Exam II will be in the usual classroom on Friday, March 25, 2011. It will cover sections 3.1-3.5, 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 do not waste time doing things that are not required. 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 (this includes 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. Theory of linear ODE's, such as the Principle of Superpostion and the form of the general solutions of homogenous and non-homogeneous linear ODE's.
2. Homogeneous linear ODE's with constant coefficients, the recipe for writing down the general solution using the characteristic polynomial.
3. The mass-spring system, underdamped, critially damped, and overdamped systems, phase-angle form.
4. The method of undetermined coefficients--- writing trial solutions, solving for the coefficients.
5. The method of variation of parameters.

Let's talk about the method of variation of parameters. Depending on how one breaks them up, there are about four basic things that one should understand about it:

1. To what kind of ODE's does it apply, and what does it do for us?
2. How does one write the trial solutions y_p = u_1y_1 + u_2y_2 for a specific ODE? That is, what are u_1, u_2, y_1, and y_2 in this expression?
3. Why is it that is we choose u_1 and u_2 to satisfy the two equations y_1u_1'+y_2u_2'=0 and y_1'u_1'+y_2'u_2'=f(x), then y_p satisfies the ODE?
4. How does one solve this system of two equations, and use the result to find a particular solution and the general solution of the original ODE?

Items 1, 2, and 4 are rather straightforward, and most everyone ought to be able to apply them in an example. Understanding number 3 is desirable, but takes more effort and can be made a lower priority by most students.

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 even some different topics, 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.