## 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 1: January 15 – 19

##### January 16: Syllabus and Functions

- Please read the syllabus
- Claim your account on WeBWorK through Blackboard.
- Read Professor Bonin’s advice on study skills
- Slides from today’s class
- 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

##### January 18: 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

##### January 19: Recitation on Estimation

## Week 2: January 22 – 26

##### January 23: Continuity and Computing Limits

- Mastery Quiz 1 due
- Topics: S1
- Single Sheet
- Answer Blanks

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

##### January 25: More on Limits

- Read the solutions to mastery quiz 1
- 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

##### January 26: Recitation 2 on Computing Limits

## Week 3: January 29 – February 2

##### January 30: Infinite Limits

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

- 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

##### February 1: Intro to Derivatives

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

##### February 2: Recitation 3 on Advanced Limits

- Skills quiz on M1: computing limits
- Covers all our limit computation techniques, starting from August 31

- Recitation 3 Worksheet

## Week 4: February 5 – 9

##### February 6: Computing Derivatives

- Mastery Quiz 3 due
- Topics: M1
- Single Sheet
- Answer Blanks

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

##### February 8: Trig Derivatives and Chain Rule

- Read the solutions to mastery quiz 3
- 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.

##### February 9: Recitation 4 on taking derivatives

## Week 5: February 12 – 16

##### February 13: Linear Approximations and Speed

- Mastery Quiz 4 due
- Topics: M1, M2, S2
- Single Sheet
- Answer Blanks

- Read the solutions to skills quiz 1
- Read Sections 2.6 and 2.7.1 of the online notes

##### February 15: Rates of Change and Tangent Lines

- Read the solutions to Mastery Quiz 4
- Read Sections 2.7.2 and 2.8 of the online notes
- See also Strang and Herman, section 3.4 and also you can look back at 3.1.1-3.1.2

##### February 16: Recitation 5 on linear approximation

## Week 6: February 19 – 23

##### February 20: Implicit Differentiation and Tangent Lines

- Mastery Quiz 5 due
- Topics: M1, M2, S2, S3
- In order to post solutions as soon as possible, I will probably not accept late submissions.
- Single Sheet
- Answer Blanks

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

##### February 22: Midterm 1

- Read the solutions to Mastery Quiz 5
- Look at Practice Midterm 1

##### February 23: Recitation 6 on Rates of Change

## Week 7: February 26 – March 1

##### February 27: Related Rates

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

- Read Section 2.10 of the online notes
- See also Strang and Herman, section 4.1

##### February 29(!): Absolute Extrema

- Read the [solutions] to Midterm 1
- Read the [solutions] to Mastery Quiz 6
- Read Section 3.1 of the online notes
- See also Strang and Herman, section 4.3

##### March 1: Recitation 7 on Related Rates

- [Recitation 7 Worksheet]
- [Solutions]

## Week 8: March 4 – 8

##### March 5: Mean Value Theorem

- Mastery Quiz 7 due
- Topics: M2, S4, S5, S6

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

##### March 7: Classifying Extrema

- Read the [solutions] to Mastery Quiz 7
- Read Section 3.3 of the online notes
- See also Strang and Herman, section 4.5

##### March 8: Recitation 8 on absolute extrema and the Mean Value Theorem

- [Recitation 8 Worksheet]
- [Solutions]

## Spring Break: March 11-15

No class! Go have fun!

## Week 9: March 18 – 22

##### March 19: Concavity and Curve Sketching

- Mastery Quiz 8 due
- Topics: M3, S5, S6

- Read Section 3.4-5 of the online notes
- See also Strang and Herman, section 4.5

##### March 21: Physical Optimization Problems

- Read the [solutions] to Mastery Quiz 8
- Read Section 3.6 of the online notes
- See also Strang and Herman, section 4.7

##### March 22: Recitation 9

- Skills Quiz 3 on Major Topic 3
- [Recitation 9 Worksheet]
- [Solutions]

## Week 10: March 25 – March 29

##### March 26: The Area Problem

- Mastery Quiz 9 due
- Topics: M3, S7, S8
- Like with the last midterm, I will not be accepting late submissions so I can get the solutions up quickly

- Midterm next class! Do the practice midterm!
- 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.

