Long, Keller & Schlicker

Active Calculus Multivariable

Multivariable calculus in the same activity-driven style as Active Calculus: vectors and vector-valued functions, functions of several variables, partial derivatives and optimization, multiple integrals, and the vector calculus of line and surface integrals through Green's, Stokes' and the Divergence theorems.

213 exercises44 sections

Status

Sections

FlagsLoading your progress…

Precalculus of Multivariable Functions

Three Dimensional Space3

Common Graphs in Three Dimensions1

Polar, Cylindrical, and Spherical Coordinates3

Vector-Valued Functions of One Variable

Vector-Valued Functions of One Variable10

Calculus of Vector-Valued Functions of One Variable4

Arc Length4

The TNB Frame3

Curvature7

Splitting the Acceleration Vector8

Derivatives of Multivariable Functions

Functions of Several Variables5

Limits6

First-Order Partial Derivatives7

Second-Order Partial Derivatives5

Linearization: Tangent Planes and Differentials8

The Multivariable Chain Rule5

Directional Derivatives and the Gradient6

Higher Dimensions4

Optimization8

Constrained Optimization: Lagrange Multipliers7

Multiple Integrals

Double Riemann Sums and Double Integrals over Rectangles4

Iterated Integrals5

Double Integrals over General Regions3

Applications of Double Integrals4

Double Integrals in Polar Coordinates4

Triple Integrals4

Triple Integrals in Cylindrical and Spherical Coordinates3

Change of Variables6

Vector Calculus

Vector Fields1

The Idea of a Line Integral1

Using Parameterizations to Calculate Line Integrals6

Path-Independent Vector Fields and the Fundamental Theorem of Calculus for Line Integrals7

Line Integrals of Scalar Functions2

The Divergence of a Vector Field3

The Curl of a Vector Field3

Green's Theorem3

Parameterizations of Surfaces and Surface Area5

Surface Integrals of Scalar Valued Functions3

Stokes' Theorem4

The Divergence Theorem5

Adapted from Active Calculus Multivariable © 2013–2026 Nicholas Long, Mitchel T. Keller, and Steven Schlicker. Licensed under CC BY-SA 4.0. Source: Active Calculus Multivariable. Imported at revision 692c03c.