**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.

Clicking on each day leads you to a document with basic announcements, the daily exercise, solutions, and room for making a study guide.

**UNIT 1: Applications of Integrals**

*Week 1:*

*Tue Jan 7.*Introduction to the course (see the syllabus in the right margin of this page), and some review of derivatives and indefinite integrals.- 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.
- Quick refresher of some Calculus I concepts

*Wed Jan 8*. Sections 1.1 through 1.3: Riemann sums for area, Fundamental Theorem.*Fri Jan 10*. Section 1.4, start 1.5: Net change, u-substitutions.- We'll have more examples of u-substitutions next Monday, but you may want to read ahead in Section 1.5 to get your WW done earlier!

*No quiz this week: it starts next week.*

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

- Here's a demonstration assignment, to show what my standards look like.
- Here are solutions to the demonstration assignment. (Notice how I briefly indicate what I'm planning to do before I do it, so that I can provide some context without being overly wordy.)

*Week 2**:*

*Mon Jan 13*. Finish 1.5: substitution with definite integrals.*Tue Jan 14*. 2.1: area between two curves.- Even if you've seen this topic before, you might not have seen the technique of using functions of y instead of x. (I call it "horizontal slicing.") You may want to look for further examples in the textbook, since we will use this technique quite a bit soon!

*Wed Jan 15*. Start 2.2: volumes and cross-sections, revolution by disks.*Fri Jan 17*. Finish 2.2: revolution by washers.

*Quiz this week:* Integration question based on Chapter 1 Review (indefinite and/or indefinite)

- As the syllabus mentions, quizzes are a single question. Most quizzes are 8 minutes, unless otherwise announced.
- We start quiz days with a short review problem, which is a good chance to ask any last questions you have.

**Paper HW 1, due on Friday 1/17/2020** (click on this text to download the assignment)

- Take a look at the demo HW from last week to see examples of my presentation expectations.
- Some solutions to paper HW are put on eLC (in the Content area) on the Monday after assignments are due.

*Week 3:*

*No class on Mon Jan 20 due to Martin Luther King, Jr., Day**Tue Jan 21*: Start 2.3: revolution by shells.*Wed Jan 22*: Finish 2.3: contrasting the methods of washers and shells for volumes of revolution.*Fri Jan 24*: Start 2.4: arc length of curves, review of perfect squares- You may want to read ahead in the book to go over surface area, if you want to finish WW 2.4 over the weekend!

*Quiz this week:* Disk question based on the early problems in Section 2.2

**Paper HW 2, due on Friday 1/24/2020**

- Notice how
**Problem #1 does not want you to finish your integral**. Instead, it wants you to provide drawings! Read the problem to see what detail I expect in those drawings.

*Week 4:*

*Mon Jan 27*. Finish 2.4: surface area of solids of revolution.*Tue Jan 28*. Start 2.5: determining spring force and work via integrals.- We will skip most of 2.5 in the text, except for the sub-sections about Force And Work as well as Pumping A Tank.

*Wed Jan 29*. Finish 2.5: work (in physics) applied to weight, density, and tank-pumping*Fri Jan 31*. 4.3: Separable differential equations.

*Quiz this week (10 minutes)*: Shells (2.3)

**Paper HW 3, due on Friday 1/31/2020**

TEST 1 IS NEXT TUESDAY (FEB 4) IN CLASS.

- You have all 75 minutes of class time for your test if you need them.
- This test can cover topics ranging from the Fundamental Theorem up to separable differential equations. The WW assignment list goes from Chapter 1 Review up to 4.3. (We have skipped Ch 3 for now and will revisit it later.)
- You may want to re-skim the Orientation WW set, now that you've had more experience typing answers!

- Expect 6-8 questions on it similar to past assignments (generally easier than paper HW). You do not have to write long sentences in answers, but you may be asked for a bit of explanation.
- Non-graphing calculators are allowed as the syllabus describes. Keep in mind that you may leave unsimplified answers similar to WW standards.
- Topic list for the exam
- Practice questions for the exam
- We will go over some of these on Monday, but also bring or email your own questions!
- The solutions to star-marked problems will go on eLC on Monday.

**UNIT 2: Advanced Integration Techniques**

*Week 5:*

*Mon Feb 3*. Test 1 Review- Some review solutions are available in the eLC content area.

*Tue Feb 4*.**TEST 1***Wed Feb 5*. Start 3.1: Integration by parts- For other styles of writing parts, try a tabular method or a "tic-tac-toe" approach.

