## Daily Assignments

#### December 20 at 5:20 PM: Final Exam

- Final Exam on Tuesday, December 20, 5:20 - 7:20 PM
- As scheduled by the registrar
- Practice Final

- Test Rules:
- You are not allowed to consult books or notes during the test, but you may use a one-page, two-sided, handwritten cheat sheet you have made for yourself ahead of time.
- You may not use a calculator. You may leave answers unsimplified, except you should compute trigonometric functions as far as possible.
- The exam covers all the mastery topics from this course, but primarily the major topics and topic S8.
- Each part of each major topic is worth 10 points. The question on topic S8 is worth 10 points.
- The questions on topics S1 through S6 are
**optional**. Answering one correctly can earn you up to two bonus points on the test. More importantly, answering one correctly can raise your overall mastery score.

- Solutions to Mastery Quiz 11.

#### December 8: Volumes of Solids of Revolution

- Mastery Quiz 11 due Thursday, December 8
- Topics M5, M6
- Single Sheet
- Answer Blanks

- Read section 6.4 of the online notes.
- See also Strang and Herman, section 6.2

#### December 7: Recitation 14 on Integral Applications

#### December 6: Physical Applications

- Read the Solutions to Mastery Quiz 10
- Read sections 6.2-3 of the online notes.
- See also Strang and Herman, section 6.5

#### December 1: Areas

- Mastery Quiz 10 due
- Topics M4, M5, S8
- Single Sheet
- Answer Blanks

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

#### November 30: Recitation 13 on Integration

#### November 29: Integration by Substitution

- Read the Midterm 2 Solutions
- Read the solutions to Mastery Quiz 9
- Read section 5.5 of the online notes.
- See also Strang and Herman, section 5.5

#### November 22: Computing Integrals and the Fundamental Theorem of Calculus, Part II

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

#### November 17: Integral Properties and the Fundamental Theorem of Calculus, Part I

- Mastery Quiz 9 due
- Topics M4, S6, 28
- Single Sheet
- Answer Blanks

- Read section 5.3 of the online notes.
- See also Strang and Herman, section 5.3

#### November 16: Recitation 12 on Riemann Sums

#### November 15: Riemann Sums and the Definite Integral

- The class recording is posted under “Zoom Meetings” on Blackboard
- Read section 5.2 of the online notes.
- See also Strang and Herman, section 5.2

#### November 10: Integration and Area

- 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 9: Recitation 11 physical optimization problems

#### November 8: Midterm 2

- Practice Midterm 2

#### November 3: Physical Optimization Problems

- Mastery Quiz 8 due
- Topics M3, M4, S6
- Single Sheet
- Answer Blanks

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

#### November 2: Recitation 10 on Curve Sketching

#### November 1: The Shape of a Graph

- Read the solutions to Mastery Quiz 7
- Read sections 3.4-5 of the online notes.
- See also Strang and Herman, section 4.5

#### October 27: Classifying Extrema

- Read the Solutions to mastery quiz 6.
- Mastery Quiz 7 due
- Topics M2, M3, M4, S5
- Single Sheet
- Answer Blanks

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

#### October 26: Recitation 9 on Extrema and the Mean Value Theorem

#### October 20: The Mean Value Theorem

- Mastery Quiz 6 due
- Topics M2, M3, S4, S5
- Single Sheet
- Answer Blanks

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

#### October 19: Recitation 8 on Related Rates and Extrema

#### October 18: Extrema and Critical Points

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

#### October 13: Related Rates

- Mastery Quiz 5 due Thursday, October 13
- Topics M1, M2, M3, S4
- Single Sheet
- Answer Blanks

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

#### October 12: Recitation 7 on Derivative Applications

#### October 11: Implicit Differentiation

- Read the Midterm 1 Solutions
- Read Section 2.9 of the online notes.
- See also Strang and Herman, section 3.8

#### October 6: Rates of Change and Tangent Lines

- Read Section 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

#### October 5: Recitation 6 on Linear Approximation and Rates of Change

#### October 4: Midterm 1

- You may bring a one-sided, handwritten cheat sheet on letter-size or A4-size paper. You may not bring a calculator.
- See the solutions to mastery quiz 4
- Practice Midterm 1

#### September 29: Linear Approximation and Rates of Change

- Mastery Quiz 4 due Thursday, September 29
- Topics M1, M2, S3
- Single Sheet
- Answer Blanks

- Read Section 2.6 and 2.7.1 of the online notes.

