**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.

**UNIT 1: Integral Applications**

*Week 1:*

*Mon Aug 13.*Introduction to the course (see the syllabus at the top of this page), and some slight 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.

*Tue Aug 14*. Start Chapter 5 Review: the definite and indefinite integral, Fundamental Theorem of Calculus.*Wed Aug 15*. Chapter 5 Review: u-substitution.*Fri Aug 17*. Finish Chapter 5 Review: area between two curves.- In-class practice
- The first WW set (review of Chapter 5 on integration) is due on Monday, but it's pretty long; make sure you start it this week.
- (Most WW due dates will not be advertised on this site, but I'll point out the first due date.)

*Quiz this week:* None

*There's no paper HW this week: it starts next week**.*

- Here's a demo assignment, together with solutions, to show what my standards for paper HW answers is like.

*Week 2:*

*Mon Aug 20*. Start 6.1: 3D volumes by integrating cross-sections*Tue Aug 21*. 6.1: Volumes of revolution using disks*Wed Aug 22*. Finish 6.1: Volumes of revolution using washers- Fri Aug 24. Start 6.2: Volumes of revolution using shells

*Quiz this week*: Chapter 5 Review (either u-substitution or area between curves)

**Paper HW 1, due Friday August 24**

- You may want to look at last week's demo assignment to see the kind of explanations I include.
- Usually, (partial) solutions are uploaded to eLC one class day after the due date.

*Week 3:*

*Mon Aug 27*. Finish Section 6.2: Comparing washers and shells.*Tue Aug 28*. Section 6.3: arc length.*Wed Aug 29*. Section 6.4: surface area of solids of revolution.*Fri Aug 31*. Start Section 6.5: work in 1 dimension (weight, emptying a tank).

*Quiz this week:* Section 6.1

- There's no class on Monday September 3 (Labor Day), but there is a quiz on the day after that when we return!

**Paper HW 2, due Friday August 31**

*Week 4:*

*Tue Sep 4*. Finish Section 6.5. Spring force and work, average values of curves.*Wed Sep 5*. Start Section 7.2. Separable differential equations.*Fri Sep 7*. Finish Section 7.2. Exponential word problems based on the diff eq dA/dt = kA.

*Quiz this week:* Section 6.2.

**Paper HW 3, due Friday September 7**

*TEST 1 IS NEXT TUESDAY, SEPTEMBER 11, IN CLASS*.

- This test covers Chapter 5 Review, Sections 6.1, 6.2, 6.3, 6.4, 6.5, and 7.2.
- Expect 6 to 8 questions, somewhere between quiz problems and paper set problems in difficulty.
- You may have a problem which asks you to set up an integral but not actually finish getting an antiderivative.
- You may get a question testing if you know definitions of the terminology used in class!

- Calculators may be used as long as they cannot do derivatives, integrals, or graphs. (A TI-30XS Multiview is definitely a safe choice.)
- You have to show work, but you usually don't have to write detailed explanations like in paper HW.
- If a question asks for explanation, you can keep it brief (i.e. one sentence).

- Here's a topic list for Test 1.
- Here are some practice problems for Test 1.
- We will have a review day in class on Monday September 10, mostly to go over practice problems or any other questions you may have.

Week 5:

*Mon Sep 10*. In-class Test 1 Review. (See the review handouts from the previous week!)*Tue Sep 11*.**TEST 1***Wed Sep 12*. Start Section 8.1: Integration by Parts.- In-class practice
- To use parts multiple times, there's a "tabular method" for writing the work that may be useful.
- For another way of presenting the tabular method, here's a "TicTacToe" variant.

*Fri Sep 14*. Finish Section 8.1: Reduction Formulas, using parts multiple times.- Here's a difficult example of a reduction formula for sine powers, if you want to see a few different skills of integration by parts pulled together into one place.

*No quiz for this week*

*No paper HW for this week*

**UNIT 2: Integral Techniques**

*Week 6:*

*Mon Sep 17*. Start Section 8.2: Integrating powers of sine and cosine.*Tue Sep 18*. Finish Section 8.2: Integrating powers of tangent and secant.- Wed Sep 19. Start Section 8.3: Trigonometric substitution, form 1 with sqrt(a^2 - x^2).
*Fri Sep 21*. Continue Section 8.3: Other forms of trigonometric substitution.

*Quiz this week:* Section 8.1.

**Paper HW 4, due Friday September 21**

*Week 7:*

*Mon Sep 24*. Finish Section 8.3: more trig sub practice, combining trig sub with other u-subs.*Tue Sep 25*. Start Section 8.4: partial fractions, linear factors.*Wed Sep 26*. Continue Section 8.4: repeated linear factors.- Fri Sep 28. Finish Section 8.4: irreducible quadratic factors, and introduction to long division.
- You'll need to do some long division in WeBWorK, so here's some more background that may help.

