Math 1231: Single-Variable Calculus I
Section 11
Fall 2026

Contact Info
Fall 2026

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

Office Hours:

Course Information

Lecture:

  • MW 3:45 PM–5:00 PM
  • 1957 E St B12

TA

TA Office Hours:

  • TBD
  • TBD

Official textbook:

Recitations

Section 33:

  • F 8:00 AM–8:50 AM
  • Phillips 110

Section 34:

  • F 9:35 AM–10:25 AM
  • MPA 302

Section 35:

  • F 11:10 AM–12 Noon
  • Bell 106

Course Information

Lecture:

  • MW 3:45 PM–5:00 PM
  • 1957 E St B12

TA

TA Office Hours:

  • TBD
  • TBD

Official textbook:

Recitations

Section 33:

  • F 8:00 AM–8:50 AM
  • Phillips 110

Section 34:

  • F 9:35 AM–10:25 AM
  • MPA 302

Section 35:

  • F 11:10 AM–12 Noon
  • Bell 106

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 24-28
August 24: Syllabus and Functions
August 26: 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 28: Recitation 1 on Estimation
  • [Recitation 1 Worksheet]
  • Mastery Quiz 1 due
    • Topics: S1
    • [Single-Sheet Worksheet]
    • [Printable Worksheet]
Week 2: August 31 – September 4
August 31: Continuity and Computing Limits
September 2: More on Limits
September 4: Recitation 2 on Computing Limits
  • [Recitation 2 Worksheet]
  • Mastery Quiz 2 due
    • Topics: M1, S1
    • [Single-Sheet Worksheet]
    • [Printable Worksheet]
Week 3: September 7 – 11
September 7: No Class for Labor Day
September 9: Infinite Limits
September 11: Recitation 3 on Advanced Limits
  • [Recitation 3 Worksheet]
  • Mastery Quiz 3 due
    • Topics:
    • [Single-Sheet Worksheet]
    • [Printable Worksheet]
Week 4: September 14 – 18
September 14: Intro to Derivatives
September 16: Computing Derivatives
  • Read Section 2.3 of the online notes
    • See also Strang and Herman, section 3.3.
September 18: Recitation 4 on taking derivatives
  • [Recitation 4 Worksheet]
  • Mastery Quiz 4 due
    • Topics:
    • [Single-Sheet Worksheet]
    • [Printable Worksheet]
Week 5: September 21 – 25
September 21: Trig Derivatives and Chain Rule
  • Read the [solutions] to Mastery Quiz 4
  • Read Section 2.4-5 of the online notes
    • See also Strang and Herman, sections 3.5 and 3.6.
  • It is very important to practice taking derivatives quickly and easily.
September 23: Linear Approximations and Speed
  • Read Sections 2.6 and 2.7.1 of the online notes
    • See also Strang and Herman, sections 4.2 and 3.4
September 25: Recitation 5 on linear approximation
  • [Recitation 5 Worksheet]
  • Mastery Quiz 5 due
    • Topics:
    • [Single-Sheet Worksheet]
    • [Printable Worksheet]
Week 6: September 28 – October 2
September 28: Rates of Change and Tangent Lines
  • Read the [solutions] to Mastery Quiz 5
  • Read Sections 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
September 30: Implicit Differentiation and Tangent Lines
  • Look at Practice Midterm 1
  • Read Section 2.9 of the online notes
    • See also Strang and Herman, section 3.8
October 2: Recitation 6 on Rates of Change
  • [Recitation 6 Worksheet]
  • Mastery Quiz 6 due
    • Topics:
    • [Single-Sheet Worksheet]
    • [Printable Worksheet]
Week 7: October 5 – 9
October 5: Midterm 1
  • [Recitation 7 Worksheet]
  • Mastery Quiz 7 due
    • Topics:
    • [Single-Sheet Worksheet]
    • [Printable Worksheet]
Week 8: October 12 – 16
October 12: No Class for Fall Break
October 14: Absolute Extrema
  • Read the [solutions] to Mastery Quiz 7
  • Read Section 3.1 of the online notes
    • See also Strang and Herman, section 4.3
October 16: Recitation 8
  • [Recitation 8 Worksheet]
