Math 1232: Single-Variable Calculus II
Section 13
Spring 2026

Contact Info
Spring 2025

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

Office Hours:

Course Information

Lecture:

  • TR 2:20 PM–3:35 PM
  • Funger 223

TA

TA Office Hours:

  • R 12–2
  • Phillips 720G

Official textbook:

Recitations

Section 33:

  • W 8:00 AM–8:50 AM
  • 1776 G C-106

Section 34:

  • W 9:35 AM–10:25 AM
  • 1776 G C-112

Section 35:

  • W 11:10 AM–12 Noon
  • Phillips 348

Course Information

Lecture:

  • TR 2:20 PM–3:35 PM
  • Funger 223

TA

TA Office Hours:

  • R 12–2
  • Phillips 720G

Official textbook:

Recitations

Section 33:

  • W 8:00 AM–8:50 AM
  • 1776 G C-106

Section 34:

  • W 9:35 AM–10:25 AM
  • 1776 G C-112

Section 35:

  • W 11:10 AM–12 Noon
  • Phillips 348

Daily Assignments

Optional Review Stuff

Going into this course it’s really important that you have strong skills in derivatives and integrals from Calculus 1. You should try to brush up on those before the course starts. You can find materials on this in the course textbook, and specifically in

You should also 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: January 12 – 16
January 13: Syllabus and Inverse Functions
January 14: Recitation on Invertible Functions
  • [Recitation 1 Worksheet]
January 15: The Exponential and the Logarithm
Week 2: January 19 – 23
January 20: Derivatives of the Logarithm and Exponential
January 21: Recitation 2 on Invertible Functions
  • [Recitation 2 Worksheet]
January 22: Integrals Involving the Logarithm and Exponential
Week 3: January 26 – 30
January 27: Inverse Trigonometric Functions
January 28: Recitation 3 on Inverse Trig Functions and Transcendental Limits
  • [Recitation 3 Worksheet]
January 29: L’Hospital’s Rule
Week 4: February 2 – 6
February 3: Integration by Parts
February 4: Recitation 4 on Integration by Parts and Trig Integrals
  • [Recitation 4 Worksheet]
February 5: Trigonometric Integrals
Week 5: February 9 – 13
February 10: Integration by Partial Fraction Decomposition
February 11: Recitation 5 on Partial Fractions and Numeric Integration
  • [Recitation 5 Worksheet]
February 12: Numeric Integration
  • Mastery Quiz 4 due
    • Topics: M1, M2, S2
  • Read section 2.4 of the online notes
    • See also Strang and Herman §3.6
Week 6: February 16 – 20
February 17: Improper Integrals
February 18: Recitation 6 on Improper Integrals
  • [Recitation 6 Worksheet]
February 19: Arc Lengths and Surface Area
Week 7: February 23 – 27
February 24: Differential Equations
  • Read the [solutions] to Mastery Quiz 5
  • Read section 3.3 of the online notes
  • Bonus content
    • We can use differential equations to model epidemics. In 2020 I wrote a blog post about the SIR model of epidemics, which is useful for thinking about how diseases spread
    • 3Blue1Brown series on differential equations
    • I encourage you to skim section 4.2 of Strang and Herman. It covers material that’s really useful for both understanding and applying differential equations that we don’t really have time to cover in this course.
February 25: Recitation 7 on Geometric Integral Applications
  • [Recitation 7 Worksheet]
February 26: Solving Separable Differential Equations
Week 8: March 2 – 6
March 3: Midterm
March 4: Recitation 8 on differential equations
  • [Recitation 8 Worksheet]
March 5: Sequences
Spring Break: March 9-13

No class! Go have fun!

