Daily Assignments
Wednesday December 15, 5:20–7:20 PM: Final Exam!
December 8: Volumes
- Read the solutions to quiz 12
- Read section 6.4 of the online notes
- See also Strang and Herman section 6.2
December 6: Physical Applications
- Due in class: Mastery Quiz 12
- Topics: M5, S9
- You may (and should) submit both
- Read section 6.3 of the online notes
- See also Strang and Herman section 6.5
December 1: Averages and Areas
- Read the solutions to Mastery Quiz 11
- 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 29: Integration by Substitution
- Due in Class: Mastery Quiz 11
- Topics: M5, S8
- You may submit both
- Read the solutions to Mastery Quiz 10
- Read section 5.5 and 5.6 of the online notes
- See also Strang and Herman the end of §5.5
November 22: FTC2 and Computing Integrals
- Due in Class: Mastery Quiz 10
- Topics: M4, S7, S8
- You may submit all 3
- Read section 5.4 of the online notes
November 17: The Fundamental Theorem of Calculus, part 1
- Read Solutions to Mastery Quiz 9
- 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 15: The Definite Integral
- Due in class: Mastery Quiz 9
- Topics: M4, S6, S7
- You can submit all 3
- Read section 5.2 of the online notes
- See also Strang and Herman section 5.2
November 10: Integration and Area
- Read the Solutions to quiz 8
- Read section 5.1 of the online notes
- See also Strang and Herman section 5.1
November 8: Interlude on Approximation
- Read Midterm Solutions
- Due in Class: Mastery Quiz 8
- Topics: M3, M4, S6
- Read the Interlude section of the online notes
- See also Strang and Herman section 4.9
November 3: Optimization
- Read the solutions to mastery quiz 7
- Read section 3.6 of the online notes
- See also Strang and Herman section 4.7
November 1: Sketching Graphs
- Due in class: Mastery Quiz 7
- Topics: M2, M3, M4, S5
- Do no more than 3
- Read section 3.5 of the online notes §3.5
- We’ll Strang and Herman §4.5 from a different perspective.
October 27: Classifying Extrema
- Read Solutions to Mastery Quiz 6
- Read sections 3.3-4 of the online notes §3.3-4
- See also Strang and Herman §4.5
October 25: Mean Value Theorem
- Due in class: Mastery Quiz 6
- Topics: M2, M3, S4, S5
- Do no more than three
- I will try to get the mastery scores from the midterm updated over the weekend, but I don’t know when that will happen (and they definitely won’t all be uploaded; there is little chance of M2 or M3 getting up before this quiz is due, sorry.)
- Read section 3.2 of the notes §3.2
- See also Strang and Herman section 4.4
October 20: Midterm!
October 18: Maxima and Minima
- Read the solutions to mastery quiz 5
- Read section 3.1 of the notes
- See also Strang and Herman section 4.3
October 13: Related Rates
October 11: Tangent Lines and Implicit Differentiation
- Be nice to Professor Lewis
- Due in Class: Mastery Quiz 5
- Topics: M2, M3, S4
- 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 6: Rates of Change and Tangent Lines
- Read the solutions to Mastery Quiz 4
- Optional worksheet on derivatives
- 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.
October 4: Linear Approximation and Rates of Change
- Due in class: Mastery Quiz 4
- 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 29: Trigonometric Derivatives and the Chain Rule
- Read the solutions to mastery quiz 3
- 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
September 27: Computing Derivatives
- Due in class: Mastery Quiz 3
- Topics: M1 and S2, S3
- Read Solutions to Mastery Quiz 2
- 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 22: Linear Approximation and the Derivative
- Due: in class: Mastery Quiz 2
- Topics: M1 and S1, S2
- Read Sections 2.1 and 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 20: Infinite Limits
- Mastery Quiz 1: M1 and S1
- Due in class
- 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: Trigonometry and the Squeeze Theorem
- Mastery Quiz 1: M1 and S1
- Due in class
- Read one of
- Section 1.6 of the online notes.
- See also Strang and Herman, section 2.3 on the Squeeze Theorem
- Optional videos
September 13: Computing Limits
- Edfinity due at midnight
-
- 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
September 8: 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.
- See also Strang and Herman:
- 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 1: 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 30: 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
- Mastery Quiz 2: M1 and S1, S2
- Mastery Quiz 3: M1 and S1, S2, S3
- Mastery Quiz 4: M1, M2, S3
- Mastery Quiz 5: M2, M3, S4
- Mastery Quiz 6: M2, M3, S4, S5
- Mastery Quiz 7
- Topics: M2, M3, M4, S5
- Solutions
- Mastery Quiz 8
- Topics: M3, M4, S6
- Solutions
- Mastery Quiz 9
- Topics: M4, S6, S7
- Solutions
- Mastery Quiz 10
- Topics: M4, S7, S8
- Solutions
- Mastery Quiz 11
- Topics: M5, S8
- Solutions
- Mastery Quiz 12
- Topics: M5, S9
- Solutions
Major Topics
- Computing Limits
- Computing Derivatives
- Linear Approximation
- Extrema and Optimization
- Integration
Secondary Topics
- Definition of a limit
- Squeeze theorem
- Definition of derivative
- Rates of change and models
- Related rates
- Curve sketching
- Numeric approximation
- Riemann sums
- Integral Applications [EDIT!]
Tests
- Midterm on October 20
- Final Exam
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 1231-16. To enroll, please follow the steps below:
- If you already have an Edfinity account from a previous course, please sign into it. Otherwise, go to step 2.
- Go to the following registration link: https://edfinity.com/join/E4YACCKC
- You will be prompted to pay (I believe the fee should be $25) and enroll in our section.
- 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.