Math 241, Sections E

Midterm Exam 3 Study Guide

General Information

Exam date and time: The exam will be given during the regular class time, Wednesday, 11/19/2008, 8:00 am - 8:50 am.
Exam location: The exam will be in 1310/1320 DCL (Digital Computer Lab). NOTE THE LOCATION IS NOT THE SAME AS THE LOCATION FOR THE FIRST TWO MIDTERMS. Here are links to maps:
- Map of DCL. DCL is located at the intersection of Springfield and Matthews.
- Floor plan for DCL. The Rooms 1310/1320 are adacent and located near the north-east corner of the building. If you enter from Matthews, the rooms are immediately to your right.
Room assignments: The procedures will be similar to those for the earlier midterms. Try to be there 10-15 minutes early and wait outside in the hallway. The room assignments (1310 or 1320) are by discussion section:
- Sections ED4/ED5 (9 am and 10 am, Altgeld Hall, TA: Ryan Rettberg): Room 1310. (This is the smaller of the two rooms. It seats 100.)
- All other sections (TAs: Chia-Yen Tsai and Shichang Song): Room 1320. (This room seats 200.)

Rules

General rules: The same as for the earlier midterms. No cheating, no earphones, ipods, blackberries, and similar devices. Student IDs may be checked.
Calculator policy: As with all exams and quizzes in this class, calculators are not allowed. The problems will be such that a calculator is not needed and would not be of any help.
Books/notes policy: This is a closed books/notes exam. Books, classnotes, formula sheets, etc., are not allowed, and must be securely stowed away.
Missed Exam policy. I do not give make-up exams; if you miss the exam with a valid excuse (e.g., illness), the exam will be counted as "excused". (See the Course Information Sheet for an explanation of an "excused" exam/quiz score.) The absence must be documented by an "absence letter" from the Dean's Office at 300 Student Services Building, 610 East John St., phone 333-0050; other documentation (e.g., note from McKinley) is not sufficient. A missed exam without a valid excuse, documented by a Dean's letter, counts as 0 points.

Exam content

The exam will cover Chapter 13 and Chapter 14 through 14.3, except for those parts that have not been covered in class and are explicitly marked in the lecture summaries as material that can be skipped. See below for a detailed syllabus.

The format of the exam will be similar to that of the earlier midterms. Expect a total of 6 - 8 questions, usually with multiple parts. Some of the questions are aimed at testing your knowledge of basic concepts, definitions, properties, and formulas. These questions may be in multiple choice or true/false format, they generally involve no (or only trivial) computations and they should take very little time. (You either know the concept/formula/property in question, or you don't.)

Past exams: Below are links to exams from past years covering roughly the same material. Note that those exams were based on different texts with different syllabi, and there are differences in the topics covered, the notation, and terminology.

Note on the last (2007) exam: The 2000, 2004, 2005 exams do not cover vector calculus since that wasn't on the Calculus III syllabus at the time. I have therefore provided another exam, from 2007, which is the first one since the syllabus was changed to include vector calculus. The material covered by the 2007 exam roughly corresponds to Chapter 14 of Smith/Minton. However, since our midterm focuses on Chapter 13 and includes only a small portion of Chapter 14 (Sections 14.1 - 14.3), problems on that exam relating to the remaining parts of Chapter 14 (namely, problems 1, 2, 5, 7) are not relevant for this midterm. (However, they will be relevant for the Final Exam, which will cover all of Chapter 14.)

The above exams are pretty representative of what you can expect for our exam in terms of the difficulty level, nature of problems, and length of the exam, though not in terms of specific questions or topics covered. The latter is due, in part, to the differences in the syllabus, but also to the simple statistical fact that the topics that can be covered on any given exam represent only a small random snapshot of the entire syllabus, and another such random snapshot is likely to result in different questions and topics. Thus, simply studying the problems of these exams will not adequately prepare you. The only way to be fully prepared for the exam is to work through the entire exam material in a systematic manner, as described below.

Advice for exam day

Here are some tips on getting the most out of the exam (aside from studying for the exam - see below for more on that). Many of these are common sense test-taking strategies, and not specific to this class.