*Fri Feb 7*. Finish 3.1: Repeated use of integration by parts

*No quiz or paper set on test weeks*

*Week 6:*

*Mon Feb 10*. Start 3.2: Powers of sine and cosine.*Tue Feb 11*. Finish 3.2: Powers of tangent and secant (and their co-versions).- Several backup strategies for tangent and secant problems
- Your WW has a few questions that rely on the techniques linked in the handout above!

*Wed Feb 12*. Start 3.3: Trigonometric substitution with sqrt(a^2 - x^2)*Fri Feb 14*. Continue 3.3: Trig subs with sqrt(a^2 + x^2) and sqrt(x^2 - a^2)- Summary of trigonometric substitution procedures, and some technicalities
- We will finish Section 3.3 on Monday with more difficult examples.

*Quiz this week:* Section 3.1 (parts)

**Paper HW 4, due on Friday 2/14/2020**

*Week 7:*

*Mon Feb 17*. Finish 3.3: Some trig sub practice, combining u-substitution and trig sub together.*Tue Feb 18*. Start 3.4: partial fractions, simple linear factor case only.*Wed Feb 19*. Continue 3.4: partial fractions, repeated linear factors.*Fri Feb 21*. Continue 3.4: partial fractions, irreducible quadratic factors, long division of polynomials.- For more details about how long division works, here's a Wikipedia link from your textbook, and here's another link I found with a good demo.
- Here's another worked-out example of an integral using long division.
- We will do a bit more practice with this on Monday, mostly combining u-subs with partial fractions, but you can finish the WW over this weekend if you read the book.

*Quiz this week ( 12 minutes):* Section 3.3 (trig sub)

**Paper HW 5, due on Friday 2/21/2020**

*Week 8:*

*Mon Feb 24*. Finish 3.4: Mixing substitutions and partial fractions.*Tue Feb 25*. Advanced uses of u-substitution.- This material has a short WW set called Advanced_Subs, due on this Friday!

*Wed Feb 26*. Start 3.7: Improper integrals (with one asymptote).*Fri Feb 28*. Finish 3.7: Improper integrals (with multiple asymptotes).

*Quiz this week** ( 12 minutes)*: Section 3.4 (partial fraction decomposition)

- You will only have to produce a decomposition (i.e. give the right form and find constants). You will not have to compute any integrals on this quiz.

**Paper HW 6, due on Friday 2/28/2020**

TEST 2 IS NEXT TUESDAY (MAR 3) IN CLASS.

- You have all 75 minutes of class time for your test if you need them.
- This test covers Chapter 3: Sections 3.1, 3.2, 3.3, 3.4, 3.7, and the Advanced_Sub assignment. We skipped 3.5 and 3.6.
- Expect 6 or 7 questions on it similar to past assignments (generally easier than paper HW). You do not have to write long sentences in answers, but you may be asked for a bit of explanation.
- Test 2 usually has longer calculations than Test 1, so expect fewer total problems.

- Non-graphing calculators are allowed as the syllabus describes. Keep in mind that you may leave unsimplified answers similar to WW standards.
- Much like Quiz 5, I will allow you to introduce abbreviations for numbers you don't feel like recopying over and over.

- Topic list for the exam
- Practice questions for the exam
- Next Monday is our in-class review day.

**UNIT 3: Series and Taylor Polynomials**

*Week 9:*

*Mon Mar 2*. Test 2 review.- Some practice question solutions are now stored on eLC.

*Tue Mar 3*.**TEST 2***Wed Mar 4*. Start 5.1: Defining sequences, limits of basic sequences involving n^p or r^n*Fri Mar 6*. Finish 5.1: Limits involving exponentials and logarithms, Squeeze Theorem.- More advanced uses of Squeeze to prove results about n! and n^n
- We will skip the Monotone Convergence Theorem in the text.

*No quiz or paper set on test weeks*

*WE HAD A TWO-WEEK SUSPENSION AFTER SPRING BREAK DUE TO COVID-19.*

*SEE YOUR SYLLABUS, YOUR EMAIL, AND eLC FOR MORE DETAILS.*

UGA resources pertaining to the coronavirus

DAE at a Distance: tips for working with online classes

Test recording, to review the limit techniques from the week before break

**Class sessions will be held via Collaborate Ultra in eLC. Past recordings are available.**

**The same goes for office hours: look for an eLC announcement with the link.**

*Week 10:*

*Mon Mar 30*. Start 5.2: The concept of a series, telescoping and geometric series.- For sequence review, look at the "test recording" link above this week in the calendar!

*Tue Mar 31*. Finish 5.2 and start 5.3: Geometric practice, Divergence Test.*Wed Apr 1*. Finish 5.3: Integral Test and p-series.*Fri Apr 3*. 5.4: Limit Comparison and Comparison Tests.

