## Daily Assignments

## March 21: Classifying Extrema

- Mastery Quiz 8 due
- Topics: M3, M4, S4
- Single Sheet
- Answer Blanks

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

## March 10: Recitation 8 on Extreme and Mean Values

## March 9: The Mean Value Theorem

- Read the solutions to Mastery Quiz 7
- Read Section 3.2 of the online notes
- See also Strang and Herman, section 4.4

## March 7: Extrema and Critical Points

- Mastery Quiz 7 due
- Topics: M2, M3, S3, S4
- Single Sheet
- Answer Blanks

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

## March 3: Recitation 7 on Implicit Differentiation and Related Rates

## March 2: Related Rates

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

## February 28: Implicit Differentiation and Tangent Lines

- Mastery Quiz 6 due Tuesday, February 28
- Topics: M2, M3, S3
- Single Sheet
- Answer Blanks

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

## February 24: Recitation 6 on linear approximation and rates of change

## February 23: Rates of Change and Tangent Lines

- Read the solutions to Mastery Quiz 5
- Read the solutions to the midterm.
- 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 21: Linear Approximation and Velocity

- Mastery Quiz 5 due Tuesday, February 21
- Topics: M1, M2, S2
- Single Sheet
- Answer Blanks

- Read Sections 2.6 and 2.7.1 of the online notes

## February 17: Recitation 5 on derivatives and the chain rule

## February 16: Midterm 1

- Read the solutions to Mastery Quiz 4
- Midterm on February 16
- Topics: M1, M2, S1, S2
- Practice Midterm 1

## February 14: Trigonometric Derivatives and the Chain Rule

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

- 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 10: Recitation 4 on the definition of derivative

## February 9: Basic Derivative Rules

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

## February 7: Defining the Derivative

- Mastery Quiz 3 due Tuesday, February 7
- 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.

## February 3: Recitation 3 on Trig and Infinite Limits

## February 2: Infinite Limits

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

## January 31: Trigonometric 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

## January 27: Recitation 2 on Computing Limits

## January 26: Continuity and Computing Limits

- Read the Solutions to Mastery Quiz 1
- Read Section 1.4 of the online notes
- Optional Videos:

## January 24: Approximation and Limits

- Mastery Quiz 1 due Tuesday, January 24
- Topics: S1
- Single Sheet
- Answer Blanks

- finish Section 1.3 of the online notes

## January 20: Recitation 1 on Approximation

## January 19: Approximation and Limits

- Read Section 1.3 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 17: Syllabus and Functions

- Please read the syllabus
- Claim your account on WeBWorK through Blackboard.
- Read Professor Bonin’s advice on study skills
- Read Section 1.1-2 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

## Course notes

## Mastery Quizzes

- Mastery Quiz 1 due Tuesday, January 24
- Topics: S1
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 2 due Tuesday, January 31
- Topics: M1, S1
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 3 due Tuesday, February 7
- Topics: M1
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 4 due Tuesday, February 14
- Topics: M1, M2, S2
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 5 due Tuesday, February 21
- Topics: M1, M2, S2
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 6 due Tuesday, February 28
- Topics: M2, M3, S3
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 7 due Tuesday, March 7
- Topics: M2, M3, S3, S4
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 8 due Tuesday, March 21
- Topics: M3, M4, S4
- Single Sheet
- Answer Blanks

#### Major Topics

- Computing Limits
- Computing Derivatives
- Linear Approximation
- Extrema and Optimization
- Integration
- Integral Applications

#### Secondary Topics

- Estimation
- Definition of derivative
- Rates of change and models
- Related rates
- Curve sketching
- Numeric Approximation
- Riemann sums

## Tests

- Midterm on February 16
- Topics: M1, M2, S1, S2
- Practice Midterm 1
- Midterm 1 Solutions

- Midterm on March 30
- Practice Midterm 2

- Final Exam on Tuesday, May 9, 5:20–7:20 PM
- As scheduled by the registrar
- 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.