Read the problems carefully. This is one of the most important tips. All the information you need to solve a problem is given in the statement of the problem. If a problem doesn't seem to make sense at first glance, read it again; perhaps you missed a key piece of information given in the problem. Try to categorize the problem by topic or section in the book, and think of the concepts and problems associated with this topic; chances are that a similar problem has come up before.
Use common sense. The problems on the exam have been carefully selected to be appropriate for an hour exam. They are intended to test your knowledge of the material and techniques and should be neither ridiculously easy, nor excessively hard or lengthy. There are no trick questions. If your solution seems too easy to be true, it probably is, and you may have mis-interpreted the problem or missed a key assumption. Similarly, if you get entangled in a lengthy computation, you are likely on the wrong path.
Show all work, write legibly, and circle/box your final answer. An answer alone, without justification, will not earn credit. (An exception are questions in multiple choice or true/false format; for these problems only the circled answer matters.) Write legibly: if your handwriting cannot easily be deciphered by the graders, it cannot be considered for grading.
If you make a mistake, cross out all of your incorrect work. The graders will take points off for incorrect work that is not crossed out, even if the correct answer is given. (This is a common sense grading policy. Without such a policy, someone who isn't sure which of two possible methods is the correct one, would be assured to get credit simply by working out both methods, thereby covering all bases!)
Budget your time wisely. You have 50 minutes for the entire exam. This is more than adequate if you are well prepared and have the relevant concepts and formulas at your finger tips, but you need to work efficiently and not waste time. Computational problems should generally take no more than about 5 minutes each; non-computational problems, or problems in multiple choice or true/false format, should take even less time. There will be a total of 6 - 8 problems on the exam, which works out to an average of 6 - 8 minutes per problem. Take a look at the sample exams above to get a sense of the length of a typical exam; all of these were written as 50 minute exams, though the best students usually finished in 30 minutes or less.
Bottomline: If you find yourself working 10 minutes or more on a single problem, chances are that you are on the wrong track, and you will be better off moving on to the next problem. You can always get back to this problem if you have time left over at the end.
Note on calculations. The calculations required for the exam are very minimal. Many of the problems require no calculations whatsoever, and for those that do the computations are simple and can easily be performed in your head (recall that calculators are not allowed in this course). You can generally leave answers in "raw" form, such as 3/Sqrt{14}, 3 Pi/5, etc. (though you should evaluate standard trig values, e.g., sin(Pi/4)). If you get entangled in a lengthy calculation, you are likely on the wrong track, perhaps missing an easier approach. (With some problems, there may be two possible approaches, one quick and easy, and the other lengthy and messy; it is your job to know and use the more efficient approach.)
Bottomline: If you spend more than a few minutes total time on calculations, you are wasting your time.

Advice on studying for the exam

To prepare for the exam in a systematic manner, use the lecture summaries as a guide and proceed as follows. (I encourage you to get together with other students to do this.)

For each section, print out the corresponding lecture summary.
Go through the items listed under "Topics" in the lecture summary, and quiz yourself about each item. E.g., if it is a formula, write down the formula; if it is a concept, state its definition and properties, etc. If you are uncertain, look it up in your notes.
Go through your class notes (both for the lecture and associated discussions) corresponding to the section. These often provide an alternate (and perhaps easier to understand) perspective on the material with a somewhat different emphasis than the text, and they may point out things that are particularly important as well as traps and pitfalls to avoid.
Next, go through each of the assigned hw problems, and ask yourself how you would do the problem. In most cases, you should be able to recognize the type of problem, know off the bat how to approach it, and feel confident that you could do a problem of similar type on an exam; in that case, just move on to the next problem. Do the same for the problems and examples worked out in class, covering up the solutions with a sheet of paper, and trying to work them out on your own.
If you are a bit shaky on a particular problem, redo/review the problem, and any relevant examples in the book. For additional practice, you might want to do a similar problem from the same batch. (Most problems in the book are grouped in batches of problems of similar type; the assignments usually do not contain more than one problem from each batch.)

For convenience, here are the links to the lecture summaries, followed by a checklist of topics.

Checklist of topics

This list is essentially a combination of the topics listed in the above lecture summaries. For the corresponding homework and reading assignments see the lecture summaries.

Computation of double integrals via iterated integrals (13.1)
Reversing order of integration (13.1)
Volumes by double integrals (13.2)
Area of region R by double integrals (13.2)
Average value of f(x,y) over a region R (13.2)
Mass, center of mass, moments of inertia of lamina (13.2)
Double integrals in polar coordinates (13.3)
Evaluation of the "Gaussian integral", the integral of exp(-x²) from -infinity to infinity (13.3)
Surface area (13.4)
Triple integrals in rectangular coordinates (13.5)
Volumes by triple integrals (13.5)
Mass, center of mass, and moments of inertia of 3-dimensional solid (13.5)
Cylindrical and spherical coordinates (13.6, 13.7)
Converting equations between rectangular, cylindrical, and spherical coordinates (13.6, 13.7)
Triple integrals in cylindrical and spherical coordinates (13.6, 13.7)
Jacobian of a transformation (13.8)
Change of variables formula for double and triple integrals (13.8)
Vector fields (14.1)
Potential function (14.1)
Conservative vector fields (14.1)
Finding a potential function (14.1)
Line integrals with respect to arc length (14.2)
Line integrals with respect to coordinate variables (14.2)
Line integrals of vector fields, work (14.2)
Mass and center of mass of wire (14.2)
Fundamental theorem for line integrals (14.3)
Independence of path property (14.3)
Loop integral zero property (14.3)
Connected regions and simply connected regions (14.3)
The "mixed partials test" for "conservativeness" (2 dimensional case) (14.3)

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Last modified Sat 15 Nov 2008 03:14:23 PM CST