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
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.
- 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.
- 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
- Optional videos
September 10: Edfinity due
September 9: Computing Limits
- Read one of
- Optional Videos
September 7: Formal Limits
- Read Section 1.4 of the online notes
- 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
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.
- Computing Limits
- Computing Derivatives
- Linear Approximation
- Extrema and Optimization
- Integral Applications
- Definition of a limit
- Squeeze theorem
- Definition of derivative
- Rates of change and models
- Related rates
- Curve sketching
- Numeric approximation
- Riemann sums
- Midterm around October 19
- 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 1231-10. 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/BXWHNRJU
- You will be prompted to pay (I believe the fee should be $25) and enroll in our section.
- Start working on your assignments :)
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.