Math 1231: Single-Variable Calculus II
Section 12
Spring 2023

Contact Info
Spring 2023

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

Office Hours:

Often in office:

Course Information

Lecture:

  • TR 2:20 PM–3:35 PM
  • Phillips B152

TA

TA Office Hours:

  • TR 12:30–1:00
    F 1:00–2:00
  • Phillips 720G

Official textbook:

Recitations

Section 36:

  • F 8:00 AM–8:50 AM
  • Duques 259

Section 37:

  • F 9:35 AM–10:25 AM
  • Phillips 111

Section 38:

  • F 11:10 AM–12 Noon
  • Tompkins 301

Course Information

Lecture:

  • TR 2:20 PM–3:35 PM
  • Phillips B152

TA

TA Office Hours:

  • TR 12:30–1:00
    F 1:00–2:00
  • Phillips 720G

Official textbook:

Recitations

Section 36:

  • F 8:00 AM–8:50 AM
  • Duques 259

Section 37:

  • F 9:35 AM–10:25 AM
  • Phillips 111

Section 38:

  • F 11:10 AM–12 Noon
  • Tompkins 301

Daily Assignments

Finals Week
  • Read the solutions to Mastery Quiz 13
  • Monday May 8
    • Office hours 3-7 (Running late, will be in more like 3:30)
      • But prioritizing Calc 1
  • Tuesday May 9
  • Wednesday May 10
    • Office hours 3:30-7 (change!)
  • Final Exam on Thursday, May 11, 3:00–5:00 PM
Reading Week Schedule
  • Monday May 1
    • Office hours 2-5 PM
  • Tuesday May 2
  • Wednesday May 3
    • Office Hours 2-5
  • Thursday May 4
    • Office Hours 3-5
  • Friday: None
  • Saturday May 6
    • Office Hours 3-6
  • Sunday: None
April 28: Recitation 14 on Parametrization
April 27: Fun with Series
April 25: Polar Coordinates
April 21: Recitation 13 on Taylor Series Applications
April 20: Parametric Coordinates
April 18: Applications of Taylor Series
April 14: Recitation 12 on Taylor Series
April 13: Computing Taylor Series
April 11: Taylor Series
April 7: Recitation 11 on Power Series
April 6: Power Series as Functions
April 4: Power Series
March 31: Recitation 10 on Series Convergence
March 30: The Divergence Test and the Integral Test
March 28: Comparison Tests
March 24: Recitation 9 on Elementary Series
March 23: The Divergence Test and the Integral Test
March 21: Series
March 10: Recitation 8 on Sequences
March 9: Sequences
March 7: Midterm
March 3: Recitation 7 on Differential Equations
March 2: Separable Differential Equations
February 28: Differential Equations
  • Mastery Quiz 6 due Tuesday, February 28
  • 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 24: Recitation 6 on Improper Integrals, arc length, and surface area
February 23: Arc Lengths and Surface Areas
February 21: Improper Integrals
February 17: Recitation 5 on Partial Fractions and Numeric Integration
February 16: Numeric Integration
February 14: Integration by Partial Fractions
February 10: Recitation 4 on Integration by Parts and Trig Integrals
February 9: Trigonometric Integrals
February 7: Integration by Parts
February 3: Recitation 3 on inverse trig functions and transcendental limits
February 2: L'Hospital's Rule
January 31: Inverse Trigonometric Functions
January 27: Recitation 2 on Invertible Functions
January 26: Integrals Involving the Logarithm and Exponential
January 24: Derivatives of the Logarithm and Exponential
January 20: Recitation 1 on Invertible Functions
January 19: The Exponential and the Logarithm
January 17: Syllabus and Inverse Functions

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.