Quiz this week: Section 8.3 **(12 minutes)**

**Paper HW 5, due Friday September 28**

*Week 8:*

*Mon Oct 1*. Extra_Integrals WW set: some more long division practice, brief recap of integral strategies, other ways to use u-substitutions.- Here's a handout that summarizes the main ideas of our techniques, with some samples.
- For some interesting side reading, there's a famous technique called Weierstrass's substitution to turn any trigonometry integral into a partial-fractions problem.

*Tue Oct 2*. Section 8.6: Estimating definite integrals with Trapezoid or Simpson's Rules.- Here's a Mathematica program which you can use to experiment with some estimates. (Scroll to the bottom once you load it to find interactive controls for it.) You can load this on campus machines that have Mathematica installed.

*Wed Oct 3*. Start Section 8.7: Improper integrals.*Fri Oct 5*. Finish Section 8.7: Improper integrals involving multiple pieces.

*Quiz this week:* Section 8.4 **(12 minutes)**

**Paper HW 6, due Friday October 5**

*TEST 2 IS NEXT TUESDAY, OCTOBER 9, IN CLASS*.

- This test covers Sections 8.1, 8.2, 8.3, 8.4, 8.7, and the Extra_Integrals WeBWorK set.
- Section 8.6 (Trapezoid and Simpson's Rules) are not on the test.

- Expect 6 to 8 questions.
- Some problems will help break down long problems into smaller steps. Please read carefully.
- If you get stuck on an early part, you might be able to still get credit on later parts if you reason as consistently as you can from your earlier mistake.

- Abbreviations of numbers are legal, as long as they are clearly marked, unless the problem indicates otherwise.
- Calculators may be used as long as they cannot do derivatives, integrals, or graphs. (A TI-30XS Multiview is definitely a safe choice.)
- You have to show work, but you usually don't have to write detailed explanations like in paper HW.
- If a question asks for explanation, you can keep it brief (i.e. one sentence).

- Topic list for the test
- Practice questions for the test
- In-class review day is Monday October 8.

*Week 9:*

*Mon Oct 8*: Review for Test 2*Tue Oct 9*:**TEST 2***Wed Oct 10*: Start Section 9.1. Writing infinite sequences (explicitly or recursively), basic limits of sequences, dominant-terms shortcut.*Fri Oct 12*: Finish Section 9.1. More about dominant terms (i.e. ln(n) << n^p << b^n), limits of f(n)^{g(n)} form, a bit about the Sandwich Theorem for oscillating sequences.- Here's a handout which proves some harder limits with the Sandwich Theorem. (You won't need to repeat these proofs in class or on a test!)

*No quiz this week*

No paper HW this week

**UNIT 3: Infinite Series and Taylor Polynomials**

*Week 10:*

*Mon Oct 15*: Start Section 9.2. Infinite series, telescoping series, nth-term test, geometric series sums.*Tue Oct 16*: Finish Section 9.2. More practice with geometric series, including writing a function as a series.*Wed Oct 17*: Section 9.3. Using integrals to determine series convergence (Integral Test), p-series.*Fri Oct 19*: Section 9.4. Limit Comparison and Comparison Tests for series.

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

**Paper HW 7, due Friday October 19**

- This homework mostly involves the first day of Section 9.2. It's not about a lot of algebra; it makes you grapple with appropriate terminology and ideas related to infinite series!

*Week 11:*

*Mon Oct 22*: Section 9.5. Ratio and Root Tests for series.*Tue Oct 23*: Section 9.6. Alternating Series, contrasting absolute convergence versus conditional convergence.- We can't do much in this class to explain why absolute convergence is more desirable than conditional convergence. It turns out conditionally convergent series have some odd properties: look up the "Riemann Rearrangement Theorem."
- In-class practice

*Wed Oct 24*: Start Section 9.7. Power series (combining concepts from 9.4 through 9.6).- No class on Fri Oct 26 due to Fall Break.

*Quiz this week:* Section 9.4

- In this quiz, you have to show the work of the Limit Comparison Test, meaning you perform the algebra that verifies lim(a_n / b_n) is a positive finite number. [Note that this work was done in class, but you don't have to show it in order to get WW credit!]

**Misc Series Paper HW, due MONDAY October 29** (due to Fall Break)

- This assignment has its own custom direction page. It does not use the same point totals. Please look that over carefully to see what is expected of you.
- This assignment cannot be dropped from your grade, unlike other paper HW sets.

*Week 12:*

*Mon Oct 29*: Finish Section 9.7. Center and radius of convergence of power series.*Tue Oct 30*: Section 9.8. Computing Taylor and Maclaurin polynomials to approximate functions.- In-class practice (this also goes along well with tomorrow's handout!)