*Quiz this week ( 10 minutes)*: Section 5.1 (limits of sequences)

**Paper HW 7, due on Friday 4/3/2020**

*Week 11:*

*Mon Apr 6*. 5.6: Root and Ratio Tests.*Tue Apr 7*. 5.5: Alternating series, absolute convergence, and conditional convergence.- There are extra topics in the text, like estimating an alternating series sum and rearrangements of series, which we will not cover. The rearrangement results are particularly mind-blowing though if you want to discuss them outside of class!

*Wed Apr 8*. Start 6.1: Finding domain of a power series.*Fri Apr 10*. End 6.1: Radius of convergence, more examples of power series.

*Quiz this week ( 10 minutes):* Section 5.4 (Limit Comparison Test)

- We'll have a warm-up problem to start class again (unlike last week); the warm-up problem is in the class document for that day!

**Paper HW 8, due on Friday 4/10/2020**

- This one has 4 questions for 60 points, and it cannot be dropped from your grade. More precise details are found in the cover page of this HW.
- You should have practiced problems from Sections 5.2, 5.3, 5.4, 5.6 for this problem set!

*Week 12:*

*Mon Apr 13*. 6.2: Manipulating the geometric series to obtain other sums.*Tue Apr 14*. Start 6.3: Taylor series definition and basic introduction.- Section 6.3 is the last section of the book we will cover, finishing it by next Tuesday.

*Wed Apr 15*. Continue 6.3: Several famous Taylor series, and manipulations of them to obtain other polynomials.*Fri Apr 17*. Continue 6.3: Introduction to Taylor remainder / error.

*Quiz this week ( 12 minutes)*: Section 6.1 (power series domains of convergence)

- This is our last quiz! There is no quiz next week.

**Paper HW 9, due on Friday 4/17/2020**

- This is the last paper HW !

TEST 3 (TAKE-HOME) IS NEXT **FRIDAY** (APRIL 24). I'LL EMAIL IT TO YOU.

- Since we're doing online class,
**this is open-book and open-notes**.- You will have to sign an honor code on its cover page.

- This test covers Sections 5.1 through 5.6 and 6.1 through 6.3.
- You will have effectively 24 hours to complete the exam, due by 5pm (Eastern time) on April 24.
- I'll design the test to probably take a bit longer than previous midterms, so expect about 75-95 minutes of total time. Expect somewhere from 6 to 8 questions on it.

- Topic list for the exam
- Practice questions for the exam (with a bit of space to fill in answers)
- In-class review day is next Wednesday.

*Week 13 and final two days of class:*

*Mon Apr 20*. Continue 6.3: More practice with Remainder Estimation Theorem.**Review materials are now available for Test 3, posted at end of last week.**

*Tue Apr 21*. Finish 6.3: Miscellaneous uses of Taylor polynomials and errors to analyze convergence, limits as x -> center, and approximations of definite integrals.*Wed Apr 22*. Test 3 Review.- Bring your own questions, especially more open-ended questions like "Why do we use this test instead of another?" or "How do I tell a_n and [series] a_n apart?"
- Solutions to some of the practice problems will go on eLC on Wednesday.

*Fri Apr 24*.**TEST 3: Class does not meet.***Mon Apr 27 and Tue Apr 28 (**on a Monday's schedule!)*. Final exam review days.- We'll go over the old midterms.
**Fill out an eLC survey (more details in your email) about when you can take your final.**

FINAL EXAM INFORMATION

- The test is effectively a combination of the skills of the previous three tests.
- There will be a question at the start testing your ability to understand definitions and some basic concepts, much like what Midterm 3 had.
- Expect around 12-14 questions, worth 200 points in total, so it's like double the length of an in-class midterm.

- You'll get a time limit of 3hr20min for the test: that should be 3 hours for the test and up to 20 min to upload your results to the Assignments area of eLC.
**You should get your exam from eLC, though I might also email it to you.**(Email isn't really easily possible if many people need to start their exam at different times.)

- Like with Midterm 3, you'll have to sign an honesty agreement, whether it's on the cover sheet or on your own scratch paper.
- This is still open-book and open-notes. You may use any of the class material in eLC or on this site, as well as your own notebooks.

**Office hours for finals:**- Tuesday Apr 28: 3:15-4:45pm
- Wednesday Apr 29 and Thursday Apr 30: 8-10am and 2-4:30pm
- Or email me to suggest a time. If you need a one-on-one session, let me know.

*SUGGESTED TOOLS FOR CONVENIENT UPLOADS:*- OfficeLens app for mobile devices can help your picture focus on just the page boundaries, clean it up, and send a PDF to OneDrive.
- ilovepdf.com has free utilities to combine several PDFs in one document, among other features.

Last updated: 4/27/2020