**Class schedule:**

This calendar is updated weekly, indicating which textbook sections we plan to cover. It is where you will find paper HW assignments, test review documents, and other useful handouts.

Don't forget to check out the sidebar on the right as well! That's a convenient place to find some central resources, such as the syllabus.

**UNIT 1: Integral Applications**

*Week 1:*

*W Jan 9.*Introduction to the course and some brief review of derivatives.- Log on to WeBWorK and practice with it! Check the syllabus or email me if you're having problems.
- You will need to install VPN (virtual private network) programs if you plan to use WeBWorK off-campus. Read this to see the necessary steps.
- Here's a quick refresher of some main results in Calculus I.

*F Jan 11*. Start Chapter 5 Review: the definite and indefinite integral, Fundamental Theorem of Calculus.

*Quiz this week:* None

- The actual paper HW assignments start next week, but this shows off a bit of what my writing standards look like.
- Solutions for the demo assignment

*Week 2:*

*M Jan 14*. Chapter 5 Review: Finish FTC, u-substitution.*T Jan 15*. Finish Chapter 5 Review: area between two curves.*W Jan 16.*Start 6.1: Volume in 3D by integrating cross-section areas.*F Jan 18*. 6.1: Volumes of revolution using disks.- We finish this topic to start next week, after the school holiday on M Jan 21.

*Quiz this week:* Basic integration (Chapter 5 Review)

**Paper HW 1, due Friday Jan 18 in class**

- Check out the demo assignment from last week to see what a possible writeup could look like.
- I typically upload partial solutions to eLC one class day after the assignment is due (to allow for late handins as syllabus policy permits).

*Week 3*:

*No class on M Jan 21*.*T Jan 22*. Finish 6.1: Volumes of revolution using washers.*W Jan 23*. Start 6.2: Volumes of revolution using shells.*F Jan 25*. Finish 6.2: Contrast washers versus shells for revolution problems.

*Quiz this week*: A couple disk volume problems (Section 6.1)

**Paper HW 2, due Friday Jan 25 in class**

*Week 4:*

*M Jan 28*. Start 6.3 and 6.4: Arc length.*T Jan 29*. Finish 6.3 and 6.4: Surface areas of revolution.*W Jan 30*. Start 6.5: Work in physics, weight and fluid problems.*F Feb 1*. Finish 6.5: Spring work, average values.

*Quiz this week:* A shell volume problem (Section 6.2)

**Paper HW 3, due Friday Feb 1 in class**

**TEST 1 IS NEXT TUESDAY IN CLASS.**

- This test covers u-substitution, area between curves, and Sections 6.1 through 6.5.
- Expect 6 to 8 questions, somewhere between quiz problems and paper set problems in difficulty.
- One question may ask you to repeat definitions of the terminology we use in class!
- A problem may ask you to set up the form of an integral but not actually compute an anti-derivative or substitute numbers.

- Calculators are allowed as long as they cannot do derivatives, integrals, or graphs for you. The syllabus recommends the fairly cheap TI-30XS Multiview.
- You must show work, but you won't have to write sentences like in paper HW. If you are asked to give an explanation, keep it brief (at most one sentence).
- Topic list with study suggestions, and practice questions for Test 1
- We have an in-class review day on Monday 2/4 to answer questions you have or to go over some of the practice problems posted here.

**UNIT 2: Integration techniques**

*Week 5:*

*M Feb 4.*Review for Test 1 (see practice questions above).*T Feb 5*.**TEST 1***W Feb 6*. Start 7.2: Separable differential equations.*F Feb 8*. Finish 7.2: The exponential diff eq y' = ky, precalculus applications.

