Math 1231: Single-Variable Calculus I
Section 11
Fall 2025

Contact Info
Spring 2025

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

Office Hours:

Course Information

Lecture:

  • MW 3:45 PM–5:00 PM
  • Phillips B156

TA

TA Office Hours:

  • MW 2 – 3 PM
  • Phillips 720G

Official textbook:

Recitations

Section 33:

  • F 8:00 AM–8:50 AM
  • Bell 107

Section 34:

  • F 9:35 AM–10:25 AM
  • MPA 302

Section 35:

  • F 11:10 AM–12 Noon
  • Monroe B33

Course Information

Lecture:

  • MW 3:45 PM–5:00 PM
  • Phillips B156

TA

TA Office Hours:

  • MW 2 – 3 PM
  • Phillips 720G

Official textbook:

Recitations

Section 33:

  • F 8:00 AM–8:50 AM
  • Bell 107

Section 34:

  • F 9:35 AM–10:25 AM
  • MPA 302

Section 35:

  • F 11:10 AM–12 Noon
  • Monroe B33

Daily Assignments

Optional Review Stuff

One of the biggest sources of difficulty in calculus is weak or underprepared skills at algebra and trigonometry. If you want to succeed in this course, you should be comfortable with:

  • Multiplying and factoring polynomials;
  • Multiplying and dividing fractions and rational functions;
  • Working with exponents;
  • Working with trigonometric functions and the unit circle.

I don’t have any organized review materials for these topics, but if you want to brush up on them, you may want to look at:

Week 1: August 25-29
August 25: Syllabus and Functions
August 27: Estimation
  • Read Section 1.2-3 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.
    • Here’s another video by Krista King that some people found helpful.
August 29: Recitation 1 on Estimation
Week 2: September 1 – 5
September 1: No Classes for Labor Day
September 3: Continuity and Computing Limits
September 5: Recitation 2 on Computing Limits
Week 3: September 8 – 12
September 8: More on Limits
September 10: Infinite Limits
September 12: Recitation 3 on Advanced Limits
Week 4: September 15 – 19
September 15: Intro to Derivatives
September 17: Computing Derivatives
September 19: Recitation 4 on taking derivatives
Week 5: September 22 – 26
September 22: Trig Derivatives and Chain Rule
September 24: Linear Approximations and Speed
  • Read the solutions to Mastery Quiz 4
  • Read Sections 2.6 and 2.7.1 of the online notes
    • See also Strang and Herman, sections 4.2 and 3.4
September 26: Recitation 5 on linear approximation
Week 6: September 29 – October 3
September 29: Rates of Change and Tangent Lines
October 1: Implicit Differentiation and Tangent Lines
  • Read the solutions to Mastery Quiz 5
  • Look at Practice Midterm 1
  • Read Section 2.9 of the online notes
    • See also Strang and Herman, section 3.8
October 3: Recitation 6 on Rates of Change
Week 7: October 6 – 8
October 6: Midterm 1
October 10: No Recitation for Fall Break
Week 8: October 13 – 17
October 13: Absolute Extrema
October 15: Mean Value Theorem
October 17: Recitation 7 on absolute extrema and the Mean Value Theorem
Week 9: October 20 – 24
October 20: Classifying Extrema
October 22: Concavity and Curve Sketching
October 24: Recitation 8
Week 10: October 27 – 31
October 27: Physical Optimization Problems
October 29: The Area Problem
October 31: Recitation 9 on Physical Optimization
Week 11: November 3 – 7
November 3: The Definite Integral
November 5: The Fundamental Theorem of Calculus, Part 1
November 7: Recitation 10 on Riemann Sums
Week 12: November 10 – 14
November 10: Midterm 2
November 12: Computing Integrals and the FTC Part 2
November 14: Recitation 11 on integration
Week 13: November 17 – 21
November 17: Integration by Substitution
November 19: Finding Areas
November 21: Recitation 12 on substitution and area
Thanksgiving Break: November 24-28

No class! Happy Thanksgiving!

Week 14: December 1 – 5
December 1: Physical and Economic Applications
December 3: Volumes by Slices
December 5: Recitation 13 on integral applications
Week 15: December 8-10
December 8: Volumes by cylindrical shells
December 10: Recitation 14 on Volumes
  • [Recitation 14 Worksheet]
Finals Week
Reading Days
Office Hours Schedule
  • Tuesday December 9: Noon – 2 PM
  • Wednesday December 10: 2 – 4 PM
  • Thursday December 11: 11 AM – 2 PM
  • Sunday December 14: 1 – 4 PM
  • Tuesday December 16: 11:30 AM – 1:30 PM
Final Exam Wednesday, December 17, 5:20 – 7:20 PM

Course notes

Mastery Quizzes

Major Topics

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

Secondary Topics

  1. Estimation
  2. Definition of derivative
  3. Linear Approximation
  4. Rates of change and models
  5. Implicit Differentiation
  6. Related rates
  7. Curve sketching
  8. Physical Optimization Problems
  9. Riemann sums
  10. Integral Applications

Tests

Calculators will not be allowed on tests.

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. ll 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.

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.