**Rough 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.

This schedule will not show the topics for each day. Instead, it will outline what we plan to cover over the whole week. If you want more detail, email me or talk to me outside of class.

**UNIT 1: Limits**

*Week 0:*

- Introduction to the course (see the syllabus at the top of this page)
- Make sure to 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 an algebra pretest. (In class, I only handed out the first two pages.) Here's an algebra review if you want more help.
- I especially recommend practicing
**fraction manipulation!**If you want help with common denominators, look at these documents.

- I especially recommend practicing

- Section 2.1: average versus instantaneous slopes

*There's no paper HW or quiz for this week. (We only meet on Friday, after all!)*

*Week 1:*

- Section 2.2: pictures of limits, computing basic limits, some 0/0 forms (rationalization)
- We will mostly skip over the Sandwich Theorem (aka Squeeze Theorem) in the textbook.
- Groupwork for Tuesday's class
- If you want, you can look through the first page (with problems) before class. But don't read all the answers until after class.

- Section 2.4: one-sided limits, sin(theta)/theta when theta is close to 0
- Start Section 2.5: picturing continuity

*No quiz this week: the first quiz will be Tuesday January 16.*

**Demo paper HW,** **with solutions**

- This is meant to show the level of explanation and presentation we want with paper assignments.
- The first graded paper HW will come out at the end of this week, to be due the following Friday.

*Week 2:*

- NO CLASS MONDAY (Martin Luther King Jr day)
- Finish Section 2.5: domain and continuity, Intermediate Value Theorem
- Section 2.6: horizontal and vertical asymptotes, drawing sign diagrams for functions
- There is also a second WeBWorK set for this lesson called HWT_Asymptotes!
- Wednesday Jan 17 was a snow day.
- Here are some replacement class notes. (I recommend trying out an online graphing calculator with them.)
- Groupwork for Wed Jan 17

- Groupwork for Fri Jan 19

*Quiz this week:* Section 2.2

**Paper HW 1, due Friday January 19**

- You may want to look at the demo from last week to get an idea of the expected presentation.
- Some solutions will be uploaded to eLC on Monday January 22. (It will always be one class day after the due date.)

**TEST 1 is on next Tuesday, January 23.**

- It covers Sections 2.1 through 2.6 (from average / instantaneous slopes to asymptotes), excluding 2.3.
- Expect somewhere from 6 to 8 questions, with a 75-minute time limit.
- You do not have to explain your answers with full sentences unless the question specifically asks for it.
- Per syllabus policy, the only allowed calculator is TI-30XS Multiview calculator. (You do not need a calculator though.)

- Topic list for the exam, with some review questions
- Practice questions for the exam
- We will go over many of these in class next Monday.
- Try these out ahead of time, so you can review these with your other classmates!

Week 3:

- Monday: in-class review for Test 1
- Look just above for review documents to help with Test 1, as well as clarifying expectations.
*Make sure you understand the grading comments on Paper HW 1!*You do not want to make the same concept errors on the test.

**Tuesday: TEST 1**- Sections 3.1 and 3.2: the definition of derivative (tangent lines), notations for the derivative, when a function is not differentiable

*No quiz this week*

*No paper HW this week*

**UNIT 2: Computing derivatives**

*Week 4:*

- Section 3.3: exponential and power rules, repeated derivatives, Product and Quotient rules
- Section 3.4: derivatives as rates of change, applications to motion (velocity and acceleration)
- Section 3.5: trigonometric derivatives

*Quiz this week:* Sections 3.1 and/or 3.2 (derivative by definition)

- In this quiz, you may
**not**use any derivative rules we cover in this week of class. You have to use the definition of derivative.

**Paper HW 2, due Friday 2/2 in class**

*Week 5:*

- Section 3.6: Chain Rule
- Section 3.7: Implicit Differentiation
- Start Section 3.8: Inverse derivatives, Logarithms, Log Diff

*Quiz this week:* Sections 3.3 and/or 3.4 (Power Rule, Product and Quotient Rules, velocity and acceleration)

**Paper HW 3, due Friday 2/9 in class**

*Week 6:*

- Finish Section 3.8: derivatives of log_b(x) and of f(x)^g(x)
- Section 3.9: inverse trig derivatives
- If you want more review of inverse trig functions, look at this link.

