This page contains my public facing materials for multivariable calculus.
Flipped class videos
These videos are assigned for students to watch before attending lecture. They cover basics or motivation so students are ready to engage with the material in class. It allows for more time for group work in class.
Recorded Lectures
These videos are recorded class lectures. I'll eventually add more.
Supplementary Class Videos
Differential Forms
Standard textbooks for multivariable calculus work almost exclusive with vector fields and ignore differential forms. Often if a student wants to learn the differential forms viewpoint, the sources are at a much too advanced level for a student that is enrolled in or has just completed multivariable calculus. These videos are designed to be at the appropriate level for students in multivariable calculus (though a little linear algebra wouldn't hurt!) and explain the differential forms viewpoint and shows how to frame the results in this language as opposed to vector fields. Some of the definitions one encounters in multivariable calculus (the gradient, curl, and divergence for example) arise very naturally when one takes the differential forms approach to multivariable calculus.
Students work on problems in small groups of 2-4 students in class. Below are the problems given in class.
Function of Multiple Variables: Link
Contour Plots: Link
Partial Derivatives: Link
Tangent Plane Approximations and Differentials: Link
The Chain Rule in Multiple Variables: Link
Maximum and Minimum Values and Optimization: Link
Constrained Optimization and Lagrange Multipliers: Link
Vectors: Link
Dot and Cross Products: Link
Parametric Curves: Link
The Gradient and Directional Derivatives: Link
Line Integrals: Link
Double Integrals with Rectangular Coordinates: Link
Double Integrals with Polar Coordinates: Link
Flux Integrals: Link
Stokes' Theorem: Link
Triple Integrals with Rectangular Coordinates: Link
Triple Integrals with Cylindrical and Spherical Coordinates: Link
The Divergence Theorem: Link
Exams from courses at Occidental College
Fall 2025
Fall 2024
Exams from courses at Clemson University
Fall 2017
Fall 2016
Spring 2015
Spring 2014
Fall 2010
Integrals Review Sheet: Link