## Daily Assignments

##### May 4: It’s over!

- Final Exam due May 4 at midnight
- Read Solutions
- New WeBWorK 13 due
- All old WeBWorKs have been reopened, and will close on this date
- Final Exam due

### Week 15 Office hours

- Monday 1:30 – 3:30 on Discord
- Tuesday 5 – 7 on Zoom
- Wednesday 5:30 – 7:30 on Discord
- Thursday 2:30 – 4:30 on Zoom
- Friday 5 – 7 on Zoom
- Saturday 5 – 7 on Discord

##### April 30: Mastery Quiz 13 Due

##### April 28: Request Mastery Topics

### Week 14

##### April 23: Mastery Quiz 12 due

- Solutions to MQ 12

##### April 22: Fun with Series

- Read §5.5 of the online notes

##### April 21: WeBWorK due

- Request a topic for this week’s mastery quiz if you want to retest something before topic 1

##### April 20: Polar Coordinates

- Read one of:
- §6.2 of the online notes
- Stewart §10.3-10.4
- Strang and Herman §7.3 and §7.4

- Read the solutions to Mastery Quiz 11

### Week 13

##### April 16: Mastery Quiz 11 due

##### April 8: Parametric Coordinates

- Read one of:
- §6.1 of the online notes (not yet written)
- Stewart §10.1-10.2
- Strang and Herman §7.1 and §7.2

##### April 14: WeBWorK due

- Request a topic for this week’s mastery quiz if you want to retest something before topic 17 (Now actually live as of 3 AM April 14, sorry)
- I realize the WeBWorK is open through the 16th; that was a mistake on my part. I’m going to leave it open, but encourage you to try to finish for today as usual.

##### April 13: Applications of Taylor Series

- Read one of:
- §5.5 of the online notes (Posted 28 March)
- Stewart §11.11
- Strang and Herman §6.4

- Read the solutions to Mastery Quiz 10

### Week 12

##### April 9: Mastery Quiz 10 due

##### April 8: Computing Taylor series

- Read one of:
- §5.4 of the online notes
- Stewart §11.11
- Strang and Herman §6.4

##### April 7: WeBWorK due

- Request a topic for this week’s mastery quiz if you want to retest something before topic 15

##### April 6: Taylor Series

- Read one of:
- §5.3 of the online notes (Posted 28 March)
- Stewart §11.10
- Strang and Herman §6.3

- Read the solutions to Mastery Quiz 9

### Week 11

##### April 2: Mastery Quiz 9 due

##### April 1: Power Series as Functions

- How is it April already?
- Read one of:
- §5.2 of the online notes
- Stewart §11.9
- Strang and Herman §6.2

##### March 31: WeBWorK due

- Request a topic for this week’s mastery quiz if you want to retest something before topic 13
- What did you think about Zoom lecture?

##### March 30: Power Series

- Read one of:
- §5.1 of the online notes (Posted 28 March)
- Stewart §11.8
- Strang and Herman §6.1

- Read the solutions to Mastery Quiz 8

### Week 10

##### March 26: Mastery Quiz 8 due

##### March 25: Absolute Convergence and the Ratio and Root tests

- Read one of:
- §4.6-7 of the online notes
- Stewart §11.6 (And 11.7 might be helpful review)
- Strang and Herman second half of §5.5 and all of §5.6

##### March 24: WeBWorK due

- Request a topic for this week’s mastery quiz if you want to retest something before 11

##### March 23: Comparision Test and Alternating Series

- Read one of:
- §4.5 of the online notes (Plus bonus 4.6.1)
- Stewart §11.4-5
- Strang and Herman Volume 2 §5.4 (and first half of §5.5

- Read the Solutions for Mastery Quiz 7

### Spring Break

### Week 9

##### March 12: Mastery Quiz 7 due

##### March 11: The Integral Test

- Read one of:
- §4.3-4 of the online notes
- Stewart §11.3
- Strang and Herman Volume 2 §5.3

##### March 10: WeBWorK due

- Request a Topic for this week’s mastery quiz, if you want to reattempt a topic before topic 9

##### March 9: Series

- Read one of:
- §4.2 of the online notes
- Stewart §11.2
- Strang and Herman Volume 2 §5.2

### Week 8

##### March 5: WeBWorK not due today

Got it up late so I just made the whole thing due next Tuesday.

