Class Schedule

All textbook sections come from the official course notes written by Malcolm Adams. (See the link above.) Your homework sets also use many problems from that textbook. For more details, consult the syllabus.

Expect this calendar to update weekly. At the end of each week, we will usually have an extra handout which can either show you more examples or can go through a detailed example more thoroughly. Make sure to check this calendar at least on Mondays and Fridays.

UNIT 1

Week 1

 Day Book Sections Topics / Due Dates Monday Aug 17 1.1 Intro to course, defining sequences, recursion Wednesday Aug 19 1.2 Recap of induction and recursion Friday Aug 21 1.2 Recap of induction day 2, strong induction, well-ordering

Extra handout of the week: Arithmetic sequences and means

HW 1, due Monday, August 24, 2015

• ​Practice good style! Write most of your explanations in complete sentences, and lay out your work cleanly. It may be a good idea to try out a draft or two in office hours.
• Look this assignment over early, so you can figure out what questions you'll want to ask.
• Partial solutions will go up on eLC one class day after the due date.

Week 2

 Day Book Sections Topics / Due Dates Monday Aug 24 1.3 Laws for inequalities, bounds and monotonicity (part 1) Wednesday Aug 26 1.3 Bounds and monotonicity (part 2), subsequences, eventual properties (part 1) Friday Aug 28 1.4 Eventual properties (part 2), definition of limit (part 1)

Extra handout of the week: Help with using the limit definition

HW 2, due Monday, August 31, 2015

• For the last two problems, make sure to check out the extra handout of the week! It should help supplement what we do in class.

Week 3

 Day Book Sections Topics / Due Dates Monday Aug 31 1.4 Disproving limits via definition, uniqueness, limits and bounds (pt 1) Wednesday Sep 2 1.4 Divergence to infinity, limit of r^n, subsequences, limits and bounds (pt 2) Friday Sep 4 1.5 Limit laws (pt 1): sum & difference, product & quotient

Extra handout of the week: Proofs with limit assumptions

HW 3, due WEDNESDAY, September 9, 2015

• The due date is on Wednesday because of the Labor Day holiday on Monday, September 7.
• The extra handout of the week should help with understanding the styles of proof that we use on Wednesday.

Week 4

 Day Book Sections Topics / Due Dates Monday Sep 7 Labor Day, no class Wednesday Sep 9 1.5 Limit laws (pt 2): composites and continuity, L'Hopital Friday Sep 11 1.6 Completeness (pt 1): bounded monotone convergence, "candidate limits" for recursion, Cauchy sequences

Extra handout of the week: Completeness and recursion

Test 1 is next week, on Friday September 18, 2015. It covers material from the first day up to this Friday.

• There will be review information posted next week.
• Next Wednesday, we have review in class.

Week 5

 Day Book Sections Topics / Due Dates Monday Sep 14 1.6 Decreasing intervals, convergent subsequences, Cauchy pt. 2 This material is not on Test 1. Wednesday Sep 16 Review for Test 1: check out review topics and the practice questions! Friday Sep 18 TEST 1

Extra handout of the week: Practice questions for Test 1

There is no HW this week.

Test 1 is on Friday, September 18, in class.

Week 6

 Day Book Sections Topics / Due Dates Monday Sep 21 1.6 exercises, 1.7 Sup and inf, Bolzano's Theorem (Thm 1.7.3) See the weekly extra handout for more background. Wednesday Sep 23 1.7 Intermediate Value Theorem, boundedness of cont functions Friday Sep 25 1.7 Extreme Value Theorem

Extra handout of the week: More practice / background with sups and infs

HW 5, due Monday, September 28, 2015

Week 7

 Day Book Sections Topics / Due Dates Monday Sep 28 2.1 Series definitions, telescoping series, tails Wednesday Sep 30 2.1 Series laws, geometric series Friday Oct 2 2.1, beginning of 2.2 Start nonnegative series, induction bounds for partial sums

Extra handout of the week: Relating series to integrals, and how we discover some partial sum bounds

HW 6, due Monday, October 5, 2015

• The last problem is not really covered in the textbook. The extra handout for the week, and Friday's class, will help with it.

Week 8

 Day Book Sections Topics / Due Dates Monday Oct 5 2.2 Comparison Test (CT) and Limit Comparison Test (LCT) Wednesday Oct 7 2.2 More practice with LCT and CT, Integral (Comparison) Test Friday Oct 9 2.2 More Integral Test, Results about Logs and Exponentials, Tricks for Sums with f(a_n)

Extra handout of the week: Advanced uses of Comparison Test

HW 7, due Monday, October 12, 2015

• The book has fairly meager coverage on examples for this section. I'll be presenting more results in class, especially Friday, supplemented by the weekly handout posted later.
• My treatment of the LCT is a little different from the text. Hopefully my version is easier to use.

Test 2 is next week, on Friday October 16, 2015. It covers material from Section 1.7 up through Friday's class, including sup and inf.

• There will be review information posted next week.
• Next Wednesday, we have review in class.

Week 9

 Day Book Sections Topics / Due Dates Monday Oct 12 based on 2.2 Tricks for fixing inequality directions, estimates via Integral Test, and the Euler-Mascheroni constant gamma This material is not on Test 2. Wednesday Oct 14 Review for Test 2: check out review topics and the practice questions! Friday Oct 16 TEST 2

Extra handout of the week: Practice Questions for Test 2

There is no HW this week.

Test 2 is on Friday, October 16, in class.

Week 10

 Day Book Sections Topics / Due Dates Monday Oct 19 2.3 Absolute convergence, conditional convergence, Alt Series Test Wednesday Oct 21 2.3 Practice with Alt Series Test, Ratio and Root Tests Friday Oct 23 2.3 More Ratio / Root practice, Riemann Rearrangement Theorem

Extra handout of the week: More about alternation and rearrangements

HW 8, due Monday, October 26, 2015

• This has an optional extra credit problem you can do! It deals with the last topic we cover this week. The extra handout of the week will be a big help.

Week 11

 Day Book Sections Topics / Due Dates Monday Oct 26 2.4 Power series definition, going from geometric series to closed forms and vice versa Wednesday Oct 28 2.4 Interval Convergence Theorem, finding domains of power series Friday Oct 30 Fall Break: no class

Extra handout of the week: Prelude to next week... limits and "sup distance" between functions

HW 9, due Monday, November 2, 2015

Look over the handout for this week. It should help with the material of Section 3.1 next week.

Week 12

 Day Book Sections Topics / Due Dates Monday Nov 2 3.1 Pointwise vs. uniform convergence, basic concepts and examples. Read the handout below! Wednesday Nov 4 3.1 Uniform convergence of series, continuity and uniformity Friday Sep 4 3.1 Uniformity with integrals, differentiating and integrating power series

Extra handout of the week: Worked examples of uniform and non-uniform convergence

(This should help demonstrate some of the work from Monday.)

HW 10, due Monday, November 9, 2015

Test 3 is next week!

Week 13

 Day Book Sections Topics / Due Dates Monday Nov 9 3.2 Definitions of Taylor polynomials and series, derivatives and integrals This material is not on Test 3. Wednesday Nov 11 Review for Test 3: check out review topics and the practice questions! Friday Nov 13 TEST 3

Extra handout of the week: Practice questions for Test 3

There is no HW this week.

Test 3 is on Friday, November 13, in class.

Week 14

 Day Book Sections Topics / Due Dates Monday Nov 16 3.2 Taylor polynomial recap, agreement to order n as x -> 0 (Theorem 3.2.5) Wednesday Nov 18 3.2 Theorem 3.2.6: using agreement to order n to compute Taylor polynomials efficiently Friday Nov 20 3.2 Taylor's Theorem, proving f(x) equals its Taylor series, approximations (pt 1)

Extra handout of the week: A function which doesn't equal its Taylor series

• This is the last HW assignment of the course! It is a little longer (10 problems).
• We should be able to cover material for the first 8 problems during this week. Anything else can be finished on Monday November 30.

Week 15 and the final two days

 Day Book Sections Topics / Due Dates Monday Nov 30 3.2 A bit of Taylor review, estimating integrals with Taylor Wednesday Dec 2 3.2, misc Miscellaneous uses of Taylor series, mostly not in the book (physics approximations, power series and diff eq) You may also wish to look up a topic called "generating functions". Friday Dec 4 3.3 A quick introduction to complex sequences and series, Euler's e^(ix) formula Monday Dec 7 Review Review for the final exam, day 1 Tuesday Dec 8 Review Review for the final exam, day 2

Extra handout of the week: Using Taylor error to prove e is irrational

Final Exam Details and Handouts

The final exam will take place on Friday, December 11, from noon to 3pm, in the usual classroom.

Last updated: 12/7/15