Below are the handouts (with solutions) that I used while teaching Math 2153 recitations at the Ohio State University in the Fall of 2021. I did not provide practice exams since the lecturer was already providing the students with additional practice problems before each exam. Students from future sections of this class may use these as a list of practice problems with solutions to study with. TAs for future sections of this class may decide to present these problems in their recitation sections, possibly even presenting their own solutions, then making these typed solutions available to their students for review later on. For the documents that are typed, I have also separately included the source files in case any other instructor wants to use a modified version of them in their own courses. My latex source files use this class file.
Introduction to Vectors
There are no practice problems and solutions since this is the first recitation of the semester.
Calculating Work and Vector Decompositions
Modeling the Game of Pool, Equations of Planes, Lines in 3-Space
Parameterization of Curves and Differentiation Rules for Vector Valued Functions
Motion (Position, Velocity, Acceleration) and Arclength
Curvature and Torsion
Limits and Differentiability in Several Variables
Gradient Vectors, Directional Derivatives, and the Second Derivative Test
The Method of Lagrange Multipliers, Absolute Minima and Maxima
Polar Coordinates and Triple Integration (Optional Handout for Fall Break)
Changing the order of Integration, Spherical and Cylindrical Coordinates
Line Integrals, Conservative Vector Fields, and Green’s Theorem
While we did not cover change of variables, surface integrals, Stoke’s theorem, or the divergence theorem during the recitations this semester, I have a handouts on these topics from when I was a TA for Math 2153 in the spring of 2022.