## Daily Assignments

## Optional Review Stuff

One of the biggest sources of difficulty in calculus is weak or underprepared skills at algebra and trigonometry. If you want to succeed in this course, you should be comfortable with:

- Multiplying and factoring polynomials;
- Multiplying and dividing fractions and rational functions;
- Working with exponents;
- Working with trigonometric functions and the unit circle.

I don’t have any organized review materials for these topics, but if you want to brush up on them, you may want to look at:

- OpenStax College Algebra chapters 1 and 5;
- OpenStax Precalculus chapter 5.

## Week 0: August 24 – 25

##### August 25: Recitation 1 on Estimation

## Week 1: August 28 – September 1

##### August 28: Syllabus and Functions

- Please read the syllabus
- Claim your account on WeBWorK through Blackboard.
- Read Professor Bonin’s advice on study skills
- Read Section 1.1 of the online notes (about a page)
- Skim Strang and Herman §1.1-3 to remind yourself of precalculus material.
- Optional/bonus: Watch Essence of Calculus, Chapter 1 by 3Blue1Brown

##### August 30: Estimation

- Read Section 1.2-3 of the online notes
- Optional: Play with this Geogebra widget for visualizing the relationships between ε and δ for different functions.
- Optional videos:
- Watch the first ten minutes of Essence of Calculus, Chapter 7
- If you haven’t seen derivatives before, don’t worry too much about when he mentions them. The key material I want starts about five minutes in.

- Khan Academy has a series of videos that might be helpful. I’m linking the second, but the third and fourth in this series are also good for understanding limit arguments better.

- Watch the first ten minutes of Essence of Calculus, Chapter 7

##### September 1: Recitation 2 on \(\varepsilon-\delta\) proofs

## Week 2: September 4 – 8

##### September 4: No Class for Labor Day

##### September 6: Continuity and Computing Limits

- Mastery Quiz 1 due Wednesday, September 6
- Topics: S1
- Single Sheet
- Answer Blanks

- Read Section 1.4 of the online notes
- Optional Videos:

##### September 8: Recitation 3 on Computing Limits

## Week 3: September 11 – 15

##### September 11: More on Limits

- Mastery Quiz 2 due
- Topics: M1, S1
- Single Sheet
- Answer Blanks

- Read Section 1.5 of the online notes
- You can also consult Strang and Herman 2.3.6

- Bonus video: Math at Andrews on the Squeeze Theorem
- Slides from class

##### September 13: Infinite Limits

- Read the Solutions to Mastery Quiz 2
- Read Section 1.6 of the online notes
- You can also consult Strang and Herman the part of section 2.2 on infinite limits and section 4.6

##### September 15: Recitation 4 on Advanced Limits

- Skills quiz on M1: computing limits
- Recitation 4 Worksheet

## Week 4: September 18 – 22

##### September 18: Intro to Derivatives

- Mastery Quiz 3 due Monday, September 18
- Topics: M1
- Single Sheet
- Answer Blanks

- Read Section 2.1-2 of the online notes
- You may find the 3Blue1Brown Essence of Calculus, Chapter 2 helpful.

##### September 20: Computing Derivatives

- Read the Solutions to Mastery Quiz 3.
- Read the Solutions to Skills Quiz 1
- Read Section 2.3 of the online notes
- See also Strang and Herman, section 3.3.

##### September 22: Recitation 5 on Basic Derivatives

## Week 5: September 25 – 29

##### September 25: Advanced Derivative Rules

- Mastery Quiz 4 due
- Topics: M1, S2
- Single Sheet
- Answer Blanks
- We’re not doing M2, because on reflection we’re not quite ready for it

- Read Section 2.4-5 of the online notes
- It is
*very important to practice*taking derivatives quickly and easily.- There are a collection of practice problems at IXL.
- I have a practice worksheet of especially challenging derivatives, with solutions. Nothing anywhere near this challenging will appear on this test, but these are a good way to push yourself if you want some extra-challenging practice.

