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:
 OpenStax College Algebra chapters 1 and 5;
 OpenStax Precalculus chapter 5.
Week 1: January 15 – 19
January 16: Syllabus and Inverse Functions
 Please read the syllabus
 Read Professor Bonin’s advice on study skills
 Slides from today’s class
 Read Section 1.1 of the online notes
 See also Volume 1 §1.4
 Bonus material:
 Video on how the inverse of a function involves reflecting the graph across the line \(y=x\).
January 18: The Exponential and the Logarithm
 Read Section 1.2 of the online notes
 See also Strang and Herman Volume 1 §1.5
January 19: Recitation on Invertible Functions
Week 2: January 22 – 26
January 23: Derivatives of the Logarithm and Exponential
 Mastery Quiz 1 due
 Topics: S1
 Single Sheet
 Answer Blanks
 Read Section 1.3 of the online notes
 See also Strang and Herman Volume 1 §3.9
January 25: Integrals Involving the Logarithm and Exponential
 Read the solutions to mastery quiz 1
 Read Section 1.4 of the online notes
 See also Strang and Herman Volume 2 §1.6
January 26: Recitation 2 on Invertible Functions
Week 3: January 29 – February 2
January 30: Inverse Trigonometric Functions
 Mastery Quiz 2 due
 Topics: M1, S1
 Single Sheet
 Answer Blanks
 See also Strang and Herman Volume 1 §1.4 and Volume 1 § 3.7 the bits on inverse trigonometric functions, and Volume 2 §1.7
February 1: L’Hospital’s Rule
 Read the Solutions to Mastery Quiz 2
 Read Section 1.6 of the online notes
 See also: Strang and Herman Volume 1 §4.8
 Optional 3Blue1Brown video on limits and L’Hospital’s Rule. First half is review of how limits and εδ arguments work; the new part, on L’Hospital’s Rule, begins at the 10:00 mark.
February 2: Recitation 3 on Inverse Trig Functions and Transcendental Limits
Week 4: February 5 – 9
February 6: Integration by Parts
 Mastery Quiz 3 due
 Topics: M1, S2
 Single Sheet
 Answer Blanks
 Read section 2.1 of the online notes
 See also Strang and Herman Volume 2§3.1
February 8: Trigonometric Integrals
 Read the solutions to mastery quiz 3
 Read section 2.2 of the online notes
 See also Strang and Herman Volume 2§3.2 and §3.3
February 9: Recitation 4 on Integration by Parts and Trig Integrals
Week 5: February 12 – 16
February 13: Integration by Partial Fraction Decomposition
 Mastery Quiz 4 due
 Topics: M1, M2, S2
 Single Sheet
 Answer Blanks
 Read the solutions to skills quiz 1
 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 15: Numeric Integration
 Read the solutions to Mastery Quiz 4
 Read section 2.4 of the online notes
 See also Strang and Herman §3.6
February 16: Recitation 5 on Partial Fractions and Numeric Integration
Week 6: February 19 – 23
February 20: Improper Integrals
 Mastery Quiz 5 due
 Topics: M1, M2, S3
 Single Sheet
 Answer Blanks
 Read section 3.1 of the online notes
 See also Strang and Herman Volume 2§3.7
February 22: Arc Lengths and Surface Area
 Read the solutions to Mastery Quiz 5
 Read section 3.2 of the online notes
 See also Strang and Herman Volume 2§2.4
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
 Topics: M2, S3, S4, S5
 Single Sheet
 Answer Blanks
 Read section 3.3 of the online notes
 See also Strang and Herman Volume 2§4.1
 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
 Read the solutions to Mastery Quiz 6
 Read sections 3.45 of the online notes
 See also Strang and Herman Volume 2 §4.3 and §4.4
March 1: Recitation 7 on Differential Equations
Week 8: March 4 – 8
March 5: Midterm
 Midterm on March 7
 Topics: M1, M2, S15
 Practice Midterm
 No mastery quiz today!
March 7: Sequences
 Read the solutions to the midterm
 Read section 4.1 of the online notes
 See also Strang and Herman Volume 2 §5.1
March 8: Recitation 8 on sequences
Spring Break: March 1115
No class! Go have fun!
