First Midterm: during class on Wednesday, October 10, 2012
The midterm covers Chapter 1, 2, and some of chapter 3 in the text.Doing all of the homework problems prior to the exam is a very good idea. Doing additional problems from the text can be helpful.
For the exam, make sure that you know
- The precise statement of basic definitions (this is not an exhaustive list): supremum, infimum, upper- and lower-bounds, accumulation points, etc.; what it means for a sequence to converge, the limit of a function, etc.
- The statements of the major theorems: Bolzano-Weierstrauss, Intermediate Value Theorem, Extreme Value Theorem, etc.;
- how to do a proof by induction;
- how to write a careful proof that a sequence converges, or that a function has a limit, etc.
- how to calculate (but not necessarily prove) limits of sequences, sums of series, etc.
- all sorts of other important things that I might ask you but didn't think of just now.
If you wish to use a calculator on the exam you may, although it is by no means necessary and unlikely to be of any help: all problems may be readily done without one.
To give you some idea of what to expect, here is
the first exam from 2010 and
the first exam from 2009.
Keep in mind,
however, that I didn't write the 2009 exam, so the format and choice of problems
will certainly differ. In addition, their exam was a bit earlier and they
hadn't yet covered any of chapter 3. Also, problem 6 uses the series
definition for
which we didn't discuss. Problem 4 relies on knowing that i=√-1 and then being able to calculate its powers.
Still, it is probably worth seeing the exam.
Here are the the solutions to the 2010 midterm and to the 2009 exam. Please make a serious attempt at the exam before looking at them!
Monday's class will be devoted to review/answering any questions you may have. I suspect Robert will primarily do review material on Tuesday, as well.
Here is a copy of the exam so you can relive the magic. Also, here are the solutions to the exam.
Second Midterm: in class on Monday, November 19
The second midterm will cover the material we have covered since the first exam, specifically material from chapters 3 and 4 (through section 4.5). As on the previous exam, you should expect to be asked to give some definitions or state some theorems precisely, do a proof or two, and do a few problems that are more calculational in nature.
For the exam, make sure that you know
- The precise statement of basic definitions (this is not an exhaustive list): the limit of a function, what it means for a function to be strictly increasing or decreasing, the inverse of a function f, supremum and infimum of a function, the definition of a function being continuous, a function with a removable (or essential) discontinuity, the logarithm with a given base, the derivative of a function.
- The statements of the major theorems: (Intermediate Value Theorem, Squeeze Theorem, Extreme Value Theorem)
- The various rules and techniques for taking derivatives, including the product, quotient, and chain rules; derivatives of trigonometric, inverse trigonometric, exponential, and logarithmic functions; logarithmic and implicit differentiation.
- Expect a proof involving induction, and another proof of some sort.
- all sorts of other important things that I might ask you but didn't think of just now.
As on the first midterm, a calculator is allowed but almost certainly of little use.
The second midterm from Fall 2009, and the
second midterm from 2010 are available.
On the 2009 midterm, you should be able to do all of the problems, while on
the 2010 midterm, problems 1b and 4 use material we haven't yet covered
(specifically, the mean value theorem and L'Hopital's rule),
since there wasn't a "superstorm" in 2010. While we have covered related
rates before the exam, this topic won't be on it.
Here are the solutions to the 2009 exam,
and the and to the 2010 exam.
Please attempt the problems on your own before consulting the solutions.
For your pleasure, here is a copy of the exam. Also, here are the solutions to the exam.
Final Exam: 8:00am on Monday, December 17, 2012
The final will be cumulative, covering everything that we have done in the class. However, extra emphasis will be on material since the second midterm, specifically that on integration (chapter 5).
Half of the final will be MAT131-style problems. If you can do well on these, you will get at least a B in the course. If you cannot do well on these, don't expect a decent grade, no matter how many theorems you can prove.