- Three days on Section 3.10: related rates

*Quiz this week:* Section 3.6 (Chain Rule)

**Paper HW 4, due Friday 2/16 in class**

**TEST 2 is on next Tuesday, February 20.**

- It covers Sections 3.1 through 3.10.
- Expect somewhere from 6 to 8 questions, with a 75-minute time limit.
- Most questions will not ask for proofs will full sentences.
**Proofs you may be expected to be able to do on the test:**- Compute a derivative just by definition (like in Sections 3.1 and 3.2).
- Proof of the sum or difference law of derivatives (i.e. (f+g)' = f' + g')
- Proof of the derivatives for (sin x)' and (cos x)' if we provide you the right trig identities
- Rewrite an inverse function in an implicit style to discover derivatives like (ln x)', (arcsin x)', or similar

- Per syllabus policy, the only allowed calculator is TI-30XS Multiview calculator. (You do not need a calculator though.)
- Topic list for the test
- Practice questions
- We will go over practice questions in class next Monday. Try these out ahead of time, so you can review these with your other classmates!

*Week 7:*

- Review for Test 2
**TEST 2**- Section 3.11: Linearization and differentials
- Start Section 4.1: Extreme Values, Critical Values

*No quiz this week*

*No paper HW this week*

**UNIT 3: Applications of the derivative**

*Week 8:*

- Finish Section 4.1: absolute max and min, critical values, EVT
- Group-work for Monday February 26
- Our 8am class was guest-taught by Amy Grady from Clemson! Here is her set of group-work problems.

- Section 4.2: Mean Value Theorem, beginning antiderivatives (i.e. getting f(x) back from f'(x))
- For more background on how MVT / Rolle's Theorem can be used to study how many roots a function has, you may like to consider this site or this video demonstration. (We won't do much with this topic in class, but it can be a good way to test your understanding of these theorems.)
- Group-work for Wednesday February 28

- Section 4.3: Using the sign of f'(x) to study f(x), First Derivative Test for local extrema
- For practice getting a picture of f(x) from a picture of f'(x), try this "puzzle" applet!

*Quiz this week:* Section 3.11 (linearization and differentials)

**Paper HW 5, due Friday 3/2 in class**

Week 9:

- Section 4.4 (2.5 days): Concavity, inflection points, Second-Derivative Test
- For a good summary and example of sketching a curve, check out this handout.
- Group-work for Tuesday March 6

- Section 4.5 (1.5 days, 1 more after break): Limits of 0/0 or infty/infty form using L'Hopital's Rule, 0*infty form

*Quiz this week (12 minutes):* Section 4.3 (analyzing the signs of f'(x) to determine rise, fall, extrema)

**Paper HW 6, due Friday 3/9 in class**

- If you're going to leave early for break, you should make arrangements with me to hand in your HW before leaving.

*Week 10:*

- Finish Section 4.5: Indeterminate power forms (0^0, infinity^0, 1^infinity), brief mention of infinity - infinity form
- Section 4.6 (3 days): Optimization
- Here's a handout which summarizes the main ideas and works out an example.
- Group-work for Wednesday March 21, covering some 2D examples
- Group-work for Friday March 23, covering some 3D examples
- On Friday, we mention a travel-time example. An interesting article about a similar problem is called "Do Dogs Know Calculus?" The article is pretty detailed, so here's a different presentation explaining the article more easily.

*Quiz this week (12 minutes)*: Section 4.5 (L'Hopital's Rule) on 0/0 or infinity/infinity forms only

**Paper HW 7, due Friday 3/23 in class**

**TEST 3 is on next Tuesday, March 27.**

- It covers Sections 3.11 through 4.6
- Expect somewhere from 6 to 8 questions, with a 75-minute time limit.
- A couple questions may ask for brief, one-sentence explanations of your reasoning, similar to the Paper HW standards.
- There is a question where f'(x) and f''(x) are both important, but you're already given f''(x) for free. (You need to compute f'(x) yourself though.)
**You should know how to state important theorems from this unit (Extreme Value Theorem, MVT, etc.)**- This is because, in order for these theorems to be used, we have to check their hypotheses!
- (For example, you have to check for 0/0 or infty/infty before you can use L'Hopital's Rule.)

