Math 1232: Single-Variable Calculus II
Section 12
Spring 2024

Contact Info
Spring 2024

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

Office Hours:

Often in office:

Course Information

Lecture:

  • TR 2:20 PM–3:35 PM
  • 1957 E ST NW, B17

TA

TA Office Hours:

  • W 9:30 &ndash 11:30 AM
  • Phillips 720G

Official textbook:

Recitations

Section 36:

  • F 8:00 AM–8:50 AM
  • Bell 309

Section 37:

  • F 9:35 AM–10:25 AM
  • Bell 309

Section 38:

  • F 11:10 AM–12 Noon
  • Duques 360

Course Information

Lecture:

  • TR 2:20 PM–3:35 PM
  • 1957 E ST NW, B17

TA

TA Office Hours:

  • W 9:30 &ndash 11:30 AM
  • Phillips 720G

Official textbook:

Recitations

Section 36:

  • F 8:00 AM–8:50 AM
  • Bell 309

Section 37:

  • F 9:35 AM–10:25 AM
  • Bell 309

Section 38:

  • F 11:10 AM–12 Noon
  • Duques 360

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 15 – 19
January 16: Syllabus and Inverse Functions
January 18: The Exponential and the Logarithm
January 19: Recitation on Invertible Functions
Week 2: January 22 – 26
January 23: Derivatives of the Logarithm and Exponential
January 25: Integrals Involving the Logarithm and Exponential
January 26: Recitation 2 on Invertible Functions
Week 3: January 29 – February 2
January 30: Inverse Trigonometric Functions
February 1: L’Hospital’s Rule
February 2: Recitation 3 on Inverse Trig Functions and Transcendental Limits
Week 4: February 5 – 9
February 6: Integration by Parts
February 8: Trigonometric Integrals
February 9: Recitation 4 on Integration by Parts and Trig Integrals
Week 5: February 12 – 16
February 13: Integration by Partial Fraction Decomposition
February 15: Numeric Integration
February 16: Recitation 5 on Partial Fractions and Numeric Integration
Week 6: February 19 – 23
February 20: Improper Integrals
February 22: Arc Lengths and Surface Area
February 23: Recitation 6 on Improper Integrals and Geometric Integral Applications
Week 7: February 26 – March 1
February 27: Differential Equations
  • Mastery Quiz 6 due
  • 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 29(!): Solving Separable Differential Equations
March 1: Recitation 7 on Differential Equations
Week 8: March 4 – 8
March 5: Midterm
March 7: Sequences
March 8: Recitation 8 on sequences
Spring Break: March 11-15

No class! Go have fun!

Week 9: March 18 – 22
March 19: Series
  • Mastery Quiz 7 due
    • Topics: M3, S4, S5, S6
March 21: The Divergence Test and the Integral Test
  • Read the [solutions] to Mastery Quiz 7
  • Read sections 4.5 and 4.6 of the online notes
March 22: Recitation 9 on Elementary Series
Week 10: March 25 – March 29
March 26: Comparison Tests
  • Mastery Quiz 8 due
    • Topics: S6, S7
March 28: The Ratio Test
  • Read the [Solutions] to Mastery Quiz 8
  • Read sections 4.5 and 4.6 of the online notes
March 29: Recitation 10 on Series Convergence
Week 11: April 1 – 5
April 2: Power Series
  • Mastery Quiz 9 due
    • Topics: M3, S7
April 4: Power Series as Functions
  • Read the [solutions] to Mastery Quiz 9
  • Read sections 5.2 of the online notes
    • See also Strang and Herman §6.2
April 5: Recitation 11 on Power Series
Week 12: April 8 – 12
April 9: Taylor Series
  • Mastery Quiz 10 due
    • Topics: M3, S8, S9
April 11: Computing Taylor Series
  • Read the [Solutions] to Mastery Quiz 10
  • Read sections 5.4 of the online notes
    • See also: Strang and Herman §6.4
April 12: Recitation 12 on Taylor Series
Week 13: April 15 – April 19
April 16: Applications of Taylor Series
  • Mastery Quiz 11 due
    • Topics: M3, M4, S8
April 18: Parametric Coordinates
  • Read the [solutions] to mastery quiz 11
  • Read sections 6.1 of the online notes
April 19: Recitation 13 on Taylor Series Applications
Week 14: April 22 – 26
April 23: Polar Coordinates
  • Mastery Quiz 12 due
    • Topics: M3, M4, S9, S10
April 25: Fun with Series
April 26: Recitation 14 on Parametrization
Finals Week
April 30: Optional Mastery Quiz Due
  • Optional Mastery Quiz 13 due
    • Topics: M4, S9, S10
Office Hours Schedule
Final Exam: Thursday May 9, 3 – 5 PM
  • Practice Final

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.