Math 223 - Multivariable Calculus - Spring 2025

Math 223 - Multivariable Calculus
Spring 2025
Emily Proctor

Here are the videos for our course, arranged chronologically by topic.

Vectors

Sections 1.1 and 1.2 (vectors in R^2 and R^3): Part 1/notes.

Sections 1.3 and 1.4 (the dot and cross products): Part 1, Part 2, Part 3, and notes.

Sections 1.5 and 1.6 (planes and n-dimensional geometry): Part 1, Part 2, Part 3, and notes.

Section 1.7 (cylindrical and spherical coordinates): Part 1/notes, Part 2/notes, and Part 3/notes.

Multivariable Functions

Section 2.1 (multivariable functions): Part 1/notes, Part 2/notes, Part 3/notes, Part 4/notes, and Part 5/notes.

Section 2.2 (limits of multivariable functions): Part 1/notes, Part 2/notes, and Part 3/notes.

The Derivative in Higher Dimensions

Sections 2.3 and 2.4 (partial derivatives): Part 1/notes and Part 2/notes.

Section 2.3 (tangent planes and differentiability): Part 1/notes, Part 2/notes, and Part 3/notes.

Section 2.3 (the total derivative): Part 1/notes, Part 2/notes, and Part 3/notes.

Section 2.5 (the chain rule): Part 1/notes, Part 2/notes, and Part 3/notes.

Section 2.6 (the directional derivative and the gradient vector): Part 1/notes, Part 2/notes, and Part 3/notes.

Parametrized Curves, Vector Fields, and Tangent Planes

Section 3.1 (parametrized curves): Part 1/notes and Part 2/notes.

Section 2.6 (tangent planes to level surfaces): Part 1/notes, Part 2/notes, and Part 3/notes.

Section 3.2 (arclength): Part 1/notes, Part 2/notes, and Part 3/notes.

Section 3.3 (vector fields): Part 1/notes.

Section 3.4 (div, grad, and curl): Part 1/notes and Part 2/notes.

Optimization

Section 4.1 (Taylor polynomials): Part 1/notes and Part 2/notes.

Section 4.2 (local and absolute maxima and minima): Part 1/notes, Part 2/notes, and Part 3/notes.

Section 4.3 (Lagrange multipliers): Part 1/notes and Part 2/notes.

Integration

Section 5.1/5.2 (introduction to double integrals): Part 1/notes, Part 2/notes, and Part 3/notes.

Section 5.2 (integration of general rectangular regions): Part 1/notes, Part 2/notes, and Part 3/notes.

Section 5.3 (changing the order of integration): Part 1/notes.

Section 5.4 (triple integrals): Part 1/notes, Part 2/notes, Part 3/notes, and Part 4/notes.

Change of Variables

Section 5.5 (change of variables): Part 1/notes, Part 2/notes, Part 3/notes, and Part 4/notes.

Section 5.5 (integration in polar coordinates): Part 5/notes.

Section 5.5 (integration in cylindrical and spherical coordinates): Part 6/notes and Part 7/notes.

Line Integrals and Generalizations of the Fundamental Theorem of Calculus

Section 6.1 (line integrals of scalar functions): Part 1/notes, Part 2/notes, and Part 3/notes.

Section 6.1 (line integrals of vector fields): Part 4/notes, Part 5/notes, and Part 6/notes.

Section 6.2 (Green's theorem): Part 1/notes and Part 2/notes.

Section 6.3 (the fundamental theorem of line integrals): Part 1/notes, Part 2/notes, Part 3/notes, Part 4/notes, and Part 5/notes.

Section 6.2 (a nod to Stokes' and diverence theorems): Part 3/notes.