A

acceleration vector3.4 Motion in Space

angular coordinate1.3 Polar Coordinates

angular frequency7.3 Applications

arc-length function3.3 Arc Length and Curvature

arc-length parameterization3.3 Arc Length and Curvature

Archimedean spiral1.3 Polar Coordinates

B

Bessel functions7.4 Series Solutions of Differential Equations

binormal vector3.3 Arc Length and Curvature

boundary conditions7.1 Second-Order Linear Equations

boundary point4.2 Limits and Continuity

boundary-value problem7.1 Second-Order Linear Equations

Brahe3.4 Motion in Space

C

cardioid1.3 Polar Coordinates

chain rule3.2 Calculus of Vector-Valued Functions

characteristic equation7.1 Second-Order Linear Equations

circulation6.2 Line Integrals

cissoid of Diocles1.4 Area and Arc Length in Polar Coordinates

Clairaut’s theorem6.1 Vector Fields

closed set4.2 Limits and Continuity

Cobb-Douglas function4.8 Lagrange Multipliers

Cobb-Douglas production function4.3 Partial Derivatives

complementary equation7.2 Nonhomogeneous Linear Equations

complex conjugates7.1 Second-Order Linear Equations

complex number7.1 Second-Order Linear Equations

component functions3.1 Vector-Valued Functions and Space Curves

components2.1 Vectors in the Plane

conic section1.5 Conic Sections

connected region6.3 Conservative Vector Fields

connected set4.2 Limits and Continuity

conservative field6.1 Vector Fields

constant multiple rule3.2 Calculus of Vector-Valued Functions

constraints4.8 Lagrange Multipliers

coordinate planes2.2 Vectors in Three Dimensions

critical point of a function of two variables4.7 Maxima/Minima Problems

cross product2.4 The Cross Product

cross-partial property6.1 Vector Fields

curtate cycloid1.1 Parametric Equations

curvature3.3 Arc Length and Curvature

cycloid1.1 Parametric Equations

cylinder2.6 Quadric Surfaces

cylindrical coordinate system2.7 Cylindrical and Spherical Coordinates

D

definite integral of a vector-valued function3.2 Calculus of Vector-Valued Functions

derivative3.2 Calculus of Vector-Valued Functions

derivative of a vector-valued function3.2 Calculus of Vector-Valued Functions

determinant2.4 The Cross Product

differentiable4.4 Tangent Planes and Linear Approximations

direction angles2.3 The Dot Product

direction cosines2.3 The Dot Product

direction vector2.5 Equations of Lines and Planes in Space

directional cosines4.6 Directional Derivatives and the Gradient

directional derivative4.6 Directional Derivatives and the Gradient

directrix1.5 Conic Sections

divergence6.5 Divergence and Curl

divergence theorem6.8 The Divergence Theorem

domain6.1 Vector Fields

dot product2.3 The Dot Product

double integral5.1 Double Integrals over Rectangular Regions

double Riemann sum5.1 Double Integrals over Rectangular Regions

E

Earth’s orbit1.1 Parametric Equations

eccentricity1.5 Conic Sections

electrical potential4.6 Directional Derivatives and the Gradient

Electrical power4.4 Tangent Planes and Linear Approximations

electrical resistance4.4 Tangent Planes and Linear Approximations

electrostatic fields6.8 The Divergence Theorem

ellipsoid2.6 Quadric Surfaces

Elliptic Cone2.6 Quadric Surfaces

epitrochoid1.1 Parametric Equations

equivalent vectors2.1 Vectors in the Plane

Ernest Rutherford4.3 Partial Derivatives

Euler’s formula7.1 Second-Order Linear Equations

expected values5.2 Double Integrals over General Regions

F

Faraday’s law6.7 Stokes’ Theorem

flow line6.1 Vector Fields

flux integral6.6 Surface Integrals

focal parameter1.5 Conic Sections

focus1.5 Conic Sections

Fourier’s law of heat transfer6.8 The Divergence Theorem

Frenet frame of reference3.3 Arc Length and Curvature

Fubini’s theorem5.1 Double Integrals over Rectangular Regions

Fubini’s thereom5.4 Triple Integrals

function of two variables4.1 Functions of Several Variables

Fundamental Theorem for Line Integrals6.8 The Divergence Theorem

Fundamental Theorem for Line Integrals.6.3 Conservative Vector Fields

Fundamental Theorem of Calculus6.8 The Divergence Theorem

G

Gauss’ law6.8 The Divergence Theorem

Gauss’s law for magnetism6.5 Divergence and Curl

general bounded region5.4 Triple Integrals

general form1.5 Conic Sections

general form of the equation of a plane2.5 Equations of Lines and Planes in Space

