# Class Announcements Page for Math 414, Advanced Calculus, Fall 2016

## Welcome to the class

This is where homework assignments will be posted and class announcements will be made. Here is the course syllabus, to start off with. See you on Monday!

## Test IV

will be in the final exam period. There will not be a cumulative final, but there will be opportunities to earn credit by answering advanced questions on earlier material.

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.

## Week Fifteen

• Dec 9: Expect that I will say something about the last section of chapter 22. I will post some review materials on the 8th some time, and there should be time to talk about this as well.

• Dec 7: First lecture on chapter 22. I'm hoping to lecture the last section of chapter 22 on Friday. Review materials for Test IV will appear on this page and there should be some opportunities for review in class on Friday. I will also have some office hours on Monday and/or Tuesday next week.

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).

## Week Fourteen

• Monday November 28th and Wednesday November 30th: More discussion of chapters 18 and 19.

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.

## Week Thirteen

• Friday Nov 18th: discussed results from chapters 18 and 19 on integration. Note that I added some problems to the last set.

• Monday and Wednesday, 14th and 16th: covered chapter 17.

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.

## Week Twelve

• Monday Nov 7: Covered chapter 16. This is the last section covered on Test III. Be aware that new homework not covered on the test will be posted this week, probably on Friday.

## Week Eleven

Friday, Nov 4: Homework assignment 13.3.2, 13.4.1* (optional -- probably hard: I need to state the result of section 13.4, which I skipped accidentally), 13.5.5, problem 13--1* (optional -- evil), 14.1.1 (this is standard from your calculus text, but it is the sort of thing you should certainly be able to do), 14.1.6, 14.2.3, 14.3.2 (standard calculus work), problem 14--1b* (optional), 15.1.1, 15.1.3, 15.2.1 a and b, 15.2.2, problem 15--1* (optional)

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.

## Week Ten

Other weeks did intervene; we prepared for the test and had it.
• We are currently at the end of chapter 12.

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.

## Week Seven

• Friday Oct 7: Reviewed last homework set. Brief overview of chapter 9 (which I suggest that you read, along with chapter 10).

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

• Wednesday Oct 5: I covered sections 8.3, 8.4.

• Monday Oct 3: Dr Kaiser covered 8.1, 8.2

## Week Six

• Friday Sept 30 covered sections 7.5-7.7.

• Wednesday, Sept 28 covered sections 7.1-4.

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.

• Monday, Sept 26: covered sections 6.4, 6.5.

## Week Five

• Wed Sept 21: lecturing sections 6.2, 6.3. Further review of last homework set.

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 ;-)

• Monday, Sept 19: discussed section 6.1 and reviewed the last homework set.

## Week Four

• Friday, Sept 16: more discussion of chapter 5.

• Wednesday Sept 14: discussion of chapter 4 and the first section of chapter 5.

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.

• Monday Sept 12: discussion of homework set 2 and started discussion of error limit analysis (chapter 4). Try computing some estimates of the zero of x5+x+1 using Newton's method. Also, prove Theorem 4.1, the error form principle.

## Week Three

• Friday Sept 9: We discussed sections 3.2 to 3.4 (with section 3.1 looming in the background of course). I continue to suggest working on exercise (not question) 3.2.1 (the addition property of limits of sequences). I strongly suggest working on question 3.3.1 (both parts, and I really mean question; this is about negative infinity as a limit): questions 3.1.2 and 3.2.2 are also good food for thought.

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.

• Wednesday Sept 7: The definition of limit. Please work together or separately on Questions 3.1 before the next class meeting. Also, please do exercise 3.2.1 before the next class meeting. You should know very well how to do this!

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.

## Week Two

• Friday Sept 2nd: discussed sections 2.5 and 2.6 on notions of approximation up to epsilon and the notion "for large n". You should expect a homework assignment Wednesday containing problems from these sections as well as further material.
• Wednesday August 31st: Discussed exercise 1.5.1, axioms of algebra, rules for inequalities, estimation techniques, absolute values.

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.

• Monday August 29th: proved binomial theorem and discussed completeness property further. No assignment.

## Week One

• Monday August 22nd: section 1.1, Appendix A.0. Attempt question 1.1 on p. 2 and the questions A.0 on p. 402 (you will derive no benefit if you peek at the answers given later in the text; bring your questions about them on Wednesday). No official homework problems on the first day.

• Wednesday August 24th: sections 1.2, 1.3. Attempt any of the 1.2 and 1.3 Questions which have not already been addressed in class. Again, don't peek ahead: bring your questions about these questions to class on Friday for discussion. Your first real problem set: exercises 1.2.1, 1.3.1, 1.3.2, 1.3.3, 1.3.4 (this requires mathematical induction as the author notes) and problems 1-1, 1-4, on pp. 12-14, due Wednesday August 31st.

Here is my refined definition of limit in terms of the number of decimal places of agreement.

• Friday August 26th: I lectured the examples in sections 1.4 and 1.5 and discussed the statement of the Completeness Propery in 1.6. No formal addition to the outstanding assignment, but I suggest some activities (I will talk about these on Monday when hopefully I will feel more coherent): on p. 8, try questions 1.4.2 and 1.4.3 (both involve thinking about comparison with geometric series).

## Test III date...

...will be Monday, November 14th. Here is the review sheet, which I may revise from time to time before the test.

## Test II date...

will be Wednesday, October 19th.

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.

## Test I date...

will be Friday, Sept 23. Here are some review instructions.

Here is Test I with solutions (which are in many cases references to the book).