Math 1232: Single-Variable Calculus II
Section 12
Spring 2025

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:

  • T 11–12, W 1–2
  • Phillips 725

Official textbook:

Recitations

Section 36:

  • W 8:00 AM–8:50 AM
  • 1776 G C-118

Section 37:

  • W 9:35 AM–10:25 AM
  • Hall of Government 102

Section 38:

  • W 11:10 AM–12 Noon
  • Monroe 110

Course Information

Lecture:

  • TR 2:20 PM–3:35 PM
  • Funger 223

TA

TA Office Hours:

  • T 11–12, W 1–2
  • Phillips 725

Official textbook:

Recitations

Section 36:

  • W 8:00 AM–8:50 AM
  • 1776 G C-118

Section 37:

  • W 9:35 AM–10:25 AM
  • Hall of Government 102

Section 38:

  • W 11:10 AM–12 Noon
  • Monroe 110

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 13 – 17
January 14: Syllabus and Inverse Functions
January 15: Recitation on Invertible Functions
January 16: The Exponential and the Logarithm
Week 2: January 20 – 24
January 21: Derivatives of the Logarithm and Exponential
January 22: Recitation 2 on Invertible Functions
January 23: Integrals Involving the Logarithm and Exponential
Week 3: January 27 – Feb 1
January 28: Inverse Trigonometric Functions
January 29: Recitation 3 on Inverse Trig Functions and Transcendental Limits
  • [Recitation 3 Worksheet]
January 30: L’Hospital’s Rule
Week 4: February 3 – 7
February 4: Integration by Parts
February 5: Recitation 4 on Integration by Parts and Trig Integrals
  • [Recitation 4 Worksheet]
February 6: Trigonometric Integrals
Week 5: February 10 – 14
February 11: Integration by Partial Fraction Decomposition
  • Read the [solutions] to Mastery Quiz 3
  • Read section 2.3 of the online notes
    • See also Strang and Herman Volume 2§3.4
    • You may want to skim through Strang and Hermann Volume 2§3.5 for an overview of strategies for looking up an integral.
February 12: Recitation 5 on Partial Fractions and Numeric Integration
  • [Recitation 5 Worksheet]
February 13: 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 17 – 21
February 18: Improper Integrals
February 19: Recitation 6 on Improper Integrals and Geometric Integral Applications
  • [Recitation 6 Worksheet]
February 20: Arc Lengths and Surface Area
Week 7: February 24 – 28
February 25: 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 26: Recitation 7 on Differential Equations
  • [Recitation 7 Worksheet]
February 27: Solving Separable Differential Equations
Week 8: March 3 – 7
March 4: Midterm
  • Read the [solutions] to Mastery Quiz 6
  • Midterm on March 4
    • Topics: M1, M2, S1-6
    • Practice Midterm
      • [Single Sheet]
      • [Answer Blanks]
      • [Solutions]
March 5: Recitation 8 on sequences
  • [Recitation 8 Worksheet]
March 6: Sequences
  • Mastery Quiz 7 due
    • Topics: M2, S5, S6
  • Read the [solutions] to the midterm
  • Read section 4.1 of the online notes
Spring Break: March 10-14

No class! Go have fun!

Week 9: March 17 – 21
March 18: Series
March 19: Recitation 9 on Elementary Series
  • [Recitation 9 Worksheet]
March 20: 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
  • See also Strang and Herman, §5.5 and §5.6
Week 10: March 24 – March 28
March 25: Comparison Tests
March 26: Recitation 10 on Series Convergence
  • [Recitation 10 Worksheet]
March 27: The Ratio Test
  • Mastery Quiz 9 due
    • Topics: M3, S7
  • Read sections 4.5 and 4.6 of the online notes
  • See also Strang and Herman, §5.5 and §5.6
Week 11: March 31 – April 4
April 1: 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 2: Recitation 11 on Power Series
  • [Recitation 11 Worksheet]
April 3: 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 7 – 11
April 8: 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 9: Recitation 12 on Taylor Series
  • [Recitation 12 Worksheet]
April 10: Computing Taylor Series
  • Mastery Quiz 11 due
    • Topics: M3, M4, S8, S9
  • Read sections 5.4 of the online notes
  • See also: Strang and Herman §6.4
Week 13: April 14 – April 18
April 15: Applications of Taylor Series
April 16: Recitation 13 on Taylor Series Applications
  • [Recitation 13 Worksheet]
April 17: Parametric Coordinates
  • Mastery Quiz 12 due
    • Topics: M3, M4, S9
  • Read sections 6.1 of the online notes
  • See also Strang and Herman §7.1 and §7.2
  • Practice Final posted!
    • [solutions]
Week 14: April 21 – 25
April 22: Polar Coordinates
  • Read the [solutions] to mastery quiz 12
  • Read section 6.2 of the online notes
April 23: Recitation 14 on Parametrization
  • [Recitation 14 Worksheet]
April 24: Fun with Series
Finals Week
April 29: Optional Mastery Quiz Due
  • Read the [solutions] to mastery quiz 13
  • Optional Mastery Quiz 14 due Wednesday, April 30
    • Topics: M4, S10
  • Read the [solutions] to mastery quiz 14
Office Hours Schedule

TBD

Final Exam: TBD
  • Practice Final
    • [Solutions]

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.