Daily Assignments
December 3: Averages and Area
 Mastery Quiz 12 due
 Read one of:
December 1: Integration by Substitution
 WeBWorK due
 Read solutions to mastery quiz 11.
 Read one of:
November 24: FTC2 and Antiderivatives
 Read one of:
 Videos on Riemann sums:
November 19: The Fundamental Theorem of Calculus, part 1
 Mastery Quiz 11
 Read one of:
November 17: The Definite Integral
November 12: Integration: What is Area?
 Mastery Quiz 10 due at midnight

Read the solutions to quiz 9
 Read one of:
November 10: Quadratic Approximation
 Midterm Solutions are up
 Read the notes §4.1
November 5: Optimization
 Mastery Quiz 9 due at midnight
 Look at solutions to mastery quiz 8
 Read one of:
November 3: WeBWorK due, no class
October 29: Sketching Graphs
 Mastery Quiz 8 due at midnight
 Read one of:
October 27: Classifying Extrema
 WeBWork due
 Read one of:
October 22: Mean Value Theorem
October 20: No class; midterm due
 Midterm due at midnight.
 Practice Midterm
 Check the solutions to Quiz 6
October 15: Maxima and Minima
 Mastery Quiz 6 due at midnight on Thursday, October 15
 Take a look at the Practice Midterm and Solutions
 Read one of:
October 13: Related Rates
 Webwork due
 Check the solutions to quiz 5.
 Read one of
October 8: Implicit Differentiation
 Mastery Quiz 5 due at midnight
 Watch Essence of Calculus chapter 6: Implicit Differentiation, what’s going on here?
 Read one of
 You may want to look ahead to related rates. We’ll cover it in depth next class meeting, but we may start talking about it for this meeting:
October 6: Rates of Change and Physical Models
October 1: Tangent Lines and Linear Approximation
 Mastery Quiz 4 due at midnight.
 Read one of
 The notes §2.6 (updated: make sure §2.6 is titled “Tangent Lines and Linear Approximations”, and doesn’t have any subsections.)
 Stewart the “Tangents” section of §2.1 and §2.9
 Strang and Herman §3.1.1  3.1.2 and §4.2
 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 29: Trigonometric Derivatives and the Chain Rule
 WeBWork due today
 Take a look at the quiz 3 solutions.
 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 one of:
 You can do this worksheet (with solutions) for extra derivatives practice.
September 24: Computing Derivatives
 Mastery Quiz 3 due
 Read one of
 Watch Essence of calculus, chapter 3: Derivative Formulas Through Geometry
September 22: Linear Approximation and the Derivative
 WeBWork due!
 Read §2.1 of the notes.
 Read one of:
 §2.2 of the notes
 Stewart §2.2
 Strang and Herman §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.
 Take a look at the Solutions for quiz 2
September 17: Infinite Limits
 Read one of
 §1.7 of the notes.
 Stewart §1.5 the end bit on infinite limits, and §3.4 (yes, really, but feel free to skim the “precise definition” bit)
 Strang and Herman §2.2 the part on infinite limits and §4.6
September 15: Trigonometric Limits
 WeBWork due!

Mastery Quiz 2 Due at noon Tuesday, September 15. Submit on Blackboard as one pdf file.
 Read one of
 §1.6 of the notes.
 Strang and Herman The section the Squeeze Theorem in §2.3
 You can read Stewart §1.6 from Theorem 2 to the end, but it’s a really cursory treatment and we’re covering this topic in much more depth than Stewart does.
 Optional videos
September 10: Continuity and Computing Limits
 Read one of
 §1.5 of the notes.
 Stewart §1.6 through Example 10, and §1.8.
 Strang and Herman the rest of §2.3 and §2.4.
 Optional videos
September 8: Formal Limits
 Mastery Quiz 1 Due at noon Tuesday. Submit on Blackboard.
 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.)
 Read one of:
 Optional: Play with this Geogebra widget for visualizing εδ arguments.
September 3: Informal Continuity and Limits
 Read Section 1.3 of the online notes
 Optional: Watch The BEST explanation of limits and continuity on Youtube
 Optional: read Stewart §1.5 or Strang and Herman §2.2
September 1: Syllabus and Review of Functions
 Please read the syllabus
 Claim your account on WeBWork (Username is your GWU email, password is GWID)
 Read Professor Bonin’s advice on study skills
 Read Section 1.1 of the online notes (about a page)
 Skim one of:
 Stewart §1.13
 Strang and Herman §1.13
 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 yearlong sequence in singlevariable calculus. The main topics are limits and continuity; differentiation and integration of algebraic and trigonometric functions; and applications of these ideas. This corresponds to Chapters 1–5 of Stewart and 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
The topics for the quizzes are:
 Informal Continuity and Limits
 Formal Limits
 Computing Limits
 Trigonometric Limits
 Infinite Limits
 Definition of a Derivative
 Basics of Computing Derivatives
 Trigonometry and the Chain Rule
 Linear Approximations and Tangent Lines
 Rates of Change
 Implicit Differentiation
 Related Rates
 Critical Points and Global Extrema
 First and Second Derivative Tests
 Curve Sketching
 Optimization
 Approximation (Quadratic and Newton’s Method)
 Area and Riemann Sums
 Integrals and the Fundamental Theorem of Calculus
 The Evaluation Theorem and Indefinite Integrals
 Mastery Quiz 12 due midnight on Thursday, December 3
 Mastery Quiz 11 due midnight on Thursday, November 19
 Mastery Quiz 10 due midnight on Thursday, November 12
 Mastery Quiz 9 due midnight on Thursday, November 5
 Mastery Quiz 8
 No mastery quiz 7
 Mastery Quiz 6 due at midnight on Thursday, October 15
 Mastery Quiz 5 due at midnight on Thursday, October 8
 Mastery Quiz 4 due at midnight on Thursday, October 1
 Mastery Quiz 3 due at midnight on Thursday, September 24
 Mastery Quiz 2 Due at noon Tuesday, September 15. Submit on Blackboard as one pdf file.
 Mastery Quiz 1 Due at noon Tuesday. Submit on Blackboard.
Tests
 Midterm due midnight on Tuesday, October 20
 Midterm due midnight on Tuesday, October 20
 Final Exam
 [Practice Final]
 [Solutions]
Graphing calculators will not be allowed on tests. Scientific, nonprogrammable calculators will be allowed. I will have some to share, but not enough for everyone.
Textbook
The official textbook for Math 1231 is Calculus, 8th edition by James Stewart (ISBN13: 9781285740621, ISBN10: 1285740629). It is a very good (and very expensive) textbook. If you go on to take Calculus 2 or Multivariable Calculus at GW, you will also need this book for those classes.
Another perfectly fine book is Calculus 1, by Gilbert Strang and Jed Herman. It is available for free online here.
I will be loosely following Stewart, and will attempt to give references to both books whenever I can. I will not assign problems from either book, but both will contain many problems for if you need extra practice.
Do not purchase Calculus: Early Trancendentals, also by Stewart: it is not the same book as Calculus and it is not used in any mathematics course at GW.
This section of Math 1231 will not use WebAssign.