#### September 28: Recitation 5 on computing derivatives

#### September 27: The Chain Rule

- Read the solutions to mastery quiz 3
- Read Section 2.5 of the online notes.
- See also Strang and Herman, sections 3.6

#### September 22: Computing the Derivative

- Mastery Quiz 3 due
- Topics M1, S2, S3
- Single Sheet
- Answer Blanks

- Read Sections 2.3-4 of the online notes.

#### September 21: Recitation 4 on infinite limits and the derivative definition

#### September 20: The Derivative

- Read the Solutions to Mastery Quiz 2
- Read Section 2.2 of the online notes.
- You may find the 3Blue1Brown Essence of Calculus, Chapter 2 helpful. It’s more on point for the next lesson, but you might want to watch it now.

#### September 15: Intro to the Derivative

- Mastery Quiz 2 due
- Topics M1, S1, S2
- Single Sheet
- Answer Blanks

- Read Section 2.1 of the online notes.
- See also Strang and Herman, section 3.1

#### September 14: Recitation 3 on Trig and Infinite Limits

#### September 13: Infinite Limits

- Read the solutions to Mastery Quiz 1
- 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

#### September 8: Limits, Trigonometry, and the Squeeze Theorem

- Mastery Quiz 1
- Topic S1
- Single Sheet
- Answer Blanks

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

- Optional Videos:

#### September 7: Recitation 2 on Limits

#### September 6: Continuity and Computing Limits

- Read Section 1.4 of the online notes
- You can also consult Strang and Herman 2.3 (Except 2.3.6) and 2.4.

- Optional Videos:

#### September 1: Approximation and Limits

- Read Section 1.3 of the online notes
- You can also consult Strang and Herman 2.2 and 2.5.

- 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

#### August 31: Recitation 1 on Approximation

#### August 30: Syllabus and Review of 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 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.

The course syllabus is available here.

## Course notes

## Mastery Quizzes

- Mastery Quiz 1 due Thursday, September 8
- Topic S1
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 2 due Thursday, September 15
- Topics M1, S1, S2
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 3 due Thursday, September 22
- Topics M1, S2, S3
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 4 due Thursday, September 29
- Topics M1, M2, S3
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 5 due Thursday, October 13
- Topics M1, M2, M3, S4
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 6 due Thursday, October 20
- Topics M2, M3, S4, S5
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 7 due Thursday, October 27
- Topics M2, M3, M4, S5
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 8 due Thursday, November 3
- Topics M3, M4, S6
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 9 due Thursday, November 17
- Topics M4, S6, S8
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 10 due Thursday, December 1
- Topics M4, M5, S8
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 11 due Thursday, December 8
- Topics M5, M6
- Single Sheet
- Answer Blanks
- Solutions

#### Major Topics

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

#### Secondary Topics

- Estimation
- Squeeze theorem
- Definition of derivative
- Rates of change and models
- Related rates
- Curve sketching
- [Canceled for time]
- Riemann sums

## Tests

- Midterm on October 4
- Practice Midterm 1
- Midterm 1 Solutions

- Midterm on November 8
- Practice Midterm 2

- Midterm 2 Solutions
- Final Exam on Tuesday, December 20, 5:20 - 7:20 PM
- As scheduled by the registrar
- Practice Final
- Solutions

Graphing calculators will **not** be allowed on tests. Scientific, non-programmable calculators will be allowed. I will have some to share, but not enough for everyone.

## 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.