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 12 – 16
January 13: Syllabus and Inverse Functions
- Please read the syllabus
- Read Professor Bonin’s advice on study skills
- 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 14: Recitation on Invertible Functions
January 15: The Exponential and the Logarithm
- Read Section 1.2 of the online notes
- See also Strang and Herman Volume 1 §1.5
Week 2: January 19 – 23
January 20: Derivatives of the Logarithm and Exponential
- Read Section 1.3 of the online notes
- See also Strang and Herman Volume 1 §3.9
January 21: Recitation 2 on Invertible Functions
January 22: Integrals Involving the Logarithm and Exponential
- Mastery Quiz 1 due
- Topics: S1
- Single Sheet
- Answer Blanks
- Read Section 1.4 of the online notes
- See also Strang and Herman Volume 2 §1.6
Week 3: January 26 – 30
January 27: Inverse Trigonometric Functions
- Read the solutions to Mastery Quiz 1
- Today’s slides
- Read Section 1.5 of the online notes
- 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
January 28: Recitation 3 on Inverse Trig Functions and Transcendental Limits
January 29: L’Hospital’s Rule
- Mastery Quiz 2 due
- Topics: M1, S1
- Single Sheet
- Answer Blanks
- Today’s slides
- 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 ε-δ arguments work; the new part, on L’Hospital’s Rule, begins at the 10:00 mark.
Week 4: February 2 – 6
February 3: Integration by Parts
- Read the solutions to Mastery Quiz 2
- Read section 2.1 of the online notes
- See also Strang and Herman Volume 2§3.1
February 4: Recitation 4 on Integration by Parts and Trig Integrals
February 5: Trigonometric Integrals
- Mastery Quiz 3 due
- Topics: M1, S2
- Single Sheet
- Answer Blanks
- Read section 2.2 of the online notes
- See also Strang and Herman Volume 2§3.2 and §3.3
Week 5: February 9 – 13
February 10: 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
- Lecture Slides
- You may want to skim through Strang and Hermann Volume 2§3.5 for an overview of strategies for looking up an integral.
February 11: Recitation 5 on Partial Fractions and Numeric Integration
February 12: 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 16 – 20
February 17: Improper Integrals
- Read the solutions to Mastery Quiz 4
- Read section 3.1 of the online notes
- See also Strang and Herman Volume 2§3.7
February 18: Recitation 6 on Improper Integrals
February 19: Arc Lengths and Surface Area
- Mastery Quiz 5 due
- Topics: M1, M2, S3, S4
- Read section 3.2 of the online notes
- See also Strang and Herman Volume 2§2.4
Week 7: February 23 – 27
February 24: Differential Equations
- Read the solutions to Mastery Quiz 5
- 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 25: Recitation 7 on Geometric Integral Applications
February 26: Solving Separable Differential Equations
- Mastery Quiz 6 due
- Topics: M2, S3, S4, S5
- Single Sheet
- Answer Blanks
- Read sections 3.4-5 of the online notes
- See also Strang and Herman Volume 2 §4.3 and §4.4
Week 8: March 2 – 6
March 3: Midterm
- Read the solutions to Mastery Quiz 6
- Midterm on March 4
- Topics: M1, M2, S1-6
- Practice Midterm
March 4: Recitation 8 on differential equations
March 5: Sequences
- Mastery Quiz 7 due
- Topics: M2, S5, S6
- Single Sheet
- Answer Blanks
- Read the solutions to the midterm
- Read section 4.1 of the online notes
- See also Strang and Herman Volume 2 §5.1
Spring Break: March 9-13
No class! Go have fun!
