## 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

- See also
- 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

- See also Strang and Herman

##### 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

- See also Strang and Herman

##### 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 ε-δ 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 3.4-5 of the online notes
- See also Strang and Herman Volume 2 §4.3 and §4.4

##### March 1: Recitation 7 on Differential Equations

- Recitation 7 Worksheet
- [Solutions]

## Week 8: March 4 – 8

##### March 5: Midterm

- Midterm on March 7
- Topics: M1, M2, S1-5
- 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

- Recitation 8 Worksheet
- [Solutions]

## 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

- 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

- Recitation 9 Worksheet
- [Solutions]

## Week 10: March 25 – March 29

##### March 26: Comparison Tests

- Mastery Quiz 8 due
- Topics: S6, S7

- 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

- Recitation 10 Worksheet
- [Solutions]

## Week 11: April 1 – 5

##### April 2: Power Series

- Mastery Quiz 9 due
- Topics: M3, S7

- 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

- Recitation 11 Worksheet
- [Solutions]

## Week 12: April 8 – 12

##### April 9: Taylor Series

- Mastery Quiz 10 due
- Topics: M3, S8, S9

- 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

- Recitation 12 Worksheet
- [Solutions]

## Week 13: April 15 – April 19

##### April 16: Applications of Taylor Series

- Mastery Quiz 11 due
- Topics: M3, M4, S8

- 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

##### April 19: Recitation 13 on Taylor Series Applications

- Recitation 13 Worksheet
- [Solutions]

## Week 14: April 22 – 26

##### April 23: Polar Coordinates

- Mastery Quiz 12 due
- Topics: M3, M4, S9, S10

- Read section 6.2 of the online notes

##### April 25: Fun with Series

- Read the solutions to mastery quiz 13
- Read section 5.6 of the online notes
- Check out these videos on Fourier series

##### April 26: Recitation 14 on Parametrization

- Recitation 14 Worksheet
- [Solutions]

## Finals Week

##### April 30: Optional Mastery Quiz Due

- Optional Mastery Quiz 13 due
- Topics: M4, S9, S10

- Read the solutions to mastery quiz 14

##### Office Hours Schedule

##### 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

- Mastery Quiz 8 due Tuesday, March 26
- Topics: S6, S7

- Mastery Quiz 9 due Tuesday, April 2
- Topics: M3, S7

- Mastery Quiz 10 due Tuesday, April 9
- Topics: M3, M4, S8

- Mastery Quiz 11 due Tuesday, April 16
- Topics: M3, M4, S8

- Mastery Quiz 12 due Tuesday, April 23
- Topics: M3, M4, S9, S10

- Optional Mastery Quiz 13 due Tuesday, April 30
- Topics: M4, S9, S10

#### 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

- 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 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.