 Calