Math 1232: Single-Variable Calculus II
Section 11
Fall 2024

Contact Info
Spring 2024

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

Office Hours:

Course Information

Lecture:

  • MW 9:35 PM–10:50 PM
  • Monroe 111

TA

TA Office Hours:

  • MW 4:00 &ndash 5:00 PM
  • Phillips 719

Official textbook:

Recitations

Section 33:

  • F 8:00 AM–8:50 AM
  • Duques 360

Section 34:

  • F 9:35 AM–10:25 AM
  • Duques 360

Section 35:

  • F 11:10 AM–12 Noon
  • Monroe 351

Course Information

Lecture:

  • MW 9:35 PM–10:50 PM
  • Monroe 111

TA

TA Office Hours:

  • MW 4:00 &ndash 5:00 PM
  • Phillips 719

Official textbook:

Recitations

Section 33:

  • F 8:00 AM–8:50 AM
  • Duques 360

Section 34:

  • F 9:35 AM–10:25 AM
  • Duques 360

Section 35:

  • F 11:10 AM–12 Noon
  • Monroe 351

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 0: August 22 – 23
August 23: Welcome and Recitation 0
Week 1: August 26 – 30
August 26: Syllabus and Inverse Functions
August 28: The Exponential and the Logarithm
August 30: Recitation on Invertible Functions
Week 2: September 2 – 6
September 2: No Classes for Labor Day
September 4: Derivatives of the Logarithm and Exponential
September 6: Recitation 2 on Invertible Functions
Week 3: September 9 – 14
September 9: Integrals Involving the Logarithm and Exponential
September 11: Inverse Trigonometric Functions
September 13: Recitation 3 on Inverse Trig Functions and Transcendental Limits
Week 4: September 16 – 20
September 16: L’Hospital’s Rule
September 18: Integration by Parts
September 20: Recitation 4 on Integration by Parts and Trig Integrals
Week 5: September 23 – 27
September 23: Trigonometric Integrals
  • Mastery Quiz 4 due
  • Read section 2.2 of the online notes
  • Bonus: here is a fun video doing trig-sub integrals without bringing in trig functions. I don’t think this is actually easier in practice, but it’s a fun trick!
September 25: Integration by Partial Fraction Decomposition
  • Read the solutions to Mastery Quiz 4
  • 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.
September 27: Recitation 5 on Partial Fractions and Numeric Integration
Week 6: September 30 – October 4
September 30: Numeric Integration
October 2: Improper Integrals
October 4: Recitation 6 on Improper Integrals and Geometric Integral Applications
Week 7: October 7 – 9
October 7: Arc Lengths and Surface Area
October 9: Differential Equations
  • Read the solutions to Mastery Quiz 6
  • 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.
October 11: No Recitation for Fall Break
Week 8: October 14 – 18
October 14: Solving Separable Differential Equations
October 16: Midterm
October 18: Recitation 7 on Differential Equations
Week 9: October 21 – 25
October 21: Sequences
October 23: Series
October 25: Recitation 8 on sequences
Week 10: October 28 – November 1
October 28: The Divergence Test and the Integral Test
October 30: Comparison Tests
November 1: Recitation 9 on Elementary Series
Week 11: November 4 – 8
November 4: Absolute Convergence and the Ratio Test
November 6: Power Series
November 8: Recitation 10 on Series Convergence
Week 12: November 11 – 15
November 11: Power Series as Functions
November 13: Taylor Series
November 15: Recitation 11 on Power Series
Week 13: November 18 – 22
November 18: Computing Taylor Series
November 20: Applications of Taylor Series
November 22: Recitation 12 on Taylor Series
Thanksgiving Break: November 25-29

No class! Happy Thanksgiving!

Week 14: December 2 – 6
December 2: Parametric Coordinates
December 4: Polar Coordinates
December 6: Recitation 13 on Taylor Series Applications
Week 15: December 9-11
December 9: Fun with Series
Finals Week
Reading Days
Office Hours Schedule
  • Tuesday, December 10: 3 PM – 6 PM as normal
  • Wednesday December 11: 1 PM – 4 PM
  • Thursday December 12: 11 AM – 1:30 PM
  • Friday, December 13: 3 PM – 5 PM.
  • Sunday, December 15: 1 PM – 4 PM
Final Exam: Saturday, December 14, 10:20 &ndash 12:20.

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.