Chapter 1

Functions of Several Variables

Domain and range

medium • 1 min read

Limits and continuity in two variables

medium • 2 min read

Sequential criterion for continuity

medium • 3 min read

Level curves and surfaces

medium • 4 min read

Topology of R^n basics

medium • 5 min read

Chapter 2

Partial Derivatives and Differentiability

Computation of partial derivatives

medium • 1 min read

Chain rule for several variables

medium • 2 min read

Directional derivatives and gradient

medium • 3 min read

Tangent planes and normal lines

medium • 4 min read

Extrema of functions of two variables (Hessian matrix)

medium • 5 min read

Chapter 3

Multiple Integrals (Double and Triple)

Double integrals over rectangular/general regions

medium • 1 min read

Double integrals in polar coordinates

medium • 2 min read

Triple integrals in rectangular coordinates

medium • 3 min read

Triple integrals in cylindrical/spherical coordinates

medium • 4 min read

Change of variables in multiple integrals

medium • 5 min read

Chapter 4

Vector Calculus (Gradient, Divergence, Curl)

Vector fields overview

medium • 1 min read

Line integrals of vector fields

medium • 2 min read

Fundamental theorem for line integrals

medium • 3 min read

Green's theorem

medium • 4 min read

Surface integrals, Stokes' and Divergence theorems

medium • 5 min read