##### March 28: Midterm 2

- Read the [Solutions] to Mastery Quiz 9
- Midterm 2
- Topics: M3, S4, S5, S6, S7, S8
- Practice Midterm 2

##### March 29: Recitation 10 on Physical Optimization

- [Recitation 10 Worksheet]
- [Solutions]

## Week 11: April 1 – 5

##### April 2: The Definite Integral

- Mastery Quiz 10 due
- Topics: M3, S7, S8

- Read the [solutions] to the midterm
- Read Section 5.2 of the online notes
- See also Strang and Herman, section 5.2

##### April 4: The Fundamental Theorem of Calculus, Part 1

- Read the [solutions] to Mastery Quiz 10
- 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

##### April 5: Recitation 11 on Riemann Sums

- [Recitation 11 Worksheet]
- [Solutions]

## Week 12: April 8 – 12

##### April 9: Computing Integrals and the FTC Part 2

- Mastery Quiz 11 due
- Topics: M3, S8, S9

- Read Section 5.4 of the online notes
- See also Strang and Herman, section 5.4

##### April 11: Integration by Substitution

- Read the [Solutions] to Mastery Quiz 11
- Read Section 5.5 of the online notes
- See also Strang and Herman, section 5.5

##### April 12: Recitation 12 on integration

- [Recitation 12 Worksheet]
- [Solutions]

## Week 13: April 15 – 19

##### April 16: Finding Areas

- Mastery Quiz 12 due
- Topics: M4, S9

- Read Section 6.1 of the online notes
- See also Strang and Herman, section 6.1

##### April 18: Physical Applications

- Read the [solutions] to mastery quiz 12
- Read sections 6.2-3 of the online notes
- See also Strang and Herman, section 6.5

##### April 19: Recitation 13 on substitution and area

- [Recitation 13 Worksheet]
- [Solutions]

## Week 14: April 22 – 26

##### April 23: Volumes by Slices

- Mastery Quiz 13 due
- Topics: M4, S10

- Practice final is posted; go take a look!
- Read Section 6.4 of the online notes
- See also Strang and Herman, section 6.2

##### April 25: Volumes by cylindrical shells

- Read the [solutions] to mastery quiz 13
- Read Section 6.5 of the online notes
- See also Strang and Herman, section 6.3

##### April 26: Recitation 14 on integral applications

- [Recitation 14 Worksheet]
- [Solutions]

## Finals Week

##### April 30: Optional Mastery Quiz Due

- Optional Mastery Quiz 14 due
- Topics: M4, S10

- Read the [solutions] to mastery quiz 14

##### Office Hours Schedule

##### Final Exam Tuesday, May 7 5:20 &ndash 7:20 PM

- Practice Final

## Course notes

## Skills Quiz Solutions

## Mastery Quizzes

- Mastery Quiz 1 due Tuesday, January 23
- Topics: S1
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 2 due Tuesday, January 30
- Topics: M1, S1
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 3 due Tuesday, February 6
- Topics: M1
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 4 due Tuesday, February 13
- Topics: M1, M2, S2
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 5 due Tuesday, February 20
- Topics: M1, M2, S2, S3
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 6 due Tuesday, February 27
- Topics: M2, S3, S4
- Single Sheet
- Answer Blanks
- [Solutions]

- Mastery Quiz 7 due Tuesday, March 5
- Topics: M2, S4, S5, S6

- Mastery Quiz 8 due Tuesday, March 19
- Topics: M3, S5, S6

- Mastery Quiz 9 due Tuesday, March 26
- Topics: M3, S7, S8

- Mastery Quiz 10 due Tuesday, April 2
- Topics: M3, S7, S8

- Mastery Quiz 11 due Tuesday, April 9
- Topics: M3, S8, S9

- Mastery Quiz 12 due Tuesday, April 16
- Topics: M4, S9

- Mastery Quiz 13 due Tuesday, April 23
- Topics: M4, S10

- Optional Mastery Quiz 14 due Tuesday, April 30
- Topics: M4, S10

#### 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 February 22
- Topics: M1, M2, S1, S2, S3
- Practice Midterm 1

- Midterm on March 28
- Topics: M3, S4, S5, S6, S7, S8
- Practice Midterm 2

- Final Exam Tuesday, May 7 5:20 &ndash 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 May 10.
- 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.