*Wed Oct 31*: Start Section 9.9. Reusing famous Maclaurin series to save time with other series.- Here are some famous series to use with your HW. This document will be passed out in class.
- (You may want to memorize the four main series in this document.)

*Fri Nov 2*: Finish Section 9.9. The Taylor Error / Remainder for approximations with P_n(x).- Here's a step-by-step breakdown of how Taylor error works. (I don't like the book's notes on it.)

*Quiz this week*: Section 9.7, where you determine the domain ends of a power series and check convergence of each endpoint

- This will require a good understanding of Section 9.6 involving absolute versus conditional convergence!

**Paper HW 8, due Friday November 2**

*TEST 3 IS NEXT TUESDAY, NOVEMBER 6, IN CLASS*.

- This test covers Sections 9.1 through 9.9.
- You should memorize the rules for each series test, the root limit n^{p/n} -> 1, and the basic rules of dominant terms. (You may use these without reproving those rules.)
- You DO NOT have to memorize our famous Taylor series or the Remainder Estimation Theorem; they will be provided as necessary.

- Expect 6 to 8 questions.
- Some problems will help break down long problems into smaller steps. Please read carefully.
- If you get stuck on an early part, you might be able to still get credit on later parts if you reason as consistently as you can from your earlier mistake.
**At least one question will ask you to judge convergence or divergence of a series without requiring you to show work**. (Basically, it's multiple-choice.) You may also have to indicate which test you would use, even if you don't show the work of the test. This is meant to see if you've been paying attention to which parts of a series are really important!

- Abbreviations of numbers are legal, as long as they are clearly marked, unless the problem indicates otherwise.
- Calculators may be used as long as they cannot do derivatives, integrals, or graphs. (A TI-30XS Multiview is definitely a safe choice.)
- You have to show work, but you usually don't have to write detailed explanations like in paper HW.
- If a question asks for explanation, you can keep it brief (i.e. one sentence).

- Topic list for the test
- Practice questions for the test

*Week 13:*

*Mon Nov 5*: Review for Test 3*Tue Nov 6*:**TEST 3***Wed Nov 7*: Section 11.1. Basic concepts of 3D space, introduction to vector components.*Fri Nov 9*: Start Section 11.2. Vector addition and scaling, the coordinate vectors ijk.

*No quiz this week*

*No paper HW this week*

*Week 14:*

*Mon Nov 12*: Finish Section 11.2. Direction vectors, combining lengths and directions to make multi-step paths.*Tue Nov 13*: Start Section 11.3. Introduce dot products and the "dot-angle" formula for the angle between two vectors.- Wed Nov 14: Continue Section 11.3. Applications of dot-angle to forces applied at an angle, work in more than one dimension.
*Fri Nov 16*: Finish Section 11.3. Last treatment of "effective force" (parallel component), vector projections.

*No quiz this week (the final quiz is on the week after break)*

*No paper HW this week (the final paper HW is on the week after break)*

*Week 15 and the last two days of class:*

*Mon Nov 26*: Start Section 11.4. Computing cross product u x v.*Tue Nov 27*: Continue Section 11.4. The applications of u x v for triangles.*Wed Nov 28*: Finish Section 11.4. Miscellaneous last uses of u x v: torque, triple product.*Fri Nov 30*: Vector practice test to go over Unit 4 in class- Topic list for vector material
- Here's the practice test, with solutions. We'll probably only discuss four out of the five main problems in class.

*Mon Dec 3 and Tue Dec 4*: Review for the final exam*We meet in our Monday classroom and time on both days!***You can email me review questions in advance, especially during the weekend before the last days of classes. (We'll see what we can get through in class.)**

*(Final) Quiz this week:* Sections 11.2 and 11.3 (10 minutes)

**(Final) Paper HW 9, due Friday November 30**

**FINAL EXAM INFORMATION**

Logistics:

- The 15682 section (8am MWF) takes their exam on Wednesday December 12, in Boyd 322, from 8am to 11am. The 15683 section (10:10am MWF) takes their exam on Friday December 7, in Boyd 302, from 8am to 11am.
- Expect the exam to be about twice the length of an in-class test.
- Only a couple questions will cover vector material in Unit 4. The rest will be similar to previous exams.

- For this exam, you must leave your bookbag or handbag, with any smart watches or other Internet-enabled devices, on the side of the room until your test is done.
- If you need to take a restroom break during the exam, I will let out one person at a time, and you will have to leave any Internet-enabled devices in the classroom.

Here's a collection of practice problems from the material of our in-class tests.

- We will probably look over all its problems for review, but we won't be able to solve all of them in class.

Last updated: 11/30/2018