Daily Assignments
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
- 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
Tests
- Midterm due March 2 at 7 PM
- Final Exam
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.