##### September 27: Linear Approximation

- Look at the Practice Midterm 1
- Read the Solutions to Mastery Quiz 4
- Read Sections 2.6 and 2.7.1 of the online notes

##### September 29: Recitation 6 on Taking Derivatives

- Skills Quiz 2 on Taking Derivatives
- Recitation 6 Worksheet

## Week 6: October 2 – 6

##### October 2: Speed and Rates of Change

- Mastery Quiz 5 due
- Topics: M1, M2, S2, S3
- Single Sheet
- Answer Blanks

##### October 4: Midterm

- Read the Solutions to Mastery Quiz 5

##### October 6: Recitation 7 on Rates of Change

## Week 7: October 9 – 11

##### October 9: Tangent Lines and Implicit Differentiation

- Mastery Quiz 6 due Monday
- Topics: M2, S3, S4
- Single Sheet
- Answer Blanks

- Read Section 2.9 of the online notes
- See also Strang and Herman, section 3.8

##### October 11: Related Rates

- Read the solutions to Midterm 1
- Read the solutions to Mastery Quiz 6
- Read Section 2.10 of the online notes
- See also Strang and Herman, section 4.1

##### October 13: No Recitation for Fall Break

## Week 8: October 16 – 20

##### October 16: Extreme Values and Critical Points

- Mastery Quiz 7 due Monday, October 16
- Topics: M2, S4, S5, S6
- Single Sheet
- Answer Blanks

- Read Section 3.1 of the online notes
- See also Strang and Herman, section 4.3

##### October 18: Mean Value Theorem

- Read Section 3.2 of the online notes
- See also Strang and Herman, section 4.4

##### October 20: Recitation 8 on Absolute Extrema and the Mean Value theorem

## Week 9: October 23 – 27

##### October 23: Classifying Extrema

- Mastery Quiz 8 due Monday, October 23
- Topics: M2, S5, S6
- Single Sheet
- Answer Blanks

- Read Section 3.3 of the online notes
- See also Strang and Herman, section 4.5

##### October 25: Concavity and Curve Sketching

- Read the solutions to Mastery Quiz 8
- Read Section 3.4-5 of the online notes
- See also Strang and Herman, section 4.5

##### October 27: Recitation 9

- Skills Quiz 3 on Major Topic 3
- Recitation 9 Worksheet

## Week 10: October 30 – November 3

##### October 30: Physical Optimization Problems

- Mastery Quiz 9 due Monday, October 30
- Topics: M3, S7
- Single Sheet
- Answer Blanks

- Read Section 3.6 of the online notes
- See also Strang and Herman, section 4.7

##### November 1: The Area Problem

- Read the Solutions to Mastery Quiz 9
- Read Section 5.1 of the online notes
- See also Strang and Herman, section 5.1
- Watch the first 8 minutes or so of Essence of Calculus Episode 8
- This GeoGebra widget is helpful for visualizing what’s going on.
- You may also wish to skim Section 4 of the notes, which we won’t be covering in class.

##### November 3: Recitation 10 on Physical Optimization

## Week 11: November 6 – 10

##### November 6: The Definite Integral

- Mastery Quiz 10 due
- Topics: M3, S7, S8
- Single Sheet
- Answer Blanks

- Midterm Wednesday!
- Read Section 5.2 of the online notes
- See also Strang and Herman, section 5.2

##### November 8: Midterm 2

- Read the Solutions to Mastery Quiz 10
- Midterm 2 on November 8
- Topics: M3, S4, S5, S6, S7, S8
- Practice Midterm 2

##### November 10: Recitation 11 on Riemann Sums

## Week 12: November 13 – 17

##### November 13: The Fundamental Theorem of Calculus, Part 1

- Mastery quiz 11 due
- Topics M3, S8, S9
- Single Sheet
- Answer Blanks

- Read the solutions to the midterm
- Read Section 5.3 of the online notes
- See also Strang and Herman, section 5.3

- Watch the rest of Essence of Calculus Episode 8

##### November 15: Computing Integrals and the FTC Part 2

- Read the solutions to Mastery Quiz 11
- Read Section 5.4 of the online notes
- See also Strang and Herman, section 5.4

##### November 17: Recitation 12 on integration

## Thanksgiving Break: November 20-24

Get some rest!

## Week 13: November 27 – December 1

##### November 27: Integration by Substitution

- Mastery Quiz 12 due Monday, November 27
- Topics: M3, M4, S9
- Single Sheet
- Answer Blanks

- Read Section 5.5 of the online notes
- See also Strang and Herman, section 5.5

##### November 29: Finding Areas

- Read the Solutions to mastery quiz 12
- Read Section 6.1 of the online notes
- See also Strang and Herman, section 6.1

##### December 1: Recitation 13 on substitution and area

## Week 14: December 4 – 8

##### December 4: Physical Applications

- Mastery Quiz 13 due Monday, December 4
- Topics: M4, S10
- Single Sheet
- Answer Blanks

- Practice Final is posted
- Read sections 6.2-3 of the online notes
- See also Strang and Herman, section 6.5

##### December 6: Volumes by Slices

- Read the Solutions to mastery quiz 13
- Read Section 6.4 of the online notes
- See also Strang and Herman, section 6.2

##### December 8: Recitation 14 on integral applications

## Finals Week

##### December 11: Volumes by cylindrical shells

- Optional Mastery Quiz 14 due Monday, December 11
- Topics: M4, S10
- Single Sheet
- Answer Blanks
- I will be posting these solutions Monday night. Consequently I will
*not*be accepting late submissions.

