A

acceleration vector
3.4 Motion in Space

angular coordinate
1.3 Polar Coordinates

angular frequency
7.3 Applications

arc-length function
3.3 Arc Length and Curvature

arc-length parameterization
3.3 Arc Length and Curvature

Archimedean spiral
1.3 Polar Coordinates

B

Bessel functions
7.4 Series Solutions of Differential Equations

binormal vector
3.3 Arc Length and Curvature

boundary conditions
7.1 Second-Order Linear Equations

boundary point
4.2 Limits and Continuity

boundary-value problem
7.1 Second-Order Linear Equations

Brahe
3.4 Motion in Space

C

cardioid
1.3 Polar Coordinates

chain rule
3.2 Calculus of Vector-Valued Functions

characteristic equation
7.1 Second-Order Linear Equations

circulation
6.2 Line Integrals

*cissoid of Diocles*1.4 Area and Arc Length in Polar Coordinates

Clairaut’s theorem
6.1 Vector Fields

closed set
4.2 Limits and Continuity

Cobb-Douglas function
4.8 Lagrange Multipliers

Cobb-Douglas production function
4.3 Partial Derivatives

complementary equation
7.2 Nonhomogeneous Linear Equations

complex conjugates
7.1 Second-Order Linear Equations

complex number
7.1 Second-Order Linear Equations

component functions
3.1 Vector-Valued Functions and Space Curves

components
2.1 Vectors in the Plane

conic section
1.5 Conic Sections

connected region
6.3 Conservative Vector Fields

connected set
4.2 Limits and Continuity

conservative field
6.1 Vector Fields

constant multiple rule
3.2 Calculus of Vector-Valued Functions

constraints
4.8 Lagrange Multipliers

coordinate planes
2.2 Vectors in Three Dimensions

critical point of a function of two variables
4.7 Maxima/Minima Problems

cross product
2.4 The Cross Product

*cross-partial property*6.1 Vector Fields

curtate cycloid
1.1 Parametric Equations

curvature
3.3 Arc Length and Curvature

cusps
1.1 Parametric Equations

cycloid
1.1 Parametric Equations

cylinder
2.6 Quadric Surfaces

cylindrical coordinate system
2.7 Cylindrical and Spherical Coordinates

D

definite integral of a vector-valued function
3.2 Calculus of Vector-Valued Functions

derivative
3.2 Calculus of Vector-Valued Functions

derivative of a vector-valued function
3.2 Calculus of Vector-Valued Functions

determinant
2.4 The Cross Product

differentiable
4.4 Tangent Planes and Linear Approximations

direction angles
2.3 The Dot Product

direction cosines
2.3 The Dot Product

direction vector
2.5 Equations of Lines and Planes in Space

*directional cosines*4.6 Directional Derivatives and the Gradient

directional derivative
4.6 Directional Derivatives and the Gradient

directrix
1.5 Conic Sections

divergence
6.5 Divergence and Curl

divergence theorem
6.8 The Divergence Theorem

domain
6.1 Vector Fields

dot product
2.3 The Dot Product

double integral
5.1 Double Integrals over Rectangular Regions

double Riemann sum
5.1 Double Integrals over Rectangular Regions

E

Earth’s orbit
1.1 Parametric Equations

eccentricity
1.5 Conic Sections

electrical potential
4.6 Directional Derivatives and the Gradient

Electrical power
4.4 Tangent Planes and Linear Approximations

electrical resistance
4.4 Tangent Planes and Linear Approximations

electrostatic fields
6.8 The Divergence Theorem

ellipsoid
2.6 Quadric Surfaces

Elliptic Cone
2.6 Quadric Surfaces

elliptic paraboloid
2.6 Quadric Surfaces

Elliptic Paraboloid
2.6 Quadric Surfaces

*epitrochoid*1.1 Parametric Equations

equivalent vectors
2.1 Vectors in the Plane

Ernest Rutherford
4.3 Partial Derivatives

*error term*4.4 Tangent Planes and Linear Approximations

Euler’s formula
7.1 Second-Order Linear Equations

expected values
5.2 Double Integrals over General Regions

F

Faraday’s law
6.7 Stokes’ Theorem

*flow line*6.1 Vector Fields

flux
6.2 Line Integrals

flux integral
6.6 Surface Integrals

focal parameter
1.5 Conic Sections

focus
1.5 Conic Sections

force
2.1 Vectors in the Plane

Fourier’s law of heat transfer
6.8 The Divergence Theorem

Frenet frame of reference
3.3 Arc Length and Curvature

Fubini’s theorem
5.1 Double Integrals over Rectangular Regions

Fubini’s thereom
5.4 Triple Integrals

function of two variables
4.1 Functions of Several Variables

Fundamental Theorem for Line Integrals
6.8 The Divergence Theorem

Fundamental Theorem for Line Integrals.
6.3 Conservative Vector Fields

Fundamental Theorem of Calculus
6.8 The Divergence Theorem

G

Gauss’ law
6.8 The Divergence Theorem

Gauss’s law for magnetism
6.5 Divergence and Curl

general bounded region
5.4 Triple Integrals

general form
1.5 Conic Sections

general form of the equation of a plane
2.5 Equations of Lines and Planes in Space