Week 9: March 16 – 20
March 17: Series
March 18: Recitation 9 on Elementary Series
  • [Recitation 9 Worksheet]
March 19: The Divergence Test and the Integral Test
  • Mastery Quiz 8 due
    • Topics: S6, S7
  • Read sections 4.5 and 4.6 of the online notes
Week 10: March 23 – March 27
March 24: Comparison Tests
March 25: Recitation 10 on Series Convergence
  • [Recitation 10 Worksheet]
March 26: The Ratio Test
  • Mastery Quiz 9 due
    • Topics: M3, S7
  • Read sections 4.5 and 4.6 of the online notes
Week 11: March 30 – April 3
March 31: Power Series
  • Read the [solutions] to Mastery Quiz 9
  • Read section 5.1 of the online notes
    • See also Strang and Herman §6.1
April 1: Recitation 11 on Power Series
  • [Recitation 11 Worksheet]
April 2: Power Series as Functions
  • Mastery Quiz 10 due
    • Topics: M3, S8
  • Read sections 5.2 of the online notes
    • See also Strang and Herman §6.2
Week 12: April 6 – 10
April 7: Taylor Series
  • Read the [solutions] to Mastery Quiz 10
  • Read section 5.3 of the online notes
    • See also Strang and Herman §6.3
April 8: Recitation 12 on Taylor Series
  • [Recitation 12 Worksheet]
April 9: Computing Taylor Series
  • Mastery Quiz 11 due
    • Topics: M3, M4, S8
  • Read sections 5.4 of the online notes
    • See also: Strang and Herman §6.4
Week 13: April 13 – April 17
April 14: Applications of Taylor Series
April 15: Recitation 13 on Taylor Series Applications
  • [Recitation 13 Worksheet]
April 16: Parametric Coordinates
  • Mastery Quiz 12 due
    • Topics: M3, M4, S9
  • Read sections 6.1 of the online notes
Week 14: April 20 – 24
April 21: Polar Coordinates
  • Read the [solutions] to mastery quiz 12
  • Read section 6.2 of the online notes
April 22: Recitation 14 on Parametrization
  • [Recitation 14 Worksheet]
April 23: Fun with Series
Finals Week
April 30: Optional Mastery Quiz Due
  • Read the [solutions] to mastery quiz 13
  • Optional Mastery Quiz 14 due Thursday, May 1
    • Topics: M4, S10
  • Read the [solutions] to mastery quiz 14
Office Hours Schedule
  • TBD closer to finals week
Final Exam: TBD, as scheduled by the registrar
  • Practice Final
  • You are not allowed to consult books or notes during the test, but you may use a one-page, two-sided, handwritten cheat sheet you have made for yourself ahead of time. You must have written on the physical sheet you bring to the test in your own handwriting.

Course notes

Mastery Quizzes

Major Topics

  1. Calculus of Transcendental Functions
  2. Advanced Integration Techniques
  3. Series Convergence
  4. Taylor Series

Secondary Topics

  1. Invertible Functions
  2. L’Hospital’s Rule
  3. Numeric Integration
  4. Improper Integrals
  5. Arc Length and Surface Area
  6. Differential Equations
  7. Sequences and Series
  8. Power Series
  9. Applications of Taylor Series
  10. Parametrization

Tests

Calculators will not be allowed on tests.

Textbook

The official textbook for Math 1232 is OpenStax Calculus Volume 2 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. During the first few weeks of the course we will also reference volume 1 on a regular basis.

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.

Course Goals

This is the second semester of a standard year-long sequence in single-variable calculus. The main topics are the behavior, derivatives, and integrals of inverse functions; advanced techniques of integration; sequences, series, and Taylor series; some applications of the integral; differential equations; and parametrized curves and polar coordinates. This corresponds to Chapters 6–11 of Stewart (primarily 6, 7, 11) and Chapters 1–7 of Herman–Strang (primarily 3, 5, 6).

By the end of the course, students will acquire the following skills and knowledge: Students will Define logarithm, exponential, and inverse trigonometric functions, explain their basic properties (continuity, derivatives, asymptotes, etc.) and recognize their graphs; Apply these functions to word problems, and correctly interpret the results; Solve integrals using integration by parts, trigonometric substitution and partial fractions; Analyze, create and recognize polar and parametric graphs; Categorize the convergence of an infinite series; Express algebraic and transcendental functions using Maclaurin and Taylor series.