation
  16. critical points of an autonomous differential equation
  17. equilibrium solution
  18. stable, unstable, semistable critical points
  19. bifurcation point, bifurcation diagrams
     

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.

Section 1.3, Theorem 1
Section 1.5, Theorem 1
Section 1.6, Theorem 1
Section 2.5, Theorem 1
Section 2.5, "Answer" on page 125 concerning error bounds on Improved Euler Method

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!  Since you do not have answers to all of the problems, I recommend trying some odd-numbered problems which are similar, so that you can check your answers in the back of the book.

Here are some additional review problems with answers in the back of the book:
Chapter 1 Review Problems - page 76 - all
Section 2.1, #1-8, 32,  33
Section 2.2, #1-12, 19
Section 2.4, #1-10
Section 2.5, 1-10

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