Calculus Volume 3

# Index

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
F
focal parameter1.5 Conic Sections
Fourier’s law of heat transfer6.8 The Divergence Theorem
Frenet frame of reference3.3 Arc Length and Curvature
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’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
graph of a function of two variables4.1 Functions of Several Variables
H
harmonic function6.4 Green’s Theorem
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
Hyperboloid of One Sheet2.6 Quadric Surfaces
Hyperboloid of Two Sheets2.6 Quadric Surfaces
I
implicit differentiation4.5 The Chain Rule
indefinite integral of a vector-valued function3.2 Calculus of Vector-Valued Functions
independent random variables5.2 Double Integrals over General Regions
independent variables4.5 The Chain Rule
initial-value problems7.1 Second-Order Linear Equations
intermediate variables4.5 The Chain Rule
inverse-square law6.8 The Divergence Theorem
K
Kepler’s laws of planetary motion3.4 Motion in Space
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
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
M
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
mixed partial derivatives4.3 Partial Derivatives
N
nonhomogeneous linear equation7.1 Second-Order Linear Equations
normal component of acceleration3.4 Motion in Space
normal form of Green’s theorem6.4 Green’s Theorem
O
objective function4.8 Lagrange Multipliers
optimization problem4.8 Lagrange Multipliers
orientation of a curve6.2 Line Integrals
orientation of a surface6.6 Surface Integrals
orthogonal vectors2.3 The Dot Product
P
parallelepiped2.4 The Cross Product
parallelogram method2.1 Vectors in the Plane
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
perpendicular2.3 The Dot Product
piecewise smooth curve6.2 Line Integrals
polar coordinate system1.3 Polar Coordinates
polar equations1.3 Polar Coordinates
potential function6.1 Vector Fields
principal unit normal vector3.3 Arc Length and Curvature
principal unit tangent vector3.2 Calculus of Vector-Valued Functions
projectile motion3.4 Motion in Space
Q
S
scalar line integral6.2 Line Integrals
scalar multiplication2.1 Vectors in the Plane
scalar projection2.3 The Dot Product
simple harmonic motion7.3 Applications
simply connected region6.3 Conservative Vector Fields
space-filling curve1.3 Polar Coordinates
space-filling curves1.1 Parametric Equations
spring-mass system7.3 Applications
standard equation of a sphere2.2 Vectors in Three Dimensions
standard form1.5 Conic Sections
standard unit vectors2.1 Vectors in the Plane
standard-position vector2.1 Vectors in the Plane
stream function6.4 Green’s Theorem
superposition principle7.1 Second-Order Linear Equations
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
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
transient solution7.3 Applications
tree diagram4.5 The Chain Rule
triangle inequality2.1 Vectors in the Plane
triple integral5.4 Triple Integrals
triple integral in cylindrical coordinates5.5 Triple Integrals in Cylindrical and Spherical Coordinates
triple scalar product2.4 The Cross Product
U
unit vector field6.1 Vector Fields
W
William Thomson (Lord Kelvin)4.3 Partial Derivatives
work done by a vector field6.2 Line Integrals
work done by the force2.3 The Dot Product