##### March 4: Sequences

- Read one of:
- §4.1 of the online notes (but don’t worry much about 4.1.3-4).
- Stewart §11.1
- Strang and Herman Volume 2 §5.1

- Read the solutions to the midterm

##### March 2: Midterm due 7 PM EST.

- Read the solutions to mastery quiz 6.
- No class meeting, but I will be in the Blackboard during our usual class time. If you want to take the test and know I’ll be available to answer questions, this is a good time to do it.
- Midterm due at 7 PM

### Week 7

##### February 26: Mastery Quiz Due

(Updated Feb 25 3:15! Fixed typo in 11a)

##### February 25: Separable Differential Equations

- Read one of:
- §3.4-5 of the online notes
- Stewart §9.3-4
- Strang and Herman Volume 2 §4.3 and §4.4

- Bonus content
- In class I talked about the SIR model of epidemics, which we use to model how diseases spread and retreat. This is a blog post I wrote last March explaining it in the context of covid.
- 3Blue1Brown series on differential equations

##### February 24: WeBWorK due

- Request a topic for this week’s mastery quiz, if you want to reattempt a topic before topic 7

##### February 23: Differential Equations

- Read the solutions to mastery quiz 5.
- Read one of:
- §3.3-4 of the online notes
- Stewart §9.1 and §9.3
- Strang and Herman Volume 2§4.1 and §4.3

### Week 6

##### February 19: Mastery Quiz 5 due (updated 1:15 Feb 18)

##### February 18: Arc Length and Surface Area

- Read one of:
- §3.2 of the online notes (sloppy; I’ll try to clean them up later.)
- Stewart §8.1-2
- Strang and Herman Volume 2§2.4

- Fun bonus: This Numberphile video on Gabriel’s Horn

##### February 17: WeBWorK due

I know it’s set to due on the 19th in the system. I’m not going to change that but you should aim to have it done on Wednesday anyway.

##### February 16: Improper Integrals

- Read the solutions to mastery quiz 4.
- Read one of:
- §3.1 of the online notes
- Stewart §7.8
- Strang and Herman Volume 2§3.7

### Week 5

##### February 12: Mastery Quiz 4 due

##### February 11: Numeric Integration

- Read one of:
- §2.4 of the online notes
- Stewart §7.7
- Strang and Herman §3.6

##### February 10: WeBWorK due

##### February 9: Partial Fractions

- Read the solutions to mastery quiz 3.
- Read one of:
- §2.3 of the online notes
- Stewart §7.4
- Strang and Herman Volume 2§3.4

### Week 4

##### February 5: Mastery Quiz 3 due

##### February 4: Trigonometric Integrals

- Read one of:
- §2.2 of the online notes (not yet posted)
- Stewart §7.2 and §7.3
- Strang and Herman Volume 2§3.2 and §3.3

##### February 3: WeBWorK due

##### February 2: Integration by Parts

- Read the solutions to mastery quiz 2.
- Read one of:
- §2.1 of the online notes (not yet posted)
- Stewart §7.1
- Strang and Herman Volume 2§3.1

### Week 3

##### January 29: Mastery Quiz 2 due

##### January 28: L’Hospital’s Rule

- Read one of:
- §1.6 of the online notes
- Stewart §6.8
- 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 27: WeBWorK due

##### January 26: Inverse Trigonometric Functions

- Read the solutions to mastery quiz 1.
- Read one of:
- §1.5 of the online notes (updated Jan 24)
- Stewart §6.6
- Strang and Herman Volume 1 §1.4 and Volume 1 § 3.7 the bits on inverse trigonometric functions, and Volume 2 §1.7

