Math 1231: Single-Variable Calculus I
Section 10
Fall 2021

Daily Assignments

Tuesday Dec 14, 3:00–5:00 pm: Final Exam!

• Practice Final
• Practice Final Solutions
• Solutions to Mastery Quiz 11

December 9: Volumes

• Due in class: Mastery Quiz 11
  • Topics: M5, S9
• Read the solutions to quiz 10
• Read section 6.4 of the online notes
  • See also Strang and Herman section 6.2

December 2: Applications of the Integral

• Due in class: Mastery Quiz 10
• Topics: M5, S8, S9
• You may submit all three
• Read section 6.3 of the online notes
  • See also Strang and Herman section 6.5

November 30: Averages and Areas

• Read sections 6.1 and 6.2 of the online notes
  • See also Strang and Herman section 5.2 objective 6 and section 6.1

November 23 :Integration by Substitution

• Read the solutions to Mastery Quiz 9
• Read section 5.5 and 5.6 of the online notes
  • See also Strang and Herman the end of §5.5

November 18: FTC2 and Computing Integrals

• Due in Class: Mastery Quiz 9
  • Topics: M4, S7, S8
  • Submit all three
• Read section 5.4 of the online notes
  • See also Strang and Herman the end of §5.3
  • Watch Essence of Calculus Episode 8 and Episode 9

November 16: The Fundamental Theorem of Calculus, part 1

• Read Solutions to Mastery Quiz 8
• Read section 5.3 of the online notes
  • See also Strang and Herman §5.3 the section on the Fundamental Theorem of Calculus Part 1 (Theorem 5.2 through Checkpoint 5.18)

November 11: The Definite Integral

• Due in class: Mastery Quiz 8
  • Topics: M3, M4, S6, S7
  • Submit at most 3
• Read section 5.2 of the online notes
  • See also Strang and Herman section 5.2

November 9: Integration and Area

• Read Solutions to quiz 7
• Read Midterm Solutions
• Read section 5.1 of the online notes
  • See also Strang and Herman section 5.1

November 4: Interlude on Approximation

• Due in Class: Mastery Quiz 7
  • Topics: M2, M4, S5, S6
  • Do at most 3
• Read the Interlude section of the online notes
  • See also Strang and Herman section 4.9

November 2: Optimization

• Read the solutions to mastery quiz 6
• Read section 3.6 of the online notes
  • See also Strang and Herman section 4.7

October 28: Sketching Graphs

• Due in Class: Mastery Quiz 6
  • Topics: M2, M3, M4, S4, S5
  • Submit up to 4
• Read section 3.5 of the online notes §3.5
  • We’ll Strang and Herman §4.5 from a different perspective.

October 26: Classifying Extrema

• Read sections 3.3-4 of the online notes §3.3-4
  • See also Strang and Herman §4.5

October 21: Midterm!

• Practice Midterm
  • Practice Midterm Solutions

October 19: The Mean Value Theorem

• Read the solutions to Mastery Quiz 5
• Read section 3.2 of the notes §3.2
  • See also Strang and Herman section 4.4

October 14: Maxima and Minima

• Due in class: Mastery Quiz 5
  • Topics: M2, M3, S4
• Read section 3.1 of the notes
  • See also Strang and Herman section 4.3

October 12: Related Rates

• Read the solutions to Mastery Quiz 4
• Read section 2.10 of the notes §2.10
  • See also Strang and Herman §4.1

October 7: Implicit Differentiation

• Due in Class: Mastery Quiz 4
  • Topics: M1, M2, M3, S3
• Watch Essence of Calculus chapter 6: Implicit Differentiation, what’s going on here?
• Read section 2.9 of the notes
  • See also Strang and Herman section 3.8

October 5: Rates of Change and Tangent Lines

• Read the solutions to Mastery Quiz 3
• Optional worksheet on derivatives
  • Solutions
• Read the rest of section 2.7 and 2.8 of the notes
  • See also Strang and Herman §3.1.1 - 3.1.2
• You may find it helpful to review the 3Blue1Brown Essence of Calculus, Chapter 2. We’re engaging more with some of the geometry underlying the derivative.

