Exam I will be in the usual classroom on Friday, February 18, 2011. It will cover sections 1.1-1.6, but only the material that we discussed in class, and obviously not every single item can be covered in depth in a 50-minute exam. The current draft has 54 points possible.

Be sure you follow the instructions of each problem, and give the answers requested, but not anything that is not needed. As on any exam, it is wise to start with the problems that you feel confident that you know how to do, before moving on to others. Most of the questions will have rather short solutions, if you know how to do them, so if you find yourself doing something lengthy and unusually complicated on a problem, it might be best to move on to other problems and come back later to it later if you have time.

Calculators are not needed, although you may, if you really want to, use a non-graphics simple arithmetic calculator without even trig functions or log and exponential, but no mechanical or electronic device more sophisticated that this (including iPods, earpieces, etc.). Blank paper will be provided, so all you will need is something to write with. As on the quizzes, please write your solutions on the blank paper. You may have as many sheets as you need, and may put the problems in any order. Please put your name on your exam paper and all pages of your solutions, and hand them all in together, although without any pages of scratch work that is not to be graded.

Some of the exam problems will be very similar to homework problems, while others will draw upon the material presented in the lectures. Definitions of important concepts are perfectly reasonable questions, and although you do not need to know them word-for-word, you should be able to write down a coherent and accurate definition of any major concept or term.

The following topics are very likely to appear, although the exam is not limited to them:

1. First-order DE's, general concepts and definitions.
2. Initial value problems, using the initial condition to find a specific solution. The Existence and Uniqueness Theorem, what it says, testing its hypotheses.
3. Separable equations. Know the method of separation of variables well, and be able to calculate accurately with the logarithm and exponential functions.
4. First-order linear DE's. What they are, the method of solving them with an integrating factor.
5. Substitution methods. Know and be able to carry out the linear substitution, the substitution for a homogeneous DE, and the Bernoulli substitution v=y^{1-n}.

Except for the Existence and Uniqueness Theorem, most of the earlier material such as slope fields will receive minimal coverage. Emphasis will be on separation of variables, first-order linear equations, and substitution methods. A problem involving a tank of salt water or a polluted lake will appear.

I have taught Math 3113 three times since we went online at the turn of the millenium, and you can find the exams from those classes at the course web page, linked at course pages page). Some of those classes met twice a week, so the exams were geared to a 75-minute time period. Taking one of those exams and checking your solutions might be good practice, especially if you get a lot of test anxiety, but be aware that those were different courses with different emphases and to some extent different material (the last time was eight years ago, and some of the topics, especially those for Exam II, have been changed), so there is no reason to assume that the tests will be similar. As a point of information, when I sit down to write an exam, I never look at old exams I have written. I start with a blank page and think about what we did in the present course, and try to find problems that will give some measure of what you have learned.