- Read Section 6.5 of the online notes
- See also Strang and Herman, section 6.3

##### December 12: Office hours

- I’ll be in my office from roughly 3 to 7 PM. We may move down the hall to a bigger room, depending on attendance and room availability.

##### December 13, 5:20–7:20 PM: Final Exam

- I’ll be in my office from 2-4 PM. I will kick everyone out at 4. This is for your own good; I strongly encourage you to take at least an hour break from studying before the final starts.
- Solutions to Mastery Quiz 14
- Practice Final

## Course notes

## Mastery Quizzes

- Mastery Quiz 1 due Wednesday, September 6
- Topics: S1
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 2 due Monday, September 11
- Topics: M1, S1
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 3 due Monday, September 18
- Topics: M1
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 4 due Monday, September 25
- Topics: M1, S2
- Single Sheet
- Answer Blanks
- We’re not doing M2, because on reflection we’re not quite ready for it
- Solutions

- Mastery Quiz 5 due Monday, October 2
- Topics: M1, M2, S2, S3
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 6 due Monday, October 9
- Topics: M2, S3, S4
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 7 due Monday, October 16
- Topics: M2, S4, S5, S6
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 8 due Monday, October 23
- Topics: M2, S5, S6
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 9 due Monday, October 30
- Topics: M3, S7
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 10 due Monday, November 6
- Topics: M3, S7, S8
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 11 due Monday, November 13
- Topics: M3, S8, S9
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 12 due Monday, November 27
- Topics: M3, M4, S9
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 13 due Monday, December 4
- Topics: M4, S10
- Single Sheet
- Answer Blanks
- Solutions

- Optional Mastery Quiz 14 due Monday, December 11
- Topics: M4, S10
- Single Sheet
- Answer Blanks
- I will be posting these solutions Monday night. Consequently I will
*not*be accepting late submissions. - Solutions

#### Major Topics

- Computing Limits
- Computing Derivatives
- Extrema and Optimization
- Integration

#### Secondary Topics

- Estimation
- Definition of derivative
- Linear Approximation
- Rates of change and models
- Implicit Differentiation
- Related rates
- Curve sketching
- Physical Optimization Problems
- Riemann sums
- Integral Applications

## Tests

- Midterm on October 4
- Topics: M1, M2, S1, S2, S3
- Practice Midterm 1
- Solutions to Midterm 1

- Midterm 2 on November 8
- Topics: M3, S4, S5, S6, S7, S8
- Practice Midterm 2
- Solutions to Midterm 2

- Final Exam on Tuesday, December 13 5:20–7:20 PM
- As scheduled by the registrar
- Per the syllabus, you will not be excused from the final if you schedule travel during finals week; if you must buy your plane ticket before the registrar announces final exam, please make sure it departs after December 13.
- Practice Final

Calculators will not be allowed on tests.

## Textbook

The official textbook for Math 1231 is OpenStax Calculus Volume 1 by Gilbert Strang and Edwin Herman. It is available for free online here. You can also buy copies from Amazon; a paperback is a little under $30.

I will be loosely following the textbook, but will often be giving my own take or focusing on topics the textbook doesn’t emphasize. All my course notes will be posted to the course web page.

We will be using a (free!) online homework system called WeBWorK this term. You can access it by going to Blackboard, then to “Course Links”, and clicking the WeBWorK link. This will automatically create an account for you and log you in. You may continue to log in through Blackboard, or if you wish you may create a password within WeBWorK to log in directly.

## Course Goals

This is the first semester of a standard year-long sequence in single-variable calculus. The main topics are limits and continuity; differentiation and integration of algebraic and trigonometric functions; and applications of these ideas. This corresponds roughly to Chapters 1–6 of Herman–Strang.

By the end of the course, students will acquire the following skills and knowledge: students will know the intuitive and formal definitions of the limit, derivative, antiderivative, and definite integral of a function. Students will be able to distinguish continuous from discontinuous functions by visual and algebraic means; to calculate derivatives of functions both by definition and using various simplification rules; to formulate and solve related rates and optimization problems; to accurately sketch graphs of functions; to calculate antiderivatives and definite integrals of a variety of functions; to compute areas of regions in the plane and volumes of solids of revolution; and to explain the significance of important theoretical results such as the Extreme Value Theorem, Mean Value Theorem, and Fundamental Theorems of Calculus.