Math 1231: Single-Variable Calculus I
Section 16
Fall 2022

Contact Info
Spring 2022

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

Office Hours:

Often in office:

Course Information

Lecture:

TA

TA Office Hours:

Official textbook:

Recitations

Section 48:

Section 49:

Section 50:

Daily Assignments

December 5: Areas and Averages

December 2: Recitation 13 on Integration

November 30: Integration by Substitution

November 28: Computing Integrals and the Fundamental Theorem of Calculus, Part II

November 21: Integral Properties and the Fundamental Theorem of Calculus, Part I

November 18: Recitation 12 on Riemann Sums

November 16: Riemann Sums and the Definite Integral

November 14: The Area Problem

November 9: Midterm 2

November 7: Physical Optimization Problems

November 4: Recitation 10 on Curve Sketching

November 2: The Shape of a Graph

October 31: Classifying Extrema

October 28: Recitation 9 on Extrema and the Mean Value Theorem

October 26: The Mean Value Theorem

October 24: Fall Break, No Class

October 19: Extrema and Critical Points

October 14: Recitation 7 on Derivative Applications

October 12: Implicit Differentiation

October 10: Rates of Change and Tangent Lines

October 7: Recitation 6 on Linear Approximation and Rates of Change

October 5: Midterm 1

October 3: Linear Approximation and Rates of Change

September 30: Recitation 5 on computing derivatives

September 28: The Chain Rule

September 26: Computing the Derivative

September 23: Recitation 4 on infinite limits and the derivative definition

September 21: The Derivative

September 19: Intro to the Derivative

September 6: Recitation 3 Advanced Limits

September 14: Infinite Limits

September 12: Trigonometric Limits and the Squeeze Theorem

September 9: Recitation 2 on Computing Limits

September 7: Continuity and Computing Limits

September 2: Recitation on Approximation

August 31: Approximation and Limits

August 29: Syllabus and Review of Functions


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.

Course notes

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.