general solution to a differential equation
7.1 Second-Order Linear Equations

generalized chain rule
4.5 The Chain Rule

gradient field
6.1 Vector Fields

graph of a function of two variables
4.1 Functions of Several Variables

gravitational force
6.3 Conservative Vector Fields

grid curves
6.6 Surface Integrals

H

*harmonic function*6.4 Green’s Theorem

heat equation
4.3 Partial Derivatives

heat flow
6.6 Surface Integrals

higher-order partial derivatives
4.3 Partial Derivatives

homogeneous functions
4.5 The Chain Rule

homogeneous linear equation
7.1 Second-Order Linear Equations

Hooke’s law
7.3 Applications

hurricanes
6.1 Vector Fields

Hyperboloid of One Sheet
2.6 Quadric Surfaces

Hyperboloid of Two Sheets
2.6 Quadric Surfaces

hypocycloid
1.1 Parametric Equations

I

implicit differentiation
4.5 The Chain Rule

improper double integral
5.2 Double Integrals over General Regions

indefinite integral of a vector-valued function
3.2 Calculus of Vector-Valued Functions

independent of path
6.3 Conservative Vector Fields

independent random variables
5.2 Double Integrals over General Regions

independent variables
4.5 The Chain Rule

initial-value problems
7.1 Second-Order Linear Equations

interior point
4.2 Limits and Continuity

intermediate variables
4.5 The Chain Rule

inverse-square law
6.8 The Divergence Theorem

iterated integral
5.1 Double Integrals over Rectangular Regions

J

joint density function
5.2 Double Integrals over General Regions

L

Lagrange multiplier
4.8 Lagrange Multipliers

*Laplace operator*6.5 Divergence and Curl

level curve of a function of two variables
4.1 Functions of Several Variables

level surface of a function of three variables
4.1 Functions of Several Variables