*No quiz this week*

*No paper HW this week*

*Week 6:*

*M Feb 11*. Start 8.1: Integration by parts.- The tabular method, aka "Tic-Tac-Toe method", is a different way of showing parts done multiple times in a row. I've included two handouts of varying degrees of detail!
- In-class exercises

*T Feb 12*. Finish 8.1: Reduction formulas and "cycling" parts.- A difficult demonstration of a trig reduction formula (for extra practice)

*W Feb 13*. Start 8.2: Trigonometry Integrals, powers of sine and cosine.*F Feb 15*. Finish 8.2: Powers of tangent and secant.- A summary, with examples, of our miscellaneous tactics for these integrals

*Quiz this week:* Section 7.2

**Paper HW 4, due Friday Feb 15 in class**

*Week 7:*

*M Feb 18*. Start 8.3: Integration by trigonometric substitution, sqrt(a^2 - x^2) form.*T Feb 19*. Continue 8.3: Trig sub with all three forms.*W Feb 20*. Finish 8.3: More practice with trig sub.*F Feb 22*. Start 8.4: Integration by partial fractions using linear factors.

*Quiz this week:* Section 8.2

**Paper HW 5, due Friday Feb 22 in class**

*Week 8:*

*M Feb 25*. Continue 8.4: repeated linear factors, irreducible quadratic factors.*T Feb 26*. Finish 8.4: Improper rational functions and long division.*W Feb 27*. Slight recap of integral techniques, harder substitution examples.- If you want a complicated but interesting substitution for trigonometric problems, here's some info about the Weierstrass half-angle tangent substitution.
- Review of integral strategies

*F Mar 1*. Section 8.7: Improper integration by using limits.

*Quiz this week:* Section 8.4, linear factors **(10 minutes)**

**Paper HW 6, due Friday Mar 1 in class**

**TEST 2 IS NEXT TUESDAY IN CLASS.**

- This test covers Section 7.2 (separable differential equations), Sections 8.1 through 8.4, and 8.7.
- Like the last test, expect 6 to 8 questions.
- You may use any integration technique in problems unless the directions tell you specifically to use one approach.
- You may abbreviate constants you don't want to simplify.

- Topic list, and collection of practice questions
- In-class review takes place on Monday, March 4.

**UNIT 3: Sequences, Series, and Taylor polynomials**

*Week 9:*

*M Mar 4*. Review for Test 2.*T Mar 5*.**TEST 2***W Mar 6*. Start 9.1: Sequence formulas, recursion, basic limits of rational functions or r^n.*F Mar 8*. Finish 9.1: L'Hopital's Rule for limits, power limits f(n)^g(n), Sandwich/Squeeze Theorem.- Here are some harder examples of proofs using the Sandwich Theorem. You will not have to repeat these proofs, but they provide some background on why n! >> r^n and why n^n >> n!.

*No quiz this week*

*No paper HW this week*

- I hope you have a good Spring Break!

*Week 10:*

*M Mar 18*. Start 9.2: Definition of a series, occasional telescoping series patterns, nth-term test for divergent series, start discussing geometric series.*T Mar 19*. Finish 9.2: More practice with geometric series.*W Mar 20*. 9.3: The Integral Test and p-series.*F Mar 22*. 9.4: The Limit Comparison and Comparison Tests.

*Quiz this week:* Limits from Section 9.1 **(10 minutes)**

**Paper HW 7, due Friday Mar 22 in class**

- Start this assignment early! It uses the material from the beginning of this week, and it's designed to see how comfortably you can use the new vocabulary from this material. You want to have time to ask questions about what the terminology really means.

*Week 11:*

*M Mar 25*. 9.5: Ratio and Root Tests- There's a document about picking tests provided below the Paper HW link.

*T Mar 26*. 9.6: Alternating series, absolute and conditional convergence.- In-class exercises
- Optional: If you want to see some of the reasons why conditional convergence is generally inferior to absolute convergence, there are strange consequences that occur when you try to rearrange terms in a series! Here's some reference on the subject, with a handy video link for demonstration.

*W Mar 27*. Start 9.7: Power series, domains of convergence*F Mar 29*. Finish 9.7: More practice with power series, interval and radius of convergence

*Quiz this week:* Showing the work of Limit Comparison Test in Section 9.4 **(10 minutes)**

**Paper HW 8 (Miscellaneous Series), due MONDAY Apr 1 in class**

- This has a different set of directions and grading standards. Read its cover sheet for details.
- Reference on how to pick an appropriate series test

*Week 12:*

*M Apr 1*. 9.8: The definition of Taylor polynomials and series, computing derivatives at the center.*T Apr 2*. Start 9.9: Reusing famous Maclaurin series to generate polynomials more easily.*W Apr 3*. Continue 9.9: Remainder Estimation Theorem (i.e. Taylor's Theorem for the error).- For more help using Remainder Estimation, here's some extra coverage.
- In-class exercises

*F Apr 5*. Finish 9.9: More practice with Remainder Estimation.

