## Daily Assignments

## March 21: Series and the Divergence Test

- Mastery Quiz 7 due
- Topic M2, S4, S5, S6
- Single Sheet
- Answer Blanks

- Read the midterm solutions
- Read sections 4.2 and 4.3 of the online notes
- See also Strang and Herman Volume 2 §5.2 and the beginning of §5.3

## March 10: Recitation 8 on Sequences

## March 9: Sequences

- Read section 4.1 of the online notes
- See also Strang and Herman Volume 2 §5.1

## March 7: Midterm

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

- No mastery quiz today!

## March 3: Recitation 7 on Differential Equations

## March 2: 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

## February 28: Differential Equations

- Mastery Quiz 6 due Tuesday, February 28
- Topic 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 24: Recitation 6 on Improper Integrals, arc length, and surface area

## February 23: Arc Lengths and Surface Areas

- 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 21: Improper Integrals

- Be nice to Professor Harizanov!
- Mastery Quiz 5 due
- Topic 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 17: Recitation 5 on Partial Fractions and Numeric Integration

## February 16: 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 14: Integration by Partial Fractions

- Mastery Quiz 4 due
- Topic M1, M2, S2
- Single Sheet
- Answer Blanks

- 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 10: Recitation 4 on Integration by Parts and Trig Integrals

## February 9: 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 7: Integration by Parts

- Mastery Quiz 3 due Tuesday, February 7
- Topic M1, S2
- Single Sheet
- Answer Blanks

- Read section 2.1 of the online notes
- See also Strang and Herman Volume 2§3.1

## February 3: Recitation 3 on inverse trig functions and transcendental limits

## February 2: 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.

## January 31: Inverse Trigonometric Functions

- Mastery Quiz 2 due
- Topic M1, S1
- Single Sheet
- Answer Blanks

- 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 27: Recitation 2 on Invertible Functions

## January 26: 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 24: Derivatives of the Logarithm and Exponential

- Mastery Quiz 1 due
- Topic 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 20: Recitation 1 on Invertible Functions

## January 19: 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 17: 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

- See also
- Bonus material:
- Video on how the inverse of a function involves reflecting the graph across the line \(y=x\).

## Course notes

## Mastery Quizzes

- Mastery Quiz 1 due Tuesday, January 24
- Topic S1
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 2 due Tuesday, January 31
- Topic M1, S1
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 3 due Tuesday, February 7
- Topic M1, S2
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 4 due Tuesday, February 14
- Topic M1, M2, S2
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 5 due Tuesday, February 21
- Topic M1, M2, S3
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 6 due Tuesday, February 28
- Topic M2, S3, S4, S5
- Single Sheet
- Answer Blanks
- Solutions

- Mastery Quiz 7 due Tuesday, March 21
- Topic M2, S4, S5, S6
- Single Sheet
- Answer Blanks

#### 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 7
- Topics: M1, M2, S1, S2, S3, S4, S5
- Practice Midterm
- Midterm Solutions

- Final Exam on Thursday, May 11, 3:00–5:00 PM
- As scheduled by the registrar
- 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.