Math 1231: Single-Variable Calculus I
Section 10
Fall 2020

Contact Info
Fall 2020

Office: Blackboard
Email: jaydaigle@gwu.edu

Office Hours:

Course Information

Lecture:

Textbook:

Daily Assignments

December 3: Averages and Area

December 1: Integration by Substitution

Slides

November 24: FTC2 and Antiderivatives

Slides

November 19: The Fundamental Theorem of Calculus, part 1

Slides

November 17: The Definite Integral

Slides

November 12: Integration: What is Area?

Slides

November 10: Quadratic Approximation

Slides

November 5: Optimization

Slides

November 3: WeBWorK due, no class

October 29: Sketching Graphs

Slides

October 27: Classifying Extrema

Slides

October 22: Mean Value Theorem

Slides

October 20: No class; midterm due

October 15: Maxima and Minima

Slides

Slides

October 8: Implicit Differentiation

Slides

October 6: Rates of Change and Physical Models

Slides

October 1: Tangent Lines and Linear Approximation

Slides

September 29: Trigonometric Derivatives and the Chain Rule

Slides

September 24: Computing Derivatives

Slides

September 22: Linear Approximation and the Derivative

Slides

September 17: Infinite Limits

Slides

September 15: Trigonometric Limits

Slides

September 10: Continuity and Computing Limits

Slides from Lecture

September 8: Formal Limits

Slides from Lecture

September 3: Informal Continuity and Limits

Slides from Class

September 1: 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 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:

  1. Informal Continuity and Limits
  2. Formal Limits
  3. Computing Limits
  4. Trigonometric Limits
  5. Infinite Limits
  6. Definition of a Derivative
  7. Basics of Computing Derivatives
  8. Trigonometry and the Chain Rule
  9. Linear Approximations and Tangent Lines
  10. Rates of Change
  11. Implicit Differentiation
  12. Related Rates
  13. Critical Points and Global Extrema
  14. First and Second Derivative Tests
  15. Curve Sketching
  16. Optimization
  17. Approximation (Quadratic and Newton’s Method)
  18. Area and Riemann Sums
  19. Integrals and the Fundamental Theorem of Calculus
  20. The Evaluation Theorem and Indefinite Integrals

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 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.