The exam will cover the material in lectures 10 through 18 of the syllabus. This is also the material covered in lectures 11 (last 45 minutes!) through 19 of the diary. This is, roughly, the textbook material in sections 7 and 8 of chapter 14 and chapter 15 (including the background material on cylindrical and spherical coordinates in section 12.7). Of course, computations and ideas from earlier parts of the course are needed to understand this material.
The exam is scheduled for 80 minutes, from noon to 1:20 PM on Thursday, April 15, in our usual classroom for Thursdays.

No formula sheets and no calculators may be used on the exam.

More specifically, the cover sheet for your exam will state:

• A My second exam in fall 2008.
  This was given for a course using the same textbook and covering the almost the same material as the second exam here (but line integrals are not included in our exam, so problem 8 would not be eligible for this exam). Here are answers to that exam.
  D Please note that problem 11 of the first exam that semester is relevant (that first exam and its answers). A misprint in these answers (the answer for question 7) has been corrected (4/12/2010) thanks to Mr. Meyer.

  Students who desire to create an experience which is likely to be similar to our second exam should just print a copy of A, remove problem 8, and include problem 11 from D. Try these problems for 80 minutes in a controlled and quiet environment. Then check your answers. If you have any doubt how well you may have done, consult me. This is written to help students trying to decide whether or not to drop the course. If you follow these instructions seriously you will have a fairly good idea of your prospects.

  
  
• B My second exam in spring 2006
  This was given for a course using a different textbook and a slightly different syllabus. Here are answers to that exam. A misprint in these answers has been corrected (4/7/2010) thanks to Mr. Meyer.
  Again, line integrals are not included in our exam, so problem 8 would not be eligible for this exam.
• C A set of old review problems mostly suitable for this second exam
  Problems L, P, and S of this set of problems concern line integrals and are not relevant to preparation for our exam.
  And here are answers to most of these problems. A misprint in the answer to problem D was noted (4/10/2010) thanks to Mr. Speights. A power of ρ is missing from the Jacobian for spherical coordinates and the final answer should be (4/15)Π.

Old problems in relation to our syllabus
Here is a list of problems from those old exams "keyed" to each section of the syllabus. This may be useful to you.

Lecture	Sections and Topics	My exam problems
10	Optimization in Several Variables	D11 B3 CB,C,&E
11	14.8 Lagrange Multipliers: Optimizing with a Constraint	A1 B4 CC,F,&J
13	15.1 Integration in Several Variables
14	15.2 Double Integrals over More General Regions	A2 B5 CG,H,K,&U
15	15.3 Triple Integrals	A3 B6 CM,N,V,&X
16, 17	12.7 Cylindrical and Spherical Coordinates 15.4 Integration in Polar, Cylindrical, and Spherical Coordinates	Polar A4 B2 CT
		Cylindrical A5 CD&R
		Spherical A6 B7 CA,H,O,&W
18	15.5 Change of Variables	A7

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 3/30/2010.