Note: More information, with possible changes, will be added as the exam dates near.

Exam Rules: No calculators, notes, electronic devices (including headphones) etc. are allowed. Such items must be put away (e.g., in a backpack, pocket, ...). Some scratch paper will be provided for your convenience, but no work done on scratch paper will be graded.

If you need to use the restroom during the exam period, leave your exam along with your phone (or show your pockets are empty) with an instructor or TA at the desk at the front of the room while you are gone from the classroom.

After you have finished with the exam, turn it in (facing down) in the folder for your discussion section, which will be at the front of the classroom.

Exam Grading: Your exams will be graded on correctness, not effort. Exam problems will be of one of two types: short problems or long problems.

Short problems (possibly including true/false), will be worth 1-2 points (some you may need to show work and others not, as per instructions on exam). Partial credit will only be given sparingly, so you should focus first on solving the ones you know how to do completely correctly, and check your work. For instance, you will have a much better score if you solve half of the problems and write down nothing for others than if you get all of the problems "partially correct" (e.g., "having the right idea" but "messing up the algebra" or just "missing a sign"). You should expect many short problems, which means you should be sufficiently practiced on problems that you can solve simple problems quickly.

Long problems will require you do to several things, possibly being split into multiple parts, and will be worth more points. Partial credit for these problems will be given according to a grading rubric designed for each such problem.

exam 1: fri feb 16 (in 2:30 class)

here is a more detailed list of things you are expected to be able to do for the exam (this is not necessarily comprehensive, but covers the points most important to me; conversely, for time reasons not all of the following will be covered):

• determine when inverse functions exist, compute/graph them, know their basic properties, and compute their derivatives
• graph exponential and logarithmic functions, know basic properties (e.g., ln(ab) = ..., ln(e^x) = x, ...), and find their derivative/integrals (e^x and ln x are the most important, but there may be a question involving other bases)
• do logarithmic differentiation
• know the domains and ranges of the 6 inverse trig functions, compute their derivatives
• know the integral formulas 12 and 13 on p. 480 (derivatives of arcsin and arctan), as well as example 8 on same page
• know if a limit is in indeterminate form or not, and compute such limits with the hospital's rule
• identify when integration by parts applies and carry it out (possibly in combination with other techniques, like substitution)
• integrate various combinations of the 6 basic trig functions (this requires knowing some trig identities as discussed in class; you should also know integrals for sec x and tan x)
• possibilities for "cumulative" problems (calc i + calc ii): find minima/maxima of special functions (involving exp, log, inverse trig); graph special functions in part making use of the hospital's rule

exam 2: fri mar 16 (in 2:30 class)

while this exam is not explicitly intended to be cumulative (e.g., there will not be questions specifically about properties of inverse functions) many questions i may ask require competency with exam 1 topics. so if you did not do well on exam 1, you should understand what you missed as soon as possible. (in particular, you should definitely be able to do all of the integral from exam 1 and the associated mock exams)

what to expect: much of the 2nd exam will be similar in format to the 1st exam, however there will probably be no true/false questions (due to the nature of the material covered) and probably 1 or 2 "long problems".

here is a more detailed list of things you are expected to be able to do for the exam (this is not necessarily comprehensive, but covers the points most important to me; conversely, for time reasons not all of the following will be covered):

• compute definite and indefinite integrals involving various combinations of polynomials, rational functions, trigonometric functions, radicals, exponentials and logarithms (all integration techniques we covered up through 7.5). note some integrals may require a combination of techniques.
• determine if improper integrals converge or diverge, and compute ones that converge (section 7.8)
• compute arc length of a graph of a function (section 8.1)
• sketch curves given in parametric or polar form; and find ther tangent lines, enclosed areas and arc lengths (sections 10.1-10.4)
• translate between standard and polar coordinates in the plane (section 10.3)
• translate between equations for curves in standard form (just in terms of x and y), parametric form, and polar form. this includes being able to write down a parametrization for a given curve. (sections 10.1 and 10.3)

as i've said elsewhere, focus on being able to do problems on your own (try them on your own, get what help you need, then try on your own again). there are various exercises in the book. here are some review exercises i've selected, and we'll do some more in lecture/discussion before the exam:

• ch 7 review exercises: 1, 2, 3, 5, 7, 12, 16, 21, 23, 33, 42, 49
• ch 8 review exercises: 1, 3
• ch 10 review exercises: 2, 3, 5, 9, 11, 21, 24, 31, 35, 39

exam 3: fri apr 27 (in 2:30 class)

what to expect: this will be similar in format to previous exams. you should expect true/false like on exam 1, several short problems, and 1 or 2 longer problems. you will need to show your work for some problems but not others.

while not necessarily a comprehensive list of topics, here are the main things you should be able to do for the exam:

• be comfortable with the notation for sequences and series, and be able to write down expressions for general terms
• determine if a sequence converges or diverges, and often find its limit (relevant: use of continuous functions, monotone sequence theorem, and comparison with other sequences)
• know what it means for an infinite series to have a value (limit) in terms of partial sums, and be able to determine the limit for special types of series (geometric is the most important, with telescoping and special values of power series also possible topics)
• be able to determine if a series converges or diverges using various tests: divergence test*, integral test, p-series**, comparison*, limit comparison, alternating series test*, ratio test**. (more stars here = more likely to appear on test. if you are asked to determine convergence on a problem where you need to show your work, you must state the name of the test(s) you use.)
• know what radius and interval of convergence mean for power series, and be able to determine them.
• know power series (and radius of convergencs) for the following basic functions: 1/(1-x), e^x, ln(1+x), sin x, cos x
• know how to write down the power (Taylor) series for f(x) about x=a by manipulating the basic power series above as well as computing Taylor polynomials
• be able to use power series to compute integrals (e.g., the integral of e^(x^2)) as well as approximate definite integrals and values of functions (e.g., sin(1)). (for approximation problems, i will say something like use the first 4 nonzero terms of the power series for sin(x) to approximate sin(1), which you can leave as 1 - 1/3! + 1/5! - 1/7!)
• be familiar with the harmonic and alternating harmonic series, and understand the difference between conditional and absolute convergence

• concept check: 1-4, 5(a)-(g), 7ab, 8, 9, 10abc, 11abcdf
• true-false quiz: 1-22
• exercises: 1, 5, 6, 11-15, 23, 24, 27, 28, 31, 40, 41, 47, 48, 50, 51, 55, 57a (and use this to approximate sqrt(1.1))

final exam: th may 10 (7:30-9:30pm, nielsen hall 170, bring id)

consequently, my primary recommendation for preparing is to review your midterm exams, and similar practices problems (e.g., those above or from the mock exams).

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