## Daily Assignments

#### December 3: Mastery Quiz Due

#### December 2: Averages and Area

#### December 1: WeBWorK due

#### November 30: Integration by Substitution

- Read solutions to mastery quiz 11.
- Read one of:
- The notes §5.5-6
- Stewart §4.5
- Strang and Herman [§5.5](https://openstax.org/books/calculus-volume-1/pages/5-5-substitution

#### November 23: FTC2 and Antiderivatives

- Read one of:

#### November 23: FTC2 and Computing Integrals

#### November 19: Mastery Quiz Due

#### November 18: The Fundamental Theorem of Calculus, part 1

- Read one of:

#### November 17: WeBWorK due

#### November 16: The Definite Integral

#### November 12: Mastery quiz due

- Mastery Quiz 10 due at midnight

#### November 11: Integration: What is Area?

#### November 9: Quadratic Approximation

- Midterm Solutions are up
- Read the notes §4.1

#### November 5: Mastery quiz due

- Mastery Quiz 9 due at midnight

#### November 4: Optimization

#### November 3: WeBWorK due. No Recitation

#### November 2: Sketching Graphs

#### October 29: Mastery Quiz

- Mastery Quiz 8 due at midnight

#### October 28: Classifying Extrema

#### October 27: WeBWork due

#### October 26: Mean Value Theorem

#### No Mastery Quiz October 22

#### October 21: Maxima and Minima

#### October 20: Midterm due

- Midterm due at midnight.
- Practice Midterm
- Check the solutions to Quiz 6

#### October 19: No class

#### October 15: Mastery Quiz Due

- Mastery Quiz 6 due at midnight on Thursday, October 15

#### October 14: Related Rates

#### October 13: WeBWork due

#### October 12: Implicit Differentiation

- Check the solutions to quiz 5.
- 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 8: Mastery Quiz Due

#### October 7: Rates of Change and Physical Models

#### October 5: Tangent Lines and Linear Approximation

- Check the solutions to quiz 4.
- 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.

#### October 1

- Mastery Quiz 4 due at midnight on Thursday, October 1

#### September 30: Trigonometric Derivatives and the Chain Rule

- 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:

#### September 29: WeBWork due

#### September 28: Computing Derivatives

- Take a look at the quiz 3 solutions.
- Watch Essence of calculus, chapter 3: Derivative Formulas Through Geometry
- Read one of

#### September 24

- Mastery Quiz 3 due

#### September 23: Linear Approximation and the Derivative

- 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 22: WeBWork Due

#### September 21: 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 16: Trigonometric Limits

- 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 15: WeBWork and Mastery Quiz due

- Mastery Quiz 2 Due at noon Tuesday, September 15. Submit on Blackboard as
**one pdf file**.

#### September 14: 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
- [Math at Andrews on the Intermediate Value Theorem](https://www.youtube.com/watch?v=MPmtLX-7pUY

#### September 8/9: Formal Limits (Please try to complete before recitation)

- 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 2: 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

#### August 31: 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
- The Fundamental Theorem of Calculus and Antiderivatives
- The Evaluation Theorem and Definite 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
- Final Exam
- [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.

## 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.