About the final exam
The exam will be cumulative, and cover all of the syllabus but there will be somewhat more emphasis on the material covered since the second exam (that is, the vector calculus material).

• The final exam for Sections 12, 13, and 14 will be given on Thursday, December 23, from 12 to 3 PM, in Hill 116.
• The final exam for Sections 15, 16, and 17 will be given on Thursday, December 16, from 12 to 3 PM, in Hill 116.

In Math 251, the final exam is written by the lecturer for the sections, so your final exam will be written by your lecturer, and the "style" should be familiar. The pace of a three-hour final exam will be quite different from the two exams you've already had in this course. The final exam likely will be less than twice as long as one of the exams already given. Here are some general comments about preparing for the exam.

• Plan to stay for the entire three hours of the final exam. This is vital. Student determination (stubbornness!) and energy can really influence exam scores.
• Plan your work on the final exam. Study as suggested below, but also plan: I suggest that you first do the problems which seem very straightforward and leave other problems until later. There will be enough time to check your work. Please read the questions and answer them -- don't invent your own problems.
• A formula sheet will be distributed with the exam. Please look at it now, and use it appropriately during the exam. No other formula sheets and no calculators may be used on the exam.
• Extensive documentation of your answers is not necessary, but generally an answer alone may not receive full credit. Show your work.
• Extensive computation is not necessary, so you don't need to compute 1,234.56·7.89 exactly (if you think you must do this, you're probably not doing the problem correctly or even doing the correct problem!). However, you should find exact values of standard functions such as e⁰ and sin(Π/2).

What to study, part 1
Please assume that any question previously asked on an exam concerns material important enough to be examined again. Careful students should know answers to those exam questions which didn't earn full credit in earlier exams. This is a very serious recommendation. Therefore you should take your graded earlier exams and look at the answers to the first exam and to the second exam. This process may feel awkward, but be certain you can answer the questions now. Please do this!

• The first exam and some answers.
• The second exam and some answers.

What to study, part 2
Here are some relevant previous exams and review material that I've given in this course, going backwards in time (most recent is first).

• A My final exam in spring 2010
  This was given for a course using the same textbook and covering the the same material as our final exam. I don't prepare answers for final exams (one less job!) but some students have now prepared some answers which are available here (but not to all of the problems!).
• B My final exam in fall 2008.
  This was given for a course using the same textbook and covering the almost the same material as our final exam (but I won't include Stokes' Theorem, so problem 10 would not be eligible for this exam). Some answers are available here.
• C My final exam in spring 2006
  This was given for a course using a different textbook and a slightly different syllabus. Some answers are available here. If you wish to contribute any missing answers, again, I will be happy to receive and proofread your work, and post it if it is correct.
• D A set of old review problems concentrating on vector calculus
  Here are answers. Problems 1e) and 6d) are concerned with Stokes' Theorem and are therefore not relevant to final exam preparation here.

Studying with other students may be very helpful.

Old problems in relation to our syllabus
Here is a list of problems from those old exams "keyed" to each section of the syllabus covered since the second exam. This may be useful to you but note that only the "vector calculus" problems are listed below. Since the final exam is cumulative, you should be sure to review important earlier material (so see the earlier exams, as mentioned previously, and the earlier review pages).

Lecture	Sections and Topics	My exam problems
19	Vector Fields	A6 B12 C9
20	Line Integrals	A3 B6 C7,8 D1b,2
21	Conservative Vector Fields	A3 B6 C7 D2
23	Green's Theorem	A5 C8
24	Parameterized Surfaces and Surface Integrals	D1d
25	Surface Integrals of Vector Fields	B11 C6 D5,6a,b,c
26	Divergence Theorem	A7 B11 C6 D1c,3,4,5
27	Stokes' Theorem	Not covered in this class's final exam. B10 D1e,6d

My design criteria for calculus exams
I try to ask questions about most (hopefully all) important topics which were covered in the period to be tested. I try to avoid asking problems which require special "finicky" tricks, and do try to inquire about techniques which are broadly applicable.

I want to give, on any calculus exam, questions which require reading and writing graphical information, reading and writing symbolic information, reading and writing quantitative information ("numbers"), and, finally, some question(s) requiring students to exhibit some reasoning and explanation, appropriate to the level of the course and also recognizing the limited time of an exam. I certainly don't always "hit" this target but that's my aim.

Maintained by greenfie@math.rutgers.edu and last modified 12/1/2010.