# Math 1231: Single-Variable Calculus I Section 16 Fall 2021

#### Contact Info Fall 2021

Office: Phillips Hall 720E
Email: jaydaigle@gwu.edu

Office Hours:

• MW 3:00–4:30

Often in office:

• MW 2:00–4:30
• TR 2:15–3:15

#### Course Information

Lecture:

• MW 4:45 PM–6:00 PM
• MPA 309

TA

TA Office Hours:

Official textbook:

###### Recitations

Section 48:

• F 8:00 AM–8:50 AM
• MPA 302

Section 49:

• F 9:35 AM–10:25 AM
• MPA 302

Section 50:

• F 11:10 AM–12 Noon
• MPA 302

## Daily Assignments

#### 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 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

#### 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

#### October 18: Maxima and Minima

• Read section 2.10 of the notes §2.10

#### 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!)

#### September 15: Trigonometry and the Squeeze Theorem

• Mastery Quiz 1: M1 and S1
• Due in class
• 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
• 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
• section 2.5 (up until the one-sided and infinite limits)
• Section 2.3 up through Example 2.15 and Checkpoint 2.11.
• 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.

## 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.

## Mastery Quizzes

#### Major Topics

1. Computing Limits
2. Computing Derivatives
3. Linear Approximation
4. Extrema and Optimization
5. Integration

#### Secondary Topics

1. Definition of a limit
2. Squeeze theorem
3. Definition of derivative
4. Rates of change and models
5. Related rates
6. Curve sketching
7. Numeric approximation
8. Riemann sums
9. 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: