Daily Assignments
Final exam May 5 at 3 PM
April 26 Mastery Quiz
- Due in my office or on Blackboard: Mastery Quiz 13
- Topics: M4, S9, S10
- Solutions
Finals Week Schedule
- Monday April 25: In office 3-6 PM
- Tuesday April 26: In office 3:30 - 6:30 PM
- Wednesday April 27: In office 2-5 PM
- Thursday April 28: In office 3-6 PM
- Monday, May 2: In Office 3-5
- In Rome 771 from 5-8
April 21: Fun with Series
- Read the Solutions to mastery quiz 12
- Read section 5.6 of the online notes
- Check out these videos on Fourier series
April 19: Polar Coordinates
- Due in class: Mastery Quiz 12
- Topics: M4, S9, S10
- Read section 6.2 of the online notes
April 14: Parametric Coordinates
- Read the solutions for mastery quiz 11
- Read section 6.1 of the online notes (stay tuned for updates)
April 12: Applications of Taylor Series
- Due in class: Mastery Quiz 11
- Topics: M3, M4, S8
- Read section 5.5 of the online notes (Expect updates on Monday)
- See also Strang and Herman §6.4
April 7: Computing Taylor series
- Read the solutions to mastery quiz 10
- Read section 5.4 of the online notes
- See also: Strang and Herman §6.4
April 5: Taylor Series
- Due in class: Mastery Quiz 10
- Topics: M3, M4, S8
- Read section 5.3 of the online notes
- See alsoStrang and Herman §6.3
March 31: Power Series as Functions
- Read the Solutions to Mastery Quiz 9
- Read §5.2 of the online notes
- See also Strang and Herman §6.2
March 29: Power Series
- Due in class: Mastery Quiz 9
- Topics: M3, S7
- Read §5.1 of the online notes
- See also Strang and Herman §6.1
March 24: Absolute Convergence and the Ratio and Root tests
- Read the solutions to Mastery Quiz 8
- Read sections 4.5.2 and 4.6 of the online notes
March 22: Comparision Test and Alternating Series
- Due in class: Mastery Quiz 8
- Topics: M3, S6, S7
- Read sections 4.4 and 4.5.1 of the online notes
- See also Strang and Herman Volume 2 §5.4 and the first half of §5.5, up until the beginning of “Absolute and Conditional Convergence”
March 10: The Integral Test and the Comparison Tests
- Read the solutions to Mastery Quiz 7
- Read section 4.4 and 4.5 of the online notes
- See also Strang and Herman Volume 2 §5.3 and §5.4
March 8: Series and the Divergence Test
- Due in class: Mastery Quiz 7
- Topics: M2, S4, S5, S6
- 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 3: Sequences
- Read section 4.1 of the online notes. Maybe start section 4.2.
- See also Strang and Herman Volume 2 §5.1
March 1: Midterm!
February 24: Separable Differential Equations
- Read the solutions to Mastery Quiz 6
- Read section 3.4-5 of the online notes
- See also Strang and Herman Volume 2 §4.3 and §4.4
- 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
February 22: Differential Equations
- Due in class: Mastery Quiz 6
- Topics: M2, S3, S4, S5
- Read section 3.3 of the online notes
- See also Strang and Herman Volume 2§4.1
- Bonus: 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 17: Arc Length 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
- Fun bonus: This Numberphile video on Gabriel’s Horn
February 15: Improper Integrals
- Due in Class: Mastery Quiz 5
- Topics: M1, M2, S3
- You should definitely submit M2 and S3. You shouldn’t submit M1 if Blackboard shows a 4/4 on that, meaning you’ve gotten 2/2 at least twice already.
- Read section 3.1 of the online notes
- See also Strang and Herman Volume 2§3.7
February 10: 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 8: Integration with Partial Fractions
- Due in Class: Mastery Quiz 4
- Topics: M1, M2, S2
- You definitely should submit M2. Submit M1 unless you have gotten 2/2 on both previous attempts. Submit S2 if you didn’t get a 2/2 on last week’s attempt.
- Read Section 2.3 of the online notes
- See also Strang and Herman Volume 2§3.4
February 3: 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 1: Integration by Parts
- Mastery Quiz 3 due in class
- Topics: M1, S2
- Read section 2.1 of the online notes
- See also Strang and Herman Volume 2§3.1
January 27: 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 25: Inverse Trigonometric Functions
- Mastery Quiz 2 due in class
- Topics: M1, S1
- §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 20: Integrals with Exponentials and Logarithms
- Read the Solutions to Mastery Quiz 1
- Read section 1.4 of the online notes
- See also Strang and Herman Volume 1 §5.6 or Volume 2 §1.6
January 18: Derivatives with Exponentials and Logarithms
- Mastery Quiz 1 due in class
- Topics: S1
- Read section 1.3 of the online notes
- See also Strang and Herman Volume 1 §3.9 and possibly
January 13: The Exponential and the Logarithm
- Read Section 1.2 of the online notes
- See also Strang and Herman Volume 1 §1.5
January 11: 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 \(y=x\).
Course notes
- Course Notes
Mastery Quizzes
- Mastery Quiz 1
- Due Tuesday January 18
- Topics: S1
- Solutions
- Mastery Quiz 2
- Due Tuesday January 25
- Topics: M1, S1
- Solutions
- Mastery Quiz 3
- Due Tuesday February 1
- Topics: M1, S2
- Solutions
- Mastery Quiz 4
- Due Tuesday February 8
- Topics: M1, M2, S2
- Solutions
- Mastery Quiz 5
- Due Tuesday February 15
- Topics: M1, M2, S3
- Solutions
- Mastery Quiz 6
- Due Tuesday February 22
- Topics: M2, S3, S4, S5
- Solutions
- Mastery Quiz 7
- Due Tuesday March 8
- Topics: M2, S4, S5, S6
- Solutions
- Mastery Quiz 8
- Due Tuesday March 22
- Topics: M3, S6, S7
- Solutions
- Mastery Quiz 9
- Due Tuesday March 29
- Topics: M3, S7
- Solutions
- Mastery Quiz 10
- Due Tuesday April 5
- Topics: M3, M4, S8
- Solutions
- Mastery Quiz 11
- Due Tuesday April 12
- Topics: M3, M4, S8
- Solutions
- Mastery Quiz 12
- Due Tuesday April 19
- Topics: M4, S9, S10
- Solutions
- Mastery Quiz 13
- Due Tuesday April 26
- Topics: M4, S9, S10
- 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 1
- Final Exam
- Thursday, May 5, 3:00 &endash 5:00 PM
- Practice Final
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 1231 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.
The course syllabus is available here.