limaçon
1.3 Polar Coordinates

limit of a function of two variables
4.2 Limits and Continuity

limit of a vector-valued function
3.1 Vector-Valued Functions and Space Curves

line integral
6.2 Line Integrals

linear approximation
4.4 Tangent Planes and Linear Approximations

linearly dependent
7.1 Second-Order Linear Equations

linearly independent
7.1 Second-Order Linear Equations

*local extremum*4.7 Maxima/Minima Problems

lunes of Alhazen
5.2 Double Integrals over General Regions

M

major axis
1.5 Conic Sections

mass flux
6.6 Surface Integrals

mass of a wire
6.2 Line Integrals

method of Lagrange multipliers
4.8 Lagrange Multipliers

method of undetermined coefficients
7.2 Nonhomogeneous Linear Equations

method of variation of parameters
7.2 Nonhomogeneous Linear Equations

minor axis
1.5 Conic Sections

mixed partial derivatives
4.3 Partial Derivatives

N

nappes
1.5 Conic Sections

nonhomogeneous linear equation
7.1 Second-Order Linear Equations

*normal*2.3 The Dot Product

normal component of acceleration
3.4 Motion in Space

*normal form of Green’s theorem*6.4 Green’s Theorem

normal plane
3.3 Arc Length and Curvature

normal vector
2.5 Equations of Lines and Planes in Space

normalization
2.1 Vectors in the Plane

O

objective function
4.8 Lagrange Multipliers

octants
2.2 Vectors in Three Dimensions

one-to-one transformation
5.7 Change of Variables in Multiple Integrals

open set
4.2 Limits and Continuity

optimization problem
4.8 Lagrange Multipliers

orientation
1.1 Parametric Equations

orientation of a curve
6.2 Line Integrals

orientation of a surface
6.6 Surface Integrals

*orthogonal*2.3 The Dot Product

orthogonal vectors
2.3 The Dot Product

osculating circle
3.3 Arc Length and Curvature

*overdamped*7.3 Applications

P

parallelepiped
2.4 The Cross Product

parallelogram method
2.1 Vectors in the Plane

parameter
1.1 Parametric Equations

parameter domain
6.6 Surface Integrals

parameter space
6.6 Surface Integrals

parameterization of a curve
1.1 Parametric Equations

parameterized surface
6.6 Surface Integrals

parametric curve
1.1 Parametric Equations

parametric equations
1.1 Parametric Equations

parametric equations of a line
2.5 Equations of Lines and Planes in Space

parametric surface
6.6 Surface Integrals

partial derivative
4.3 Partial Derivatives

partial differential equation
4.3 Partial Derivatives

particular solution
7.2 Nonhomogeneous Linear Equations

path independent
6.3 Conservative Vector Fields

*perpendicular*2.3 The Dot Product

piecewise smooth curve
6.2 Line Integrals

planar transformation
5.7 Change of Variables in Multiple Integrals

plane curve
3.1 Vector-Valued Functions and Space Curves

polar axis
1.3 Polar Coordinates

polar coordinate system
1.3 Polar Coordinates

polar equations
1.3 Polar Coordinates

polar rectangle
5.3 Double Integrals in Polar Coordinates

potential function
6.1 Vector Fields

power series
7.4 Series Solutions of Differential Equations

principal unit normal vector
3.3 Arc Length and Curvature

principal unit tangent vector
3.2 Calculus of Vector-Valued Functions

product rule
3.2 Calculus of Vector-Valued Functions

projectile motion
3.4 Motion in Space

prolate cycloid
1.1 Parametric Equations

Q

Quadric surfaces
2.6 Quadric Surfaces

R

radial coordinate
1.3 Polar Coordinates

radial field
6.1 Vector Fields

radius of curvature
3.3 Arc Length and Curvature

radius of gyration
5.6 Calculating Centers of Mass and Moments of Inertia

region
4.2 Limits and Continuity

regular parameterization
6.6 Surface Integrals

reparameterization
3.1 Vector-Valued Functions and Space Curves

*resolution of a vector into components*2.3 The Dot Product

*resonance*7.3 Applications

Reuleaux triangle
5.2 Double Integrals over General Regions

right-hand rule
2.2 Vectors in Three Dimensions

*RLC series circuit*7.3 Applications

rotational field
6.1 Vector Fields

rulings
2.6 Quadric Surfaces

S

saddle point
4.7 Maxima/Minima Problems

scalar
2.1 Vectors in the Plane

scalar equation of a plane
2.5 Equations of Lines and Planes in Space

scalar line integral
6.2 Line Integrals

scalar multiplication
2.1 Vectors in the Plane

scalar projection
2.3 The Dot Product

simple curve
6.3 Conservative Vector Fields

simple harmonic motion
7.3 Applications

simple pendulum
4.4 Tangent Planes and Linear Approximations

simply connected region
6.3 Conservative Vector Fields

skew lines
2.5 Equations of Lines and Planes in Space

smooth
3.3 Arc Length and Curvature

space curve
3.1 Vector-Valued Functions and Space Curves

space-filling curve
1.3 Polar Coordinates

*space-filling curves*1.1 Parametric Equations

speed
2.1 Vectors in the Plane

spherical coordinate system
2.7 Cylindrical and Spherical Coordinates

spring-mass system
7.3 Applications

standard equation of a sphere
2.2 Vectors in Three Dimensions

standard form
1.5 Conic Sections

*standard position*3.1 Vector-Valued Functions and Space Curves

standard unit vectors
2.1 Vectors in the Plane

standard-position vector
2.1 Vectors in the Plane

steady-state solution
7.3 Applications

stream function
6.4 Green’s Theorem

sum and difference rules
3.2 Calculus of Vector-Valued Functions

superposition principle
7.1 Second-Order Linear Equations

surface area
6.6 Surface Integrals

surface independent
6.7 Stokes’ Theorem

surface integral
6.6 Surface Integrals

surface integral of a scalar-valued function
6.6 Surface Integrals

surface integral of a vector field
6.6 Surface Integrals

symmetric equations of a line
2.5 Equations of Lines and Planes in Space

T

Tacoma Narrows Bridge
7.3 Applications

tangent plane
4.4 Tangent Planes and Linear Approximations

tangent vector
3.2 Calculus of Vector-Valued Functions

tangential component of acceleration
3.4 Motion in Space

*tangential form of Green’s theorem*6.4 Green’s Theorem

three-dimensional rectangular coordinate system
2.2 Vectors in Three Dimensions

topographical map
4.1 Functions of Several Variables

Torque
2.4 The Cross Product

total differential
4.4 Tangent Planes and Linear Approximations

traces
2.6 Quadric Surfaces

transformation
5.7 Change of Variables in Multiple Integrals

*transient solution*7.3 Applications

tree diagram
4.5 The Chain Rule

triangle inequality
2.1 Vectors in the Plane

triangle method
2.1 Vectors in the Plane

triple integral
5.4 Triple Integrals

triple integral in cylindrical coordinates
5.5 Triple Integrals in Cylindrical and Spherical Coordinates

triple integral in spherical coordinates
5.5 Triple Integrals in Cylindrical and Spherical Coordinates

triple scalar product
2.4 The Cross Product

V

vector
2.1 Vectors in the Plane

vector addition
2.1 Vectors in the Plane

vector difference
2.1 Vectors in the Plane

vector equation of a line
2.5 Equations of Lines and Planes in Space

vector equation of a plane
2.5 Equations of Lines and Planes in Space

vector field
6.1 Vector Fields

vector line integral
6.2 Line Integrals

vector parameterization
3.1 Vector-Valued Functions and Space Curves

vector product
2.4 The Cross Product

vector projection
2.3 The Dot Product

vector sum
2.1 Vectors in the Plane

vector-valued function
3.1 Vector-Valued Functions and Space Curves

vector-valued functions
3.4 Motion in Space

velocity vector
3.4 Motion in Space

vertex
1.5 Conic Sections

vertical trace
4.1 Functions of Several Variables

W

wave equation
4.3 Partial Derivatives

William Thomson (Lord Kelvin)
4.3 Partial Derivatives

witch of Agnesi
1.1 Parametric Equations

work done by a vector field
6.2 Line Integrals

work done by the force
2.3 The Dot Product

Z

zero vector
2.1 Vectors in the Plane