- Per syllabus policy, the only allowed calculator is a TI-30XS Multiview calculator.
- Topic list for the test
- Practice questions
- We will go over practice questions in class next Monday. Try these out ahead of time, so you can review these with your other classmates!
- There are more practice questions in this set than usual, so this document also has solutions to many of those problems.

*Week 11:*

- Review for Test 3
**TEST 3**- Section 4.8: antiderivatives, indefinite integrals, some initial-value problems

*No quiz or paper HW this week*

**UNIT 4: Basic fundamentals of integration**

*Week 12:*

- Section 5.1: the area under a curve y = f(x), finding some exact areas by geometry, writing Riemann sums to approximate areas
- Section 5.2 (2 days): summation notation to express long sums, Riemann sums in summation form, taking limits of Riemann sums
- Here's an extra handout to summarize the main process of Riemann sum limits.
- For more information about one of the more famous sum formulas, Little Gauss's Formula for 1 + 2 + ... + n, check out this link.

- Section 5.3: basic properties of the definite integral, average value of a function

*Quiz this week:* Section 4.8 (indefinite integral notation for antiderivatives)

**Paper HW 8, due Friday April 6, 2018**

Week 13:

- Section 5.4: the Fundamental Theorem of Calculus
- Section 5.5: Substutition Rule for indefinite integrals, i.e. "u-substitution"

*Quiz this week:* Sections 5.1 and 5.2 (writing Riemann sums to estimate areas)

- We will have one last quiz on the final Tuesday of classes.

**Paper HW 9, due Friday April 13, 2018**

- This is the last paper HW set.
- I may put out some optional practice problems, with solutions, in the last week of class though.

**TEST 4 is on next Tuesday April 17, 2018.**

- It covers Sections 4.8 through 5.5. (We have skipped Section 4.7 in the text on Newton's Method.)
- We will still cover Section 5.6 after this test to finish the course.

- Expect a length similar to previous in-class tests (6 to 8 questions).
- Unsimplified numbers should generally be used for expressing sums, instead of decimal approximations in a calculator.
- You may have to draw some rectangle approximations during the exam.
- Any summation identities (like the sums of k, k^2, or k^3) will be provided on the test if you need them.

- The only allowed calculator, per syllabus policy, is the TI-30XS Multiview.
- Topic list for the test
- Practice questions

**Start your final exam review by now. See details at the bottom of this page.**

*Week 14:*

- Review for Test 4
**TEST 4**- Section 5.6, days 1 and 2 (out of 3): Substitution with definite integrals, area between two curves

*No quiz this week*

*No more paper HW*

- Start reviewing for the final exam instead! See the information below.

*Week 15:*

- Finish Section 5.6: area between curves
- Tuesday and Wednesday both involve review!
- On Tuesday, we'll look over the website with old finals and skim over the topics list.
- On Wednesday, let's go over parts of an old final (like the recent Fall 2017 final).

*Quiz this week:* Section 5.6 (substitutions with definite integrals)

Final exam details

Thursday May 3, 2018

7:00pm to 10:00pm

Miller Learning Center room 171

**If you cannot make this scheduled date and time, let me know as soon as possible**. Makeup arrangements may be possible.- This test is a mass exam for (almost) all sections of Math 2250.

Pooled office hours schedule in Boyd 628

- These office hours are open to any calculus student, whether or not your own instructor is working those hours.
- I will also have fairly flexible office hours outside of those, so stop by or message me if interested.

Math department page with more information about the final

- This page has a study guide of what topics could be tested.
- There are also plenty of old final exams to look at!

A few important policies for this test:

- Bring your student ID to the test.
**Once the test starts, there are no bathroom breaks**. Talk to me if there are issues.**You'll have to leave your backpack (or other containers) at the front of the testing room**, with your phones or smart watches turned off.

Last updated: 4/23/2018