Math 1231: Single-Variable Calculus I
Section 12
Fall 2025

Contact Info
Spring 2025

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

Office Hours: TBD; tentatively

Course Information

Lecture:

  • MW 11:10 AM–12:25 PM
  • Phillips B152

TA

TA Office Hours:

  • W 3:30 – 5:30
  • TBD

Official textbook:

Recitations

Section 33:

  • T 8:00 AM–8:50 AM
  • Duques 362

Section 34:

  • T 9:35 AM–10:25 AM
  • Duques 362

Section 35:

  • T 11:10 AM–12 Noon
  • Gelman B103

Course Information

Lecture:

  • MW 11:10 AM–12:25 PM
  • Phillips B152

TA

TA Office Hours:

  • W 3:30 – 5:30
  • TBD

Official textbook:

Recitations

Section 33:

  • T 8:00 AM–8:50 AM
  • Duques 362

Section 34:

  • T 9:35 AM–10:25 AM
  • Duques 362

Section 35:

  • T 11:10 AM–12 Noon
  • Gelman B103

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 26: Recitation 1 on Estimation
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.
Week 2: September 1 – 5
September 1: No Classes for Labor Day
September 2: Recitation 2 on Estimation and Continuity
  • [Recitation 2 Worksheet]
September 3: Continuity and Computing Limits
Week 3: September 8 – 12
September 8: More on Limits
September 9: Recitation 3 on Advanced Limits
  • [Recitation 3 Worksheet]
September 10: Infinite Limits
Week 4: September 15 – 19
September 15: Intro to Derivatives
September 16: Recitation 4 on infinity and derivatives
  • Skills quiz on M1: computing limits
    • Covers all our limit computation techniques, starting from September 3
  • [Recitation 4 Worksheet]
September 17: Computing Derivatives
  • Mastery Quiz 3 due
    • Topics: M1, S2
  • Read Section 2.3 of the online notes
    • See also Strang and Herman, section 3.3.
Week 5: September 22 – 26
September 22: Trig Derivatives and Chain Rule
  • Read the [solutions] to mastery quiz 3
  • 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: Recitation 5 on computing derivatives
  • [Recitation 5 Worksheet]
September 24: Linear Approximations and Speed
  • Mastery Quiz 4 due
    • Topics: M1, M2, S2
  • Read Sections 2.6 and 2.7.1 of the online notes
    • See also Strang and Herman, sections 4.2 and 3.4
Week 6: September 29 – October 3
September 29: Rates of Change and Tangent Lines
  • Read the [solutions] to Mastery Quiz 4
  • 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: Recitation 6 on Linear Approximation and Rates of Change
  • Skills Quiz 2 on M2: Computing Derivatives
  • [Recitation 6 Worksheet]
October 1: Implicit Differentiation and Tangent Lines
  • Mastery Quiz 5 due
    • Topics: M1, M2, S3, S4
  • Look at Practice Midterm 1
  • Read Section 2.9 of the online notes
    • See also Strang and Herman, section 3.8
Week 7: October 6 – 8
October 6: Midterm 1
October 7: Recitation 7 on Implicit Differentiation
  • [Recitation 7 Worksheet]
  • Mastery Quiz 6 due
    • Topics: M2, S3, S4
  • Read the [Solutions to Midterm 1]
  • Read Section 2.10 of the online notes
    • See also Strang and Herman, section 4.1
Week 8: October 13 – 17
October 13: Absolute Extrema
  • Read the [solutions] to Mastery Quiz 6
  • Read Section 3.1 of the online notes
    • See also Strang and Herman, section 4.3
  • [Recitation 8 Worksheet]
October 15: Mean Value Theorem
  • Mastery Quiz 7 due
    • Topics: M2, S5, S6
  • Read Section 3.2 of the online notes
    • See also Strang and Herman, section 4.4
Week 9: October 20 – 24
October 20: Classifying Extrema
  • Read the [solutions] to Mastery Quiz 7
  • Read Section 3.3 of the online notes
  • See also Strang and Herman, section 4.5
October 21: Recitation 9 on Extrema
  • [Recitation 9 Worksheet]
October 22: Concavity and Curve Sketching
  • Mastery Quiz 8 due
    • Topics: M3, S5, S6
  • Read Section 3.4-5 of the online notes
    • See also Strang and Herman, section 4.5
Week 10: October 27 – 31
October 27: Physical Optimization Problems
  • Read the [solutions] to Mastery Quiz 8
  • Read Section 3.6 of the online notes
  • See also Strang and Herman, section 4.7
October 28: Recitation 10 on Curve Sketching
  • Skills Quiz 3 on M3: Optimization
  • [Recitation 10 Worksheet]
October 29: The Area Problem
  • Mastery Quiz 9 due
    • Topics: M3, S7, S8
  • 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.
Week 11: November 3 – 7
November 3: The Definite Integral
  • Read the [solutions] to Mastery Quiz 9
  • Read Section 5.2 of the online notes
  • See also Strang and Herman, section 5.2
November 4: Recitation 11 on Physical Optimization
  • [Recitation 11 Worksheet]
November 5: The Fundamental Theorem of Calculus, Part 1
Week 12: November 10 – 14
November 10: Midterm 2
November 11: Recitation 12 on Riemann Sums
  • [Recitation 12 Worksheet]
November 12: Computing Integrals and the FTC Part 2
  • Mastery Quiz 11 due
    • Topics: M3, S9
  • Read Section 5.4 of the online notes
    • See also Strang and Herman, section 5.4
Week 13: November 17 – 21
November 17: Integration by Substitution
  • Read the [solutions] to Mastery Quiz 11
  • Read Section 5.5 of the online notes
    • See also Strang and Herman, section 5.5
November 18: Recitation 13 on Computing Integrals
  • [Recitation 13 Worksheet]
November 19: Finding Areas
  • Mastery Quiz 12 due
    • Topics: M4, S9
  • Read Section 6.1 of the online notes
    • See also Strang and Herman, section 6.1
Thanksgiving Break: November 24-28

No class! Happy Thanksgiving!

Week 14: December 1 – 5
December 1: Physical and Economic Applications
  • Read the [solutions] to mastery quiz 12
  • Read the [solutions] to Midterm 2
  • Read section 6.2 of the online notes
    • See also Strang and Herman, section 6.5
December 2: Recitation 14 on Integral Applications
  • Skills Quiz 4 on M4: Integration
  • [Recitation 14 Worksheet]
December 3: Volumes by Slices
  • Mastery Quiz 13 due
    • Topics: M4, S10
  • Read Section 6.3 of the online notes
    • See also Strang and Herman, section 6.2
Week 15: December 8-10
December 8: Volumes by cylindrical shells
  • Read the [solutions] to mastery quiz 13
  • Read Section 6.4 of the online notes
    • See also Strang and Herman, section 6.3
Finals Week
Reading Days
  • Optional Mastery Quiz 14 due Wednesday, December 10
    • Topics: M4, S10
  • Read the [solutions] to mastery quiz 14
Office Hours Schedule
  • TBA close to finals week
Final Exam Tentatively Monday, December 15, 10:20 AM – 12:20 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.