2023 Spring | Calc 2
Course Coordinator:
Recitation Instructor:
Help Session schedule (staffed by math grad students, in Cardwell 041)
Most material for this course is on Canvas.
Table of Contents
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
Supplemental video on the DI method / layout:
VIDEO
Recit 3 (Wed, Jan 25): Trig integrals
Writeup of the cases for ∫ sin p ( x ) cos q ( x ) d x \int \sin^p(x) \cos^q(x) \ dx ∫ sin p ( x ) cos q ( x ) d x ∫ tan p ( x ) sec q ( x ) d x \int \tan^p(x) \sec^q(x) \ dx ∫ tan p ( x ) sec q ( x ) d x 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 sin n , cos n , tan n , sec n n = 2 n=2 n = 2 sin 0 = cos 0 = tan 0 = sec 0 = 1 \sin^0 = \cos^0 = \tan^0 = \sec^0 = 1 sin 0 = cos 0 = tan 0 = sec 0 = 1
Recit 4 (Mon, Jan 30): Trig sub / Review for Midterm 1
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 R \mathbb{R} 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
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
Recit 11 (Wed, Feb 22): Center of mass
Recit 12 (Mon, Feb 27): Review for Midterm 2 (on Tues, Feb 28)
Recit 13 (Wed, Mar 1): Hyperbolic functions
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)
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
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
Computer Aid (For checking answers)
Math background refresher (Calc 1 & Trig)
blackpenredpen > Calc 2
Under "Videos with Worksheets", work through "Watch This Before Calc 2"
Under "Problem Set #1", work through "So you think you can take the derivative", and "Integral Battles"
Paul's Online Notes > Calc 1
Has worked out practice problems
Cheat sheets
Integration practice
I highly recommend the things made by blackpenredpen .
Particularly useful are his:
Series things