Math 1231: Single-Variable Calculus I Section 13 Fall 2022

Contact Info Fall 2022

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

Office Hours:

• TR 2:00–4:00

Often in office:

• MW 2:30–4:20

Course Information

Lecture:

• TR 4:45 PM–6:00 PM
• Corcoran 101A

TA

TA Office Hours:

Official textbook:

Recitations

Section 39:

• W 8:00 AM–8:50 AM
• Rome 204

Section 40:

• W 9:35 AM–10:25 AM
• Rome 204

Section 41:

• W 11:10 AM–12 Noon
• Rome 204

Daily Assignments

December 20 at 5:20 PM: Final Exam

• Final Exam on Tuesday, December 20, 5:20 - 7:20 PM
• Test Rules:
• You are not allowed to consult books or notes during the test, but you may use a one-page, two-sided, handwritten cheat sheet you have made for yourself ahead of time.
• You may not use a calculator. You may leave answers unsimplified, except you should compute trigonometric functions as far as possible.
• The exam covers all the mastery topics from this course, but primarily the major topics and topic S8.
• Each part of each major topic is worth 10 points. The question on topic S8 is worth 10 points.
• The questions on topics S1 through S6 are optional. Answering one correctly can earn you up to two bonus points on the test. More importantly, answering one correctly can raise your overall mastery score.
• Solutions to Mastery Quiz 11.

December 6: Physical Applications

• Read the Solutions to Mastery Quiz 10
• Read sections 6.2-3 of the online notes.

November 22: Computing Integrals and the Fundamental Theorem of Calculus, Part II

• Read section 5.4 of the online notes.

November 15: Riemann Sums and the Definite Integral

• The class recording is posted under “Zoom Meetings” on Blackboard
• Read section 5.2 of the online notes.

November 8: Midterm 2

• Practice Midterm 2

October 18: Extrema and Critical Points

• Read Section 3.1 of the online notes.

October 6: Rates of Change and Tangent Lines

• Read Section 2.7.2 and 2.8 of the online notes.
• See also Strang and Herman, section 3.4 and also you can look back at 3.1.1-3.1.2

October 4: Midterm 1

• You may bring a one-sided, handwritten cheat sheet on letter-size or A4-size paper. You may not bring a calculator.
• See the solutions to mastery quiz 4
• Practice Midterm 1

September 6: Continuity and Computing Limits

• Read Section 1.4 of the online notes
• You can also consult Strang and Herman 2.3 (Except 2.3.6) and 2.4.
• Optional Videos:

September 1: Approximation and Limits

• Read Section 1.3 of the online notes
• You can also consult Strang and Herman 2.2 and 2.5.
• Optional: Play with this Geogebra widget for visualizing the relationships between ε and δ for different functions.
• Optional videos:
• 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.
• Khan Academy has a series of videos that might be helpful. I’m linking the second, but the third and fourth in this series are also good for understanding limit arguments better.

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
6. Integral Applications

Secondary Topics

1. Estimation
2. Squeeze theorem
3. Definition of derivative
4. Rates of change and models
5. Related rates
6. Curve sketching
7. [Canceled for time]
8. Riemann sums

Tests

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 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.

We will be using a (free!) online homework system called WeBWorK this term. You can access it by going to Blackboard, then to “Course Links”, and clicking the WeBWorK link. This will automatically create an account for you and log you in. You may continue to log in through Blackboard, or if you wish you may create a password within WeBWorK to log in directly.