*Quiz this week:* Power series domain of convergence **(12 minutes)**

**Paper 9, due Friday Apr 5 in class**

**TEST 3 IS NEXT TUESDAY IN CLASS.**

- This test covers Section 9.1 (limits of sequences) to Section 9.9 (reusing famous series, Taylor error).
- You are not required to memorize the Maclaurin series for e^x, sin(x), cos(x).
- You are not required to memorize the Remainder Estimation Theorem's formula, but you should know how to perform its steps.

- Like the last test, expect 6 to 8 questions.
- At least one question on this test is
**multiple-choice**, much like the WW. - You should know the wording of the series tests discussed in class. You may have to restate one of the tests on the exam!

- At least one question on this test is
- Topic list
- Practice questions
- In-class review takes place on Monday, April 8.

*Week 13:*

*M Apr 8*. Review for Test 3.*T Apr 9*.**TEST 3.***W Apr 10*. 11.1: Basic formulas for 3D space.*F Apr 12*. Start 11.2: Basic vector algebra in 2D or 3D, picturing vector addition, the unit coordinates i,j,k.

*No quiz this week*

*No paper HW this week*

**FINAL UNIT: Brief vector introduction in 2D and 3D**

*Week 14:*

*M Apr 15*. Finish 11.2: (Unit) direction vectors dir(v), using reference angles for 2D directions.*T Apr 16*. Start 11.3: Main definition of dot product, the "dot-angle" formula.*W Apr 17*. Continue 11.3: Force applied at an angle, force and work in 2D or 3D using dot products*F Apr 19*. Finish 11.3: Projection of vectors onto lines

*Quiz this week:* Section 11.2

**Paper 10, due Friday Apr 19 in class**

*Week 15 and last two days of class:*

*M Apr 22*. Start 11.4: Cross product calculation in 3D.*T Apr 23*. Continue 11.4: Practice with computing u x v, uses for normal vectors and triangle area.*W Apr 24*. Finish 11.4: Using u x v for torque and triple product (box volume).*F Apr 26*.**Vector practice test**- Topic list for vector material
- We'll work on this together for most of class. Here are the solutions.

*M Apr 29 and T Apr 30*. Final Exam Review days- We'll probably pull up our old exams and look over how to properly read and set up these questions!
- Please come to class with questions, or
**email me ahead of time with requests**(which I will try my best to accommodate).

*Quiz this week:* The basics of Sections 11.3 AND 11.4 **(10 minutes)**

- This includes cross-product computation from Monday's class!

**Paper 11, due Friday Apr 26 in class**

**THE FINAL EXAM IS COMING SOON!**

- The exam takes place in our main classroom (Boyd 203).
- Section 25032: MONDAY MAY 6 from 8am to 11am
- Section 41458: WEDNESDAY MAY 8 from 8am to 11am

- Expect around 13-15 questions, for 3 hours of time.
- There should be about 4 questions based on each of the prior three tests, as well as 2 vector questions.
- You will have a short answer question at the very beginning to check your understanding of the terminology used in class! (See the beginning of Test 3 #1(a), for example, for an idea of what that might be like.)

- There are no specific review sheets or problem sets I will create for the final exam.
- Look at the vector review materials from Friday of this week though.
*Practice problems are important, but you mostly want to practice your problem-reading skills!*Go back to your old paper HW sets and exams, and ask yourself "What cues in the problem suggest which approach to use? What was this problem trying to emphasize, compared to other problems in my homework?"

**Policies for the final exam:**- You will have to leave your bookbags at the side of the room once you start your test.
- Turn any phones or smart watches off, and leave them inside your bags.
- Restroom breaks are allowed, but I will only allow one person to leave at a time, barring any extreme circumstances.

Last updated: 4/26/2019