2023 Spring | Calc 2

Course Coordinator:
- Dr. Lino Amorim
Recitation Instructor:
- Winston Cheong
- winstonc@ksu.edu
- Recitations: MW 11:30–12:30 and 1:30–2:30
- Office Hours: MW 12:30–1:30 & by appointment
- Zoom personal meeting room
Help Session schedule (staffed by math grad students, in Cardwell 041)

Most material for this course is on Canvas.

Update (2025 Nov): Some time after this course took place, BPRP sunset his web domain and put his PDF resources behind a paywall on Patreon. I've removed the dead links. His videos are still a good resource for students.

2023 Spring | Calc 2

Recitation Schedule / Notes

Additional problems from the OpenStax Calc 2 textbook that seem decent / relevant are listed below. A subset of them will be worked through in recitation.

Recit 1 (Wed, Jan 18): U-substitution
- Section 1.5: 277, 280, 282, 297
- Section 1.6: 331, 334, 352
- Section 1.7: 412, 414, 423, 424, 429
Recit 2 (Mon, Jan 23): Integration by parts
- Section 3.1: 26, 27, 29, 32, 36, 38
  - #30 will be used as ~5e~
- Supplemental video on the DI method / layout
Recit 3 (Wed, Jan 25): Trig integrals
- Writeup of the cases for $\int \sin^p(x) \cos^q(x) \ dx$ and $\int \tan^p(x) \sec^q(x) \ dx$
- Section 3.2: 82, 83, 89, 90, 91, 99, 100, 102
- Recommended Exercise: Rederive the reduction formulas for $\sin^n, \cos^n, \tan^n, \sec^n$ $sin^{n}, cos^{n}, tan^{n}, sec^{n}$ given in class. Also, check that they still work when $n=2$ $n = 2$ (assuming that $\sin^0 = \cos^0 = \tan^0 = \sec^0 = 1$ $sin^{0} = cos^{0} = tan^{0} = sec^{0} = 1$ ).
  - Do give this a go, before looking at my writeup of this exercise
Recit 4 (Mon, Jan 30): Trig sub / Review for Midterm 1
- Trig Sub Table
- Section 3.3: 134, 138, 139, 140
  - 147 will be used as ~4d~
Recit 5 (Wed, Feb 1): Polynomial factorization, integrals of rational functions / Partial fraction decomposition
- Factorization formulas for difference of squares, sum and difference of cubes
- The discriminant of a quadratic, and how it allows us to check factorizability over $\mathbb{R}$
- Rational root theorem
- Polynomial long division vs. synthetic division
Recit 6 (Mon, Feb 6): Partial fraction decomposition cont
- Section 3.4: 197, 199, 200, 205, 206, 207, 211, 212
  - 199, 206, 205, 207 will be used as ~3 A-E~
Recit 7 (Wed, Feb 8): Numerical integration
- Brief notes
Recit 8 (Mon, Feb 13): Improper Integrals
Recit 9 (Wed, Feb 15): Arclength, Surface area
- The formulas I explained in recitation were taken from Paul's Online Notes > Surface Area
- Extra: Gabriel's Horn, a mathematical object with infinite surface area but finite volume. After one has learned how to compute improper integrals, and knows the formulas for surface area and volume of a solid of revolution, this assertion can be checked.
Recit 10 (Mon, Feb 20): Work
- Due to the snow day, this topic is now optional and will not be in the exams. I will still cover it in recitation.
- Lecture 10 with solutions
- Paul's Online Notes > Work
Recit 11 (Wed, Feb 22): Center of mass
- Formulas all on one page
- Hw 6 Problem 6 solution (Wrote this up because the values are nasty)
Recit 12 (Mon, Feb 27): Review for Midterm 2 (on Tues, Feb 28)
- Midterm 2 Review Solutions (Try the problems for yourself, before referring to this!)
Recit 13 (Wed, Mar 1): Hyperbolic functions
- Inverse hyperbolic functions in terms of logarithms
Recit 14 (Mon, Mar 6): (Separable) Differential Equations
Recit 15 (Wed, Mar 8): Sequences
Spring break (March 12--19)
Recit 16 (Mon, Mar 20): Series
Recit 17 (Wed, Mar 22): Integral test
Recit 18 (Mon, Mar 27): Comparison tests
Recit 19 (Wed, Mar 29): Alternating Series
Recit 20 (Mon, Apr 3): Review for midterm 3 (on April 4)
- Midterm 3 Review Solutions
Recit 21 (Wed, Apr 5): Ratio and root tests
Recit 22 (Mon, Apr 10): Power series
Recit 23 (Wed, Apr 12): Taylor series
Recit 24 (Mon, Apr 17): Taylor series II
Recit 25 (Wed, Apr 19): Parametric curves
Recit 26 (Mon, Apr 24): Parametric calculus
Recit 27 (Wed, Apr 26): Polar coordinates
- Desmos > Limacon / Cardioid
- Desmos > Rose Curve
Recit 28 (Mon, May 1): Area and length in polar coordinates
Recit 29 (Wed, May 3): Review for final
Recit 29 (Mon, May 8): Review for final (do we still meet?)

KSU Math Exam Archive

https://winstoncheong.github.io/Better-KSU-Math-Exam-Archive/calc2/

Particularly relevant are the 2020 Spring, 2019 Spring, and 2018 Spring semesters.

Exam Solutions

Other Resources

Paul's Online Notes > Calc 2

Computer Aid (For checking answers)

Wolfram Alpha

Math background refresher (Calc 1 & Trig)

Paul's Online Notes > Calc 1
- Has worked out practice problems
Cheat sheets
- Paul's Online Notes > Cheat Sheets & Tables
  - Look at "Common Derivatives and Integrals" and "Trig Cheat Sheet". Maybe also "Complete Calculus Cheat Sheet"
- My Unit Circle cheatsheet

Integration practice

"Ultimate integral starter" video (6 hours)
100 integrals video (6 hours)
Trig integrals playlist
Trig sub playlist

Series things

Convergence Tests notes
BPRP's "The List" (12 mins)
- Quick way to intuit whether a series converges or diverges by comparing the relative growth of standard functions. (You'll need to argue things more thoroughly on the exam.)
BPRP's 100 Series video (6 hrs)
BPRP "What Series Convergence Test Do I Use?" livestream (1.5 hours, 15 series)
BPRP Power series study guide (3.5 hours, 26.2 power series)