general solution to a differential equation7.1 Second-Order Linear Equations

generalized chain rule4.5 The Chain Rule

gradient field6.1 Vector Fields

graph of a function of two variables4.1 Functions of Several Variables

gravitational force6.3 Conservative Vector Fields

grid curves6.6 Surface Integrals

H

harmonic function6.4 Green’s Theorem

heat equation4.3 Partial Derivatives

heat flow6.6 Surface Integrals

higher-order partial derivatives4.3 Partial Derivatives

homogeneous functions4.5 The Chain Rule

homogeneous linear equation7.1 Second-Order Linear Equations

Hooke’s law7.3 Applications

hurricanes6.1 Vector Fields

Hyperboloid of One Sheet2.6 Quadric Surfaces

Hyperboloid of Two Sheets2.6 Quadric Surfaces

hypocycloid1.1 Parametric Equations

I

implicit differentiation4.5 The Chain Rule

improper double integral5.2 Double Integrals over General Regions

indefinite integral of a vector-valued function3.2 Calculus of Vector-Valued Functions

independent of path6.3 Conservative Vector Fields

independent random variables5.2 Double Integrals over General Regions

independent variables4.5 The Chain Rule

initial-value problems7.1 Second-Order Linear Equations

interior point4.2 Limits and Continuity

intermediate variables4.5 The Chain Rule

inverse-square law6.8 The Divergence Theorem

iterated integral5.1 Double Integrals over Rectangular Regions

J

joint density function5.2 Double Integrals over General Regions

L

Lagrange multiplier4.8 Lagrange Multipliers

Laplace operator6.5 Divergence and Curl

level curve of a function of two variables4.1 Functions of Several Variables

level surface of a function of three variables4.1 Functions of Several Variables

limaçon1.3 Polar Coordinates

limit of a function of two variables4.2 Limits and Continuity

limit of a vector-valued function3.1 Vector-Valued Functions and Space Curves

line integral6.2 Line Integrals

linear approximation4.4 Tangent Planes and Linear Approximations

linearly dependent7.1 Second-Order Linear Equations

linearly independent7.1 Second-Order Linear Equations

local extremum4.7 Maxima/Minima Problems

lunes of Alhazen5.2 Double Integrals over General Regions

M

major axis1.5 Conic Sections

mass flux6.6 Surface Integrals

mass of a wire6.2 Line Integrals

method of Lagrange multipliers4.8 Lagrange Multipliers

method of undetermined coefficients7.2 Nonhomogeneous Linear Equations

method of variation of parameters7.2 Nonhomogeneous Linear Equations

minor axis1.5 Conic Sections

mixed partial derivatives4.3 Partial Derivatives

N

nappes1.5 Conic Sections

nonhomogeneous linear equation7.1 Second-Order Linear Equations

normal2.3 The Dot Product

normal component of acceleration3.4 Motion in Space

normal form of Green’s theorem6.4 Green’s Theorem

normal plane3.3 Arc Length and Curvature

normal vector2.5 Equations of Lines and Planes in Space

normalization2.1 Vectors in the Plane

O

objective function4.8 Lagrange Multipliers

one-to-one transformation5.7 Change of Variables in Multiple Integrals

open set4.2 Limits and Continuity

optimization problem4.8 Lagrange Multipliers

orientation1.1 Parametric Equations

orientation of a curve6.2 Line Integrals

orientation of a surface6.6 Surface Integrals

orthogonal2.3 The Dot Product

orthogonal vectors2.3 The Dot Product

osculating circle3.3 Arc Length and Curvature

overdamped7.3 Applications

P

parallelepiped2.4 The Cross Product

parallelogram method2.1 Vectors in the Plane

parameter1.1 Parametric Equations

parameter domain6.6 Surface Integrals

parameter space6.6 Surface Integrals

parameterization of a curve1.1 Parametric Equations

parameterized surface6.6 Surface Integrals

parametric curve1.1 Parametric Equations

parametric equations1.1 Parametric Equations

parametric equations of a line2.5 Equations of Lines and Planes in Space

parametric surface6.6 Surface Integrals

partial derivative4.3 Partial Derivatives

partial differential equation4.3 Partial Derivatives

particular solution7.2 Nonhomogeneous Linear Equations

path independent6.3 Conservative Vector Fields

perpendicular2.3 The Dot Product

piecewise smooth curve6.2 Line Integrals

planar transformation5.7 Change of Variables in Multiple Integrals

plane curve3.1 Vector-Valued Functions and Space Curves

polar axis1.3 Polar Coordinates

polar coordinate system1.3 Polar Coordinates

polar equations1.3 Polar Coordinates

polar rectangle5.3 Double Integrals in Polar Coordinates

potential function6.1 Vector Fields