September 30: Linear Approximation and Rates of Change

• Due in class: Mastery Quiz 3
  • Topics: M1, M2, S3
• Read section 2.6 and the beginning of 2.7 of the notes (updated Sept 30; make sure you have the new version!)
  • See also Strang and Herman Section 4.2 and section 3.4

September 28: Trigonometric Derivatives and the Chain Rule

• Read the Solutions to Mastery Quiz 2
• Watch Essence of calculus, chapter 4: Visualizing the Chain Rule and Product Rule. (You might also go back and watch chapter 3 if you didn’t already.)
• Read section 2.4-5 of the notes
  • See also Strang and Herman sections 3.5 and 3.6

September 23: Computing Derivatives

• Due in class: Mastery Quiz 2
  • Topics: M1 and S1, S2
• Read section 2.3 of the online notes
  • See also Strang and Herman section 3.3
• Watch Essence of calculus, chapter 3: Derivative Formulas Through Geometry

September 21: Linear Approximation and the Derivative

• Read Sections 2.1 and 2.2 of the online notes.
  • See also Strang and Herman, sections 3.1 and 3.2
• 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 16: Infinite Limits

• Read Section 1.7 of the online notes.
  • See also Strang and Herman, section 2.2 the part on infinite limits and section 4.6
• Read the solutions to quiz 1

September 15: Mastery Quiz Due

• Mastery Quiz 1: M1 and S1
  • Due in recitation

September 14: Trigonometry and the Squeeze Theorem

• Read one of
  • Section 1.6 of the online notes.
  • See also Strang and Herman, section 2.3 on the Squeeze Theorem
• Optional videos
  • Math at Andrews on the Squeeze Theorem

September 10: Edfinity due

September 9: Computing Limits

• Read one of
  • Section 1.5 of the online notes.
  • See also Strang and Herman, the rest of sections 2.3 and 2.4
• Optional Videos
  • Math at Andrews on the Intermediate Value Theorem

September 7: Formal Limits

• Read Section 1.4 of the online notes
  • See also Strang and Herman:
    • section 2.5 (up until the one-sided and infinite limits)
    • Section 2.3 up through Example 2.15 and Checkpoint 2.11.
• 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.
  • You can also ignore the L’Hospital’s Rule discussion that starts about ten minutes in. L’Hospital’s Rule is very useful, but we won’t be covering it in this class. (And even if you already know it, you may not use it in this class.)
• Optional: Play with this Geogebra widget for visualizing ε-δ arguments.

September 2: Informal Continuity and Limits

• Read Section 1.3 of the online notes
  • You can also consulst Strang and Herman 2.2 and 2.4.
• Optional: watch The BEST explanation of limits and continuity

August 31: Syllabus and Review of Functions

• Please read the syllabus
• Claim your account on Edfinity
• Read Professor Bonin’s advice on study skills
• Read Section 1.1 of the online notes (about a page)
• Skim one of:
  • Strang and Herman §1.1-3
  • Section 1.2 of the online notes.
• 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

• Course Notes
• Section 1: Functions and Limits
• Section 2: Derivatives
• Section 3: Optimization
• Section 4: Interlude on Approximation
• Section 5: Integration
• Section 6: Integral Applications

Mastery Quizzes

• Mastery Quiz 1: M1 and S1
  • Solutions
• Mastery Quiz 2
  • Topics: M1 and S1, S2
  • Solutions
• Mastery Quiz 3
  • Topics: M1 and S2, S
  • Solutions
• Mastery Quiz 4
  • Topics: M1, M2, M3, S3
  • Solutions
• Mastery Quiz 5
  • Topics: M2, M3, S4
  • Solutions
• Mastery Quiz 6
  • Topics: M2, M3, M4, S4, S5
  • Solutions
• Mastery Quiz 7
  • Topics: M2, M4, S5, S6
  • Solutions
• Mastery Quiz 8
  • Topics: M3, M4, S6, S7
  • Solutions
• Mastery Quiz 9
  • Topics: M4, S7, S8
  • Solutions
• Mastery Quiz 10
  • Topics: M5, S8, S9
  • Solutions
• Mastery Quiz 11
  • Topics: M5, S9
  • Solutions

Major Topics

1. Computing Limits
2. Computing Derivatives
3. Linear Approximation
4. Extrema and Optimization
5. Integration

Secondary Topics

1. Definition of a limit
2. Squeeze theorem
3. Definition of derivative
4. Rates of change and models
5. Related rates
6. Curve sketching
7. Numeric approximation
8. Riemann sums
9. Integral Applications

Tests

• Midterm on October 21
  • Practice Midterm
  • Practice Midterm Solutions
  • Midterm Solutions
• Final Exam
  • Tuesday Dec 14, 3:00–5:00 pm
  • Practice Final
  • 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.

Edfinity online homework system

We will be using Edfinity for Math 1231-10. To enroll, please follow the steps below:

1. If you already have an Edfinity account from a previous course, please sign into it. Otherwise, go to step 2.
2. Go to the following registration link: https://edfinity.com/join/BXWHNRJU
3. You will be prompted to pay (I believe the fee should be $25) and enroll in our section.
4. Start working on your assignments :)

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.

This section of Math 1231 will use the Edfinity online homework platform. You will need to buy a license, which I believe is $25.