Differential Equations -- Fall 2016

The final exam will occur on Tuesday, 12/13 11:20AM - 1:50PM in our normal classroom.  Between 75% and 80% of the exam will cover the material we have considered since the previous exam.  The remaining material will cover the course as a whole.  In the information below, these will be discussed separately, but on the exam itself they will not be presented as separate sections.

Portfolios will be evaluated at the final exam, and a numerical score will be assigned.  If you intend to have a portfolio contribute to your final grade, remember to bring your portfolio to the exam and to collect it before you leave.

For the part of the exam covering the last third of the course, you are responsible for the following material: sections 3.6, 3.7, 5.1, 5.2, 4.1, 4.2, 4.3, and the handout on the annihilator method.  This part of the exam will be similar to the prior two exams
: you should be able to demonstrate understanding and proper use of concepts, definitions, theorems, notation, terminology, and the various kinds of graphs we have used.  And of course you should be able to use established procedures to solve problems.  This part of the final will also be similar in length to the other exams.

For the part of the final covering the course as a whole, you might be asked some questions from prior exams.  These items, if any, will be identical to what has already appeared on an earlier exam.  In addition,  you may be asked to show what you have learned about
ideas, concepts, and themes that have appeared repeatedly over the semester.  Expect a few questions about these ideas, possibly as essay questions, multiple choice, fill-in-the-blank, or other question formats.  Here are some examples of the kinds of concepts I am referring to:

• Modeling: How differential equations are formulated to model real systems or phenomena, what sorts of analyses are undertaken in such applications, and how the results are used and interpreted.  This includes the use of parameters within differential equations, qualitative analyses, and consideration of the sensitivity of results to small variations in the parameters.

• Analytic, numerical, graphical, and qualitative approaches to studying differential equations.  What are they, when are they applicable, how are these different?   What kinds of information can they provide?  How do they complement each other?

• Qualitative Analysis.  What is it?  Why is it useful?  What are some examples we have seen?  What are some important concepts associated with qualitative analysis (for example bifurcations)?

• Linearity.  What's the difference between linear and nonlinear differential equations and systems?  What are the special properties of linear equations and systems that make them particularly useful or tractible?

• Autonomy.  What's the difference between autonomous and nonautonomous equations or systems?  What are the special properties of autonomous equations or systems that we have used repeatedly?

• Existence and Uniqueness.  In general terms, what do existence and uniqueness results tell us?  Why are these important?  How have we used them?
You might be asked to comment on one or two of these in depth in an essay question, or there might be questions covering most or all of them in a short answer, T/F, or multiple choice format.

I am not providing a sample exam for the final.  Procedural questions will be similar to those assigned in homework.  Questions that are more conceptual or that test your knowledge of terminology, definitions, and theorems will be similar in nature to what has appeared on prior exams.  For this type of question study the text and your class notes.   Although I am planning to hold a review session on the last day of class, I am not preparing specific material to go over at the review.  It is important that students bring their own questions about homework or prior exam problems, concepts, or methods that arise in their preparation for the final.