### Week 2

##### January 22: Mastery Quiz 1 due

##### January 21: Integrals with Exponentials and Logarithms

- Read one of:
- §1.4 of the online notes (As updated Jan 19)
- Stewart §6.4
- Strang and Herman Volume 1 §5.6 or Volume 2 §1.6

##### January 20: WeBWorK due

##### January 19: Derivatives with Exponentials and Logarithms

- Test WeBWorK set due
- Read one of:
- §1.3 of the online notes (Updated Jan 17)
- Stewart the rest of §6.2 and §6.3
- Strang and Herman
**Volume 1**§3.9 and possibly

### Week 1

##### January 14: The Exponential and the Logarithm

- Read one of:
- §1.2 of the online notes
- Stewart §6.2 and §6.3, ignoring the derivative and integral sections
- Strang and Herman
**Volume 1**§1.5

- WeBWorK due January 19 and another due January 20.

##### January 12: Syllabus and Inverse Functions

- Please read the syllabus
- Claim your account on WeBWorK. Username is your gwu email at gwu.edu (with no “gwmail” in the address!) and password is your student ID (please change this!)
- Read Professor Bonin’s advice on study skills
- Read one of:
- Section 1.1 of the online notes
- Stewart §6.1
- Strang and Herman
**Volume 1**§1.4

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

## 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.

The course syllabus is available here.

## Course notes

- Course Notes
- Section 1: Transcendental Functions
- Section 2: Integration Techniques
- Section 3: Applications
- Section 4: Series
- Section 5: Power Series and Taylor Series

## Mastery Quizzes

The topics for the quizzes are:

- Inverse Functions
- Exponential and Logarithm
- Derivatives of Exponentials and Logarithms
- Integrals involving Exponentials and Logarithms
- Inverse Trigonometric Functions
- L’Hospital’s rule
- Integration by Parts
- Trigonometric Integrals
- Partial Fractions
- Numeric Integration
- Improper Integrals
- Arc Length and Surface Area
- Separable Differential Equations
- Sequences
- Geometric and Telescoping Series
- Divergence and Integral Tests
- Comparison Test and Limit Comparison Test
- Absolute and Conditional Convergence
- Power Series
- Power Series as Functions
- Theory of Taylor Series
- Computing Taylor Series
- Applications of Taylor series
- Parametrization

- Mastery Quiz 1 due Friday, January 22.
- Mastery Quiz 2 due Friday, January 29.
- Mastery Quiz 3 due Friday, February 5.
- Mastery Quiz 4 due Friday, February 12.
- Mastery Quiz 5 due Friday, February 19.
- Mastery Quiz 6 due Friday, February 26.
- Mastery Quiz 7 due Friday, March 12
- Mastery Quiz 8 due Friday, March 26
- Mastery Quiz 9 due Friday, April 2
- Mastery Quiz 10 due Friday, April 9
- Mastery Quiz 11 due Friday, April 16
- Mastery Quiz 12 due Friday, April 23
- Mastery Quiz 13 due Friday, April 30

## Tests

- Midterm due March 2 at 7 PM
- Final Exam due May 4 at midnight

Graphing calculators will **not** be allowed on tests. Scientific, non-programmable calculators will be allowed. I will have some to share, but not enough for everyone.

## Textbook

The official textbook for Math 1232 is *Calculus*, 8th edition by James Stewart (ISBN-13: 978-1285740621,
ISBN-10: 1285740629). It is a very good (and very expensive) textbook. If you go on to take Calculus 2 or Multivariable Calculus at GW, you will also need this book for those classes.

Another perfectly fine book is *Calculus 2*, by Gilbert Strang and Jed Herman. It is available for free online here.

I will be loosely following Stewart, and will attempt to give references to both books whenever I can. I will not assign problems from either book, but both will contain many problems for if you need extra practice.

Do **not** purchase *Calculus: Early Trancendentals*, also by Stewart: it is not the same book as *Calculus* and it is not used in any mathematics course at GW.

This section of Math 1232 will **not** use WebAssign.