  • Mastery Quiz 8 due
    • Topics:
    • [Single-Sheet Worksheet]
    • [Printable Worksheet]
Week 9: October 19 – 23
October 19: Mean Value Theorem
  • Read the [solutions] to Mastery Quiz 8
  • Read Section 3.2 of the online notes
    • See also Strang and Herman, section 4.4
October 21: Classifying Extrema
  • Read Section 3.3 of the online notes
  • See also Strang and Herman, section 4.5
October 23: Recitation 9 on Physical Optimization
  • [Recitation 9 Worksheet]
  • Mastery Quiz 9 due
    • Topics:
    • [Single-Sheet Worksheet]
    • [Printable Worksheet]
Week 10: October 26 – 30
October 26: Concavity and Curve Sketching
  • Read the [solutions] to Mastery Quiz 9
  • Read Section 3.4-5 of the online notes
    • See also Strang and Herman, section 4.5
October 28: Physical Optimization Problems
October 30: Recitation 10 on Riemann Sums
  • [Recitation 10 Worksheet]
  • Mastery Quiz 10 due
    • Topics:
    • [Single-Sheet Worksheet]
    • [Printable Worksheet]
Week 11: November 2 – 6
November 2: The Area Problem
  • Read the [solutions] to Mastery Quiz 10
  • Read Section 5.1 of the online notes
  • See also Strang and Herman, section 5.1
  • Watch the first 8 minutes or so of Essence of Calculus Episode 8
  • This GeoGebra widget is helpful for visualizing what’s going on.
  • You may also wish to skim Section 4 of the notes, which we won’t be covering in class.
November 4: The Definite Integral
  • Read Section 5.2 of the online notes
  • See also Strang and Herman, section 5.2
November 6: Recitation 11 on integration
  • [Recitation 11 Worksheet]
  • Mastery Quiz 11 due
    • Topics:
    • [Single-Sheet Worksheet]
    • [Printable Worksheet]
Week 12: November 9 – 13
November 9: Midterm 2
November 11: The Fundamental Theorem of Calculus, Part 1
November 13: Recitation 12 on substitution and area
  • [Recitation 12 Worksheet]
  • Mastery Quiz 12 due
    • Topics:
    • [Single-Sheet Worksheet]
    • [Printable Worksheet]
Week 13: November 16 – 20
November 16: Computing Integrals and the FTC Part 2
  • Read the [solutions] to Mastery Quiz 12
  • Read Section 5.4 of the online notes
    • See also Strang and Herman, section 5.4
November 18: Integration by Substitution
  • Read Section 5.5 of the online notes
    • See also Strang and Herman, section 5.5
November 20: Recitation 13 on integral applications
  • [Recitation 13 Worksheet]
  • Mastery Quiz 13 due
    • Topics:
    • [Single-Sheet Worksheet]
    • [Printable Worksheet]
Thanksgiving Break: November 23-27

No class! Happy Thanksgiving!

Week 14: November 30 – December 4
November 30: Finding Areas
  • Read the [solutions] to mastery quiz 13
  • Read Section 6.1 of the online notes
    • See also Strang and Herman, section 6.1
December 2: Physical and Economic Applications
  • Read section 6.2 of the online notes
    • See also Strang and Herman, section 6.5
December 4: Recitation 14 on Volumes
  • [Recitation 14 Worksheet]
  • Mastery Quiz 14 due
    • Topics:
    • [Single-Sheet Worksheet]
    • [Printable Worksheet]
Week 15: December 7 – 9
December 7: Volumes by Slices
  • Read the [solutions] to mastery quiz 14
  • Read Section 6.3 of the online notes
    • See also Strang and Herman, section 6.2
December 9: Volumes by cylindrical shells
  • Read Section 6.4 of the online notes
    • See also Strang and Herman, section 6.3
Finals Week
Reading Days
  • Read the [solutions] to mastery quiz 14
Office Hours Schedule
  • TBD
Final Exam TBD as scheduled by registrar

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.