Week 9: March 16 – 20
March 17: Series
- Read the solutions to Mastery Quiz 7
- Read section 4.2 of the online notes
- See also Strang and Herman Volume 2 §5.2
March 18: Recitation 9 on Elementary Series
March 19: The Divergence Test and the Integral Test
- Mastery Quiz 8 due
- Topics: S6, S7
- Single Sheet
- Answer Blanks
- Read sections 4.5 and 4.6 of the online notes
Week 10: March 23 – March 27
March 24: Comparison Tests
- Read the solutions to Mastery Quiz 8
- Read section 4.4 of the online notes
- See also Strang and Herman Volume 2 §5.4
March 25: Recitation 10 on Series Convergence
March 26: The Ratio Test
- Mastery Quiz 9 due
- Topics: M3, S7
- Single Sheet
- Answer Blanks
- Read sections 4.5 and 4.6 of the online notes
Week 11: March 30 – April 3
March 31: 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 1: Recitation 11 on Power Series
April 2: Power Series as Functions
- Mastery Quiz 10 due
- Topics: M3, S8
- Single Sheet
- Answer Blanks
- Read sections 5.2 of the online notes
- See also Strang and Herman §6.2
Week 12: April 6 – 10
April 7: 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 8: Recitation 12 on Taylor Series
April 9: Computing Taylor Series
- Mastery Quiz 11 due
- Topics: M3, M4, S8
- Single Sheet
- Answer Blanks
- Read sections 5.4 of the online notes
- See also: Strang and Herman §6.4
Week 13: April 13 – April 17
April 14: Applications of Taylor Series
- Read the solutions to Mastery Quiz 11
- 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 15: Recitation 13 on Taylor Series Applications
April 16: Parametric Coordinates
- Mastery Quiz 12 due
- Topics: M3, M4, S9
- Single Sheet
- Answer Blanks
- Read sections 6.1 of the online notes
Week 14: April 20 – 24
April 21: Polar Coordinates
- Read the solutions to mastery quiz 12
- Read section 6.2 of the online notes
April 22: Recitation 14 on Parametrization
April 23: Fun with Series
- Mastery Quiz 13 due
- Topics: M4, S9, S10
- Single Sheet
- Answer Blanks
- Read section 5.6 of the online notes
- Check out these videos on Fourier series
Finals Week
April 30: Optional Mastery Quiz Due
- Read the solutions to mastery quiz 13
- Optional Mastery Quiz 14 due Thursday, April 30
- Topics: M4, S10
- Single Sheet
- Answer Blanks
- Read the solutions to mastery quiz 14
Office Hours Schedule
- Monday April 27: 2 – 5 PM
- Wednesday April 29: 12 – 2 PM
- Thursday April 30: 1 – 3 PM
- Saturday May 2: 1 – 3 PM
- Wednesday, May 6: 2 – 5 PM
Final Exam: Thursday, May 7, 3:00–5:00 PM
- Practice Final
- You are not allowed to consult books or notes during the test, but you may use a one-page, two-sided, handwritten cheat sheet you have made for yourself ahead of time. You must have written on the physical sheet you bring to the test in your own handwriting.
Course notes
- Course Notes
Mastery Quizzes
- Mastery Quiz 1 due Thursday, January 23
- Topics: S1
- Single Sheet
- Answer Blanks
- Solutions
- Mastery Quiz 2 due Thursday, January 30
- Topics: M1, S1
- Single Sheet
- Answer Blanks
- Solutions
- Mastery Quiz 3 due Thursday, February 6
- Topics: M1, S2
- Single Sheet
- Answer Blanks
- Solutions
- Mastery Quiz 4 due Thursday, February 13
- Topics: M1, M2, S2
- Single Sheet
- Answer Blanks
- Solutions
- Mastery Quiz 5 due Thursday, February 20
- Topics: M1, M2, S3, S4
- Single Sheet
- Answer Blanks
- Solutions
- Mastery Quiz 6 due Thursday, February 27
- Topics: M2, S3, S4, S5
- Single Sheet
- Answer Blanks
- Solutions
- Mastery Quiz 7 due Thursday, March 6
- Topics: M2, S5, S6
- Single Sheet
- Answer Blanks
- Solutions
- Mastery Quiz 8 due Thursday, March 20
- Topics: S6, S7
- Single Sheet
- Answer Blanks
- Solutions
- Mastery Quiz 9 due Thursday, March 27
- Topics: M3, S7
- Single Sheet
- Answer Blanks
- Solutions
- Mastery Quiz 10 due Thursday, April 2
- Topics: M3, S8
- Single Sheet
- Answer Blanks
- Solutions
- Mastery Quiz 11 due Thursday, April 9
- Topics: M3, M4, S8
- Single Sheet
- Answer Blanks
- Solutions
- Mastery Quiz 12 due Thursday, April 16
- Topics: M3, M4, S9
- Single Sheet
- Answer Blanks
- Solutions
- Mastery Quiz 13 due Thursday, April 23
- Topics: M4, S9, S10
- Single Sheet
- Answer Blanks
- Solutions
- Optional Mastery Quiz 14 due Thursday, April 30
- Topics: M4, 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 3
- Topics: M1, M2, S1, S2, S3, S4, S5
- Practice Midterm
- Solutions
- Final Exam
- As scheduled by the registrar
- Tentatively Thursday, May 7, 3:00–5:00 PM
- 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
- You are not allowed to consult books or notes during the test, but you may use a one-page, two-sided, handwritten cheat sheet you have made for yourself ahead of time. You must have written on the physical sheet you bring to the test in your own handwriting.
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.