Week 9: March 18 – 22
March 19: Series
 Mastery Quiz 7 due
 Topics: M3, S4, S5, S6
 Single Sheet
 Answer Blanks
 Read section 4.2 of the online notes
 See also Strang and Herman Volume 2 §5.2
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
 Single Sheet
 Answer Blanks
 Read section 4.4 of the online notes
 See also Strang and Herman Volume 2 §5.4
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
 Single Sheet
 Answer Blanks
 Read section 5.1 of the online notes
 See also Strang and Herman §6.1
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, M4, S8
 Single Sheet
 Answer Blanks
 Read section 5.3 of the online notes
 See also Strang and Herman §6.3
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
 Single Sheet
 Answer Blanks
 Read section 5.5 of the online notes
 See also Strang and Herman §6.4
 You may also find it helpful to watch Essence of Calculus, Chapter 11 from 3Blue1Brown
April 18: Parametric Coordinates
 Read the solutions to mastery quiz 11
 Read sections 6.1 of the online notes
 Practice Final posted!
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
 Single Sheet
 Answer Blanks
 Read section 6.2 of the online notes
April 25: Fun with Series
 Read the solutions to mastery quiz 12
 Read section 5.6 of the online notes
 Check out these videos on Fourier series
April 26: Recitation 14 on Parametrization
Finals Week
April 30: Optional Mastery Quiz Due
 Optional Mastery Quiz 13 due Extended to May 1
 Topics: M4, S9, S10
 Single Sheet
 Answer Blanks
 Read the solutions to mastery quiz 13
Office Hours Schedule
Monday April 29: 35:30Canceled Tuesday, April 30: 25 On Zoom (see email)
 Wednesday, May 1: 35:30
 Thursday, May 2: 25

Friday, May 3: 24:30
 Wednesday, May 8: 37
 Thursday, May 9: 12
Final Exam: Thursday May 9, 3 – 5 PM
 Practice Final
Course notes
 Course Notes
Mastery Quizzes
 Mastery Quiz 1 due Tuesday, January 23
 Topics:
 Single Sheet
 Answer Blanks
 Solutions
 Mastery Quiz 2 due Tuesday, January 30
 Topics: M1, S1
 Single Sheet
 Answer Blanks
 Solutions
 Mastery Quiz 3 due Tuesday, February 6
 Topics: M1, S2
 Single Sheet
 Answer Blanks
 Solutions
 Mastery Quiz 4 due Tuesday, February 13
 Topics: M1, M2, S2
 Single Sheet
 Answer Blanks
 Solutions
 Mastery Quiz 5 due Tuesday, February 20
 Topics: M1, M2, S3
 Single Sheet
 Answer Blanks
 Solutions
 Mastery Quiz 6 due Tuesday, February 27
 Topics: M2, S3, S4, S5
 Single Sheet
 Answer Blanks
 Solutions
 Mastery Quiz 7 due Tuesday, March 19
 Topics: M2, S4, S5, S6
 Single Sheet
 Answer Blanks
 Mastery Quiz 8 due Tuesday, March 26
 Topics: S6, S7
 Single Sheet
 Answer Blanks
 Solutions
 Mastery Quiz 9 due Tuesday, April 2
 Topics: M3, S7
 Single Sheet
 Answer Blanks
 Solutions
 Mastery Quiz 10 due Tuesday, April 9
 Topics: M3, M4, S8
 Single Sheet
 Answer Blanks
 Solutions
 Mastery Quiz 11 due Tuesday, April 16
 Topics: M3, M4, S8
 Single Sheet
 Answer Blanks
 Solutions
 Mastery Quiz 12 due Tuesday, April 23
 Topics: M3, M4, S9, S10
 Single Sheet
 Answer Blanks
 Solutions
 Optional Mastery Quiz 13 due Tuesday, April 30
 Topics: M4, S9, S10
 Single Sheet
 Answer Blanks
 Solutions
Major Topics
 Calculus of Transcendental Functions
 Advanced Integration Techniques
 Series Convergence
 Taylor Series
Secondary Topics
 Invertible Functions
 L’Hospital’s Rule
 Numeric Integration
 Improper Integrals
 Arc Length and Surface Area
 Differential Equations
 Sequences and Series
 Power Series
 Applications of Taylor Series
 Parametrization
Tests
 Midterm on March 5
 Topics: M1, M2, S1, S2, S3, S4, S5
 Practice Midterm
 Solutions
 Final Exam Thursday, May 9 3 – 5 PM
 As scheduled by the registrar
 Per the syllabus, you will not be excused from the final if you schedule travel during finals week; if you must buy your plane ticket before the registrar announces final exam, please make sure it departs after May 10.
 Practice Final
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 yearlong sequence in singlevariable 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.