Here is the test 4 review sheet. It will be updated in ways I describe when I have actually written at least a draft of test 4.
Here are the instructions and the theorem list from the current draft of Test IV with a couple of added comments of interest.
Last homework, due at the final (you should expect that this will be checked off, it is really to assist review): 20.1.1, 20.2.1a, 20.2.3 (likely to be hard), 20.4.5, 20.4.1 (more generally, prove as many of the properties of the logarithm from its definition as an integral as you can), 20.6.3, 22.1.1, 22.1.2, 22.2.2, 22.2.4 (I think this is quite direct, use big theorems), 22.2.5 (serious challenge, don't worry if you can't do it), 22.4.1, 22.4.2, problem 22--1 (it's a Problem, of course it's a puzzle. I think this is a question about clever calculations).
Homework, due on the last day of classes (there will be one more assignment, due at the exam): 18.2.1, 18.2.3 (there is one slight thing you have to be sure to say about your partitions), 18.3.2 (this will need the MVT I think), 18.4.1, 19.2.3 (looks interesting), 19.3.3 (this uses very basic theorems), 19.4.1, problem 19--1. Read problems 19--2 and 19--3: they contain useful information.
Homework, due Wednesday after the break: 16.1.1, 16.1.3, 16.1.4, 16.2.4, 17.1.1, 17.2.2, 17.2.4, 17.3.1, 17.3.2, 17.3.4, 17.4.1ac, (note three new questions added Friday!) 18.1.1, 18.2.2, 19.2.1.
Math 514 homework, due at the end of classes: Exercise 16.2.2, Problem 16--1, Problem 16--2.
This problem set is due on Friday November 11th. You are encouraged to turn in any part of the problem set you have done on Wednesday the 9th: any problems that I receive on the 9th will be returned, graded, on the 11th.
Watch for review material this weekend.
Homework, due a week from Wednesday: I have an awful lot of problems I like, so the form of the assignment is: do 12 of the following problems, choosing at least 4 from chapter 11, at least 4 from chapter 12, and at least 2 from chapter 13 (we will start talking about 13 tomorrow). 11.1.5 (a matter of understanding definitions), 11.2.1 (just from the definition!), 11.2.3 (an exercise in proof writing, not hard), 11.3.1, 11.4.2 (you just have to say something about the endpoints), 11.5.1 both parts, 11.5.2, 11.5.5 both parts (good proof writing practice), problems 11--1 or 11--3, 12.1.1, 12.1.2, 12.2.2 (might be hard, seek guidance if you need it), 12.2.3, 12.3 (follow his instructions exactly; this is a really good practice for proof writing), 12.4.1, 13.1.1a, 13.2.1, 13.1.2, 13.3.1.
The homework originally due Oct 5 will still be accepted on Monday. As I have only received two papers...
Homework set due Friday, October 14th: 7.2.1 (be sure to indicate theorems used), 7.6.1, 8.1.1 aceg (the others are left so you can ask me to do examples), 8.1.3a (hint: this is not a mystery. You know what conditions the terms of the infinite series have to satisfy for the ratio test to work: reverse engineer the conditions needed on the coefficients), 8.2.1aceg, 8.3.1, 8.4.1, problem 8--2, 9.2.1, 9.3.1, 9.4.1c
Homework due on Wednesday, Oct. 5: ex 6.1.2, 6.4.2, 6.5.4, problem 6-1, problem 6-2, 7.1.1, 7.1.2, 7.2.2, 7.3.2, 7.4.1acegj, 7.4.3 (this is the proof of the root test; the problem numbering is confusing there), one of problem 7-1 and problem 7-4.
Additional homework for 514 students, recommended for everyone: problems 6-5, 6-6, 6-7. I'd like a nice unified writeup for this block of problems, separate from any other homework. Conversation with me about how to approach this is appropriate. This is due on October 14.
Homework: 5.1.4, 5.1.5b, 5.2.1, 5.2.4, 5.3.1, 5.3.6, 5.4 (I talked about this in class a couple of times!), problem 5-7, 6.2.1, 6.2.2, 6.3.1, problem 6-4 (I think he is looking for a characteristic mistake here: try not to fall into his trap ;-)
Homework due next Wednesday: exercises 3.3.2, 3.4.2, 3.4.5, problem 3-5, exercises 4.1.1, 4.3.1, 4.3.3(i): just set up the recursion formula and give an estimate of M. Problem 4-2. exercises 5.1.1, 5.2.2, problem 5-2.
No new homework: your current homework is under Sept 7.
And no, I have not forgotten that my schedule shows a test on the 16th. If I decide to change that date I'll tell you on Monday; if not, I'll supply some sort of review material.
Homework due on the 14th: exercises 2.4.7 (just for fun), 2.5.1 (this is interesting and there are a couple of ways to approach it), 2.5.3, 2.6.1, 2.6.4a, 3.1.1ae, 3.2.2, 3.2.5 problems 2-4, 3-1 3-4.
Assignment, due next Wednesday: exercises 1.4.1, 2.1.1, 2.1.3, 2.2.1-2 (I'll do example 2.2C in class), 2.3.1a, 2.4.1, 2.4.6, problem 2-1, problem 2-2.
Here is my refined definition of limit in terms of the number of decimal places of agreement.
I will supply the theorem list for Test II sometime next week (writing on the 7th); you should examine it in case there is anything additional you want to request.
Here is the first pass at the review sheet for the test. It should be updated over time with review exercises and the theorem list which will be attached to the test. It is already a good summary of what I expect to ask about on the test.
Here is Test I with solutions (which are in many cases references to the book).