power series7.4 Series Solutions of Differential Equations

principal unit normal vector3.3 Arc Length and Curvature

principal unit tangent vector3.2 Calculus of Vector-Valued Functions

product rule3.2 Calculus of Vector-Valued Functions

projectile motion3.4 Motion in Space

prolate cycloid1.1 Parametric Equations

Q

Quadric surfaces2.6 Quadric Surfaces

R

radial coordinate1.3 Polar Coordinates

radial field6.1 Vector Fields

radius of curvature3.3 Arc Length and Curvature

radius of gyration5.6 Calculating Centers of Mass and Moments of Inertia

regular parameterization6.6 Surface Integrals

reparameterization3.1 Vector-Valued Functions and Space Curves

resolution of a vector into components2.3 The Dot Product

resonance7.3 Applications

Reuleaux triangle5.2 Double Integrals over General Regions

right-hand rule2.2 Vectors in Three Dimensions

RLC series circuit7.3 Applications

rotational field6.1 Vector Fields

rulings2.6 Quadric Surfaces

S

saddle point4.7 Maxima/Minima Problems

scalar2.1 Vectors in the Plane

scalar equation of a plane2.5 Equations of Lines and Planes in Space

scalar line integral6.2 Line Integrals

scalar multiplication2.1 Vectors in the Plane

scalar projection2.3 The Dot Product

simple curve6.3 Conservative Vector Fields

simple harmonic motion7.3 Applications

simple pendulum4.4 Tangent Planes and Linear Approximations

simply connected region6.3 Conservative Vector Fields

space curve3.1 Vector-Valued Functions and Space Curves

space-filling curve1.3 Polar Coordinates

space-filling curves1.1 Parametric Equations

spherical coordinate system2.7 Cylindrical and Spherical Coordinates

spring-mass system7.3 Applications

standard equation of a sphere2.2 Vectors in Three Dimensions

standard form1.5 Conic Sections

standard position3.1 Vector-Valued Functions and Space Curves

standard unit vectors2.1 Vectors in the Plane

standard-position vector2.1 Vectors in the Plane

steady-state solution7.3 Applications

stream function6.4 Green’s Theorem

sum and difference rules3.2 Calculus of Vector-Valued Functions

superposition principle7.1 Second-Order Linear Equations

surface area6.6 Surface Integrals

surface independent6.7 Stokes’ Theorem

surface integral6.6 Surface Integrals

surface integral of a scalar-valued function6.6 Surface Integrals

surface integral of a vector field6.6 Surface Integrals

symmetric equations of a line2.5 Equations of Lines and Planes in Space

T

Tacoma Narrows Bridge7.3 Applications

tangent plane4.4 Tangent Planes and Linear Approximations

tangent vector3.2 Calculus of Vector-Valued Functions

tangential component of acceleration3.4 Motion in Space

tangential form of Green’s theorem6.4 Green’s Theorem

three-dimensional rectangular coordinate system2.2 Vectors in Three Dimensions

topographical map4.1 Functions of Several Variables

Torque2.4 The Cross Product

total differential4.4 Tangent Planes and Linear Approximations

traces2.6 Quadric Surfaces

transformation5.7 Change of Variables in Multiple Integrals

transient solution7.3 Applications

tree diagram4.5 The Chain Rule

triangle inequality2.1 Vectors in the Plane

triangle method2.1 Vectors in the Plane

triple integral5.4 Triple Integrals

triple integral in cylindrical coordinates5.5 Triple Integrals in Cylindrical and Spherical Coordinates

triple integral in spherical coordinates5.5 Triple Integrals in Cylindrical and Spherical Coordinates

triple scalar product2.4 The Cross Product

V

vector2.1 Vectors in the Plane

vector addition2.1 Vectors in the Plane

vector difference2.1 Vectors in the Plane

vector equation of a line2.5 Equations of Lines and Planes in Space

vector equation of a plane2.5 Equations of Lines and Planes in Space

vector field6.1 Vector Fields

vector line integral6.2 Line Integrals

vector parameterization3.1 Vector-Valued Functions and Space Curves

vector product2.4 The Cross Product

vector projection2.3 The Dot Product

vector sum2.1 Vectors in the Plane

vector-valued function3.1 Vector-Valued Functions and Space Curves

vector-valued functions3.4 Motion in Space

velocity vector3.4 Motion in Space

vertex1.5 Conic Sections

vertical trace4.1 Functions of Several Variables

W

wave equation4.3 Partial Derivatives

William Thomson (Lord Kelvin)4.3 Partial Derivatives

witch of Agnesi1.1 Parametric Equations

work done by a vector field6.2 Line Integrals

work done by the force2.3 The Dot Product

Z

zero vector2.1 Vectors in the Plane