The exam is 10:00 AM to 12:00 PM on Thursday, March 22nd, in the normal classroom.

• Questions on the final will be quite similar to ones on the three "mid-term" exams. You may come to my office and look at the solutions to any of the three exams. If you want to, you can take pictures of them but, ideally, you would try any exercises you did not get or do ahead of tie and check your answers to those.
• The exam will NOT include reduction of order, Euler equations or the Laplace transform..
• As with the other exams, there will be some computational problems and some short answer/multiple choice/matching. There will some element of choice in which exercises you will need to do. So, for example, maybe there would be five computational problems and you have to do four, five short answer/multiple choice/matching and you have to do four.
• You WILL have to solve a second-order linear, constant coefficient initial value problem. (Exam 2, Exercises 1, 3, 4)

Mandatory Skills/Understanding Each of the following things will be included on the final and you will not be able to choose other things to do instead:

• Second order linear, constant coefficient equation solutions technique: Find homogeneous solution, find particular solution, apply initial conditions. (Exam 2, Exercises 1, 3, 4, 12, Exam 1, Exercise 11)
• Qualitative analysis of second order linear, constant coefficient equations: damping, transient and steady-state solutions, beats and resonance, for example. (Exam 2, Exercises 2, 5, 6, 7, 8, 9, 10)
• First order applications. (Exam 1, Exercises 3, 5, 7, 12)
• Separation of variables (Exam 1, Exercise 1), solving first order linear equations by either the integrating factor method (Exam 1, Exercise 2) or the homogeneous-particular method.

Additional Skills/Understanding You will be able to do SOME picking and choosing from amongst the following things. I would suggest preparing for all, or almost all, of them.

• Parameters, variables, initial conditions (Exam 1, Exercise 4)
• Autonomous equations and phase portraits (Exam 1, Exercise 10)
• Horizontal beams (Exam 3, Exercises 1, 4)
• Vertical columns (Exam 3, Exercises 2, 3, 8)
• Boundary value problems and eigenfunction problems (Exam 3, Exercises 6, 7)
• Eigenfunctions and eigenvalues (Exam 3, Exercise 5)

Of course there are many examples of these things in the textbook, and the various exercises from the start of class each day should be a good source of study material. I will be in my office from 10 - 1 on Monday, 10 - 2 Wednesday, and 9 - 9:50 on Thursday. I can be available earlier or later on Wednesday if you ask ahead of time via e-mail.