Office hours: Monday 1-3.

The final will be approximately twice as long as the midterms, though you'll have 2.5 hours in which to do it. It will cover everything we've done in the class. The material since the second midterm (Sections 10.3, 10.4, 10.5, 10.6, and 10.7) will account for between one-third and one-half the exam. That's why these sections are over-represented on the review problems below.

From the things we have studied since the second midterm, here are some that will definitely be on the final: the comparison and integral tests for convergence; the alternating series test and the alternating series error estimate; finding the interval of convergence of a power series; finding Taylor series starting from known series; integrating Taylor series.

You will be allowed to have one side of one 8.5 by 11 sheet of notes for the exam. All sheets must be handwritten. You can write anything you like on the sheet -- formulas, examples, mnemonics, your personal calculus mantra, etc. No magnifying devices allowed. For those who would like to decorate their sheets or otherwise artistically arrange them: I will post my favorite ones on the course website after the exam.

Review tips:

• Do the practice exam and the sheet with three more practice review problems below.
• Do the review problems below. At least one of the final exam problems will very closely resemble review problems. Note that this is not a comprehensive list of all the kinds of questions that might appear on the final, though all the major ideas of the course are represented in these problems.
• Make sure you can do the problems from the midterms. Certainly look at problems you lost points on, but it's also a good idea to redo the others.
• Go back over your homework assignments, reworking problems as necessary.
• The review problems from the two midterms are a good source of additional problems.

For a practice exam, click here. For solutions to the practice exam, click here.

For a sheet with three more practice review problems, click here. For hints and some solutions to these additional practice problems, click here.

Review Problems:

• Section 7.1 #15, 21, 23, 49
• Sections 7.2, 7.3, and 7.5 will be on the exam; problems from the Chapter 7 review exercises below cover them.
• Section 7.7 #11, 21, 63, 65
• Section 7.9 #19, 27
• Chapter 7 Review exercises, #13, 21, 23, 27, 29, 35, 37, 41, 43, 53, 57

• Section 8.1 #5, 13
• Section 8.4 #9, 13
• Chapter 8 Review exercises, #25, 33 (the Maclaurin polynomial is the Taylor polynomial at a = 0)

• Section 9.1 #5, 19, 43
• Section 9.2 Preliminary Questions #1, 4.
• Chapter 9 Review exercises, #27.

• Section 10.1, #25, 35, 48, 61.
• Section 10.2 Preliminary Questions, #1, 2, 3, 4, 5, 7 (S_N is the Nth partial sum), 8. Exercises #25, 31, 33.
• Section 10.3, #9, 53, 55, 57, 59.
• Section 10.4 Preliminary Questions, #1. Exercises #5, 7, 8, 13, 27.
• Section 10.5 #13, 51, 52, 53, 61.
• Section 10.6 #11, 13, 23, 25, 27, 59 (be sure to examine the endpoints of the interval of convergence).
• Section 10.7 #13, 15, 35, 49, 51, 65, 67, 71.
• Chapter 10 Review exercises, #101, 104, 107, 121, 127.