2022 Fall | Calc 3

• Course Coordinator:
  • Dr. Ivan Blank
• Recitation Instructor:
  • Winston Cheong
  • winstonc@ksu.edu
  • Office Hours: M 2:30--4:30 CW 127 & by appointment
  • Zoom personal meeting room

Most material for this course is on Canvas.

Recitation Supplement

• Hw 2
  • Examples for Problems 10 (b), 10 (d), 11 here
• Hw 3
  • Integral of $\sqrt{x^2 + a^2}$ writeup here (I strongly recommend you attempt it for yourself first.)
  • For #12 the formulas to use are on the cheat sheet for Test 1
• Post-Exam 1 comments
• Hw 4
  • On multidimenisonal limits
• Hw 6
  • For visualizing tangent planes: CalcPlot3D (you'll find this video helpful)
• Hw 8
  • Iterated integral example
• Hw 9
  • Triangular pyramid volume integral example
• Hw 10
  • The Jacobian is needed in this assignment. Some discussion on it is here:
    • https://tutorial.math.lamar.edu/classes/calciii/changeofvariables.aspx
    • https://math.libretexts.org/Courses/Monroe_Community_College/MTH_212_Calculus_III/Chapter_14%3A_Multiple_Integration/14.7%3A_Change_of_Variables_in_Multiple_Integrals_(Jacobians)
    • Though the main thing is to remember is that:
      • in polar, $dA = r \ dr\ d\theta$
      • in cylindrical, $dV = r\ dr\ d\theta \ dz$
      • in spherical, $dV = \rho^2 \sin \phi \ d\rho \ d\phi \ d\theta$
  • Visuals for some of the problems: https://www.wolframcloud.com/obj/winstonc/Published/calc3-hw10-visuals.nb
• Matlab Rootfinding Assignment comments
• Hw 11
  • Vector field pics for problem #2
• Solutions to Last Part of Practice Exam 3

Interesting tidbits

• "Failure" of Clairaut's theorem
• "Failure" of Fubini's theorem

Useful trig for integration

• $\sin x \cos x = \frac12 \sin(2x)$
• $\sin^2 x = \frac12(1-\cos(2x))$
• $\cos^2 x = \frac12(1+\cos(2x))$

Practice Exams

These are taken from Dr. Blank's 2020 Spring page

• Practice Test #1; solutions

• Practice Test #2; solutions

• Practice Test #3; solutions

  • 2018 Fall Test #3 Answers

• Practice Final; solutions

• Cheat Sheet for Test #1

• Cheat Sheet for Test #2

• Cheat Sheet for Final

Other Resources

• Professor Leonard's Calc 3 Youtube Playlist
• 3Blue1Brown / Khan Academy : Multivariable calc Youtube Playlist or through Khan Academy
• Paul's Online Notes > Calc 3

Integration Review

I highly recommend the things made by blackpenredpen. Particularly useful are his:

• Ultimate Calc 2 integral starter packet with accompanying video solutions
• 100 integrals packet with accompanying video solutions and video transcript
• Integration by parts worksheet
• Trig integrals worksheet (this playlist might help)
• Trig sub worksheet (this playlist might help)

Matlab Documentation

These links may ask you to make an account. Just make one that's affiliated with KSU.

• Web version: https://www.mathworks.com/help/index.html
• PDF version: https://www.mathworks.com/help/pdf_doc/matlab/index.html

KSU Math Exam Archive

• https://winstoncheong.github.io/Better-KSU-Math-Exam-Archive/calc3/
  • 2018 Fall has Exam 2 and Final (Dr. Blank coordinated this semester)
• https://archive.math.ksu.edu/course?course=math222

Recitation Grade (125 pts out of 900)

I will base your recitation grade on two things.

1. How well you know the material (effectively, your hw & exam grades)
2. If I see that you've put effort into the course.

The first overrides the second. The second is only used to move you up in the below cutoffs:

• 125 out of 125 pts: (≥ 80%) or (≥ 70% with effort)
• 100 out of 125 pts: (≥ 70%) or (≥ 60% with effort)
• 88 out of 125 pts: you exist