Daily Assignments
December 15: Final Exam
- Final Exam
- Official time slot: 10:20 am - 12:20 pm
- I will be in the Blackboard course room during this time slot, as well as on Discord
- Practice Final
- I re-extended the second half of the WeBWork sets until the end of the week.
- Solutions to mastery quiz 13
December 14: Bonus Office Hours
- 11 am - 12:30 pm
- 5 pm - 6:30 pm
- Will be around on the discord basically any time for you to message me and ask questions
December 10: Volumes and Applications
- Mastery Quiz 13 due midnight
- We’re not going to have as much time to cover applications as I’d like. We’re going to touch on all this material only briefly, but I encourage you to read a bit more of it to try to see how integrals can be used in other contexts.
December 8: Secretly a Friday
- WeBWorK due
- Read solutions to mastery quiz 12
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 ε-δ 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 §1.1-3
- 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 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
- Integration by Substitution
- Areas and Averages
- Mastery Quiz 13 due midnight on Thursday, December 10
- 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
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 Calculus, 8th edition by James Stewart (ISBN-13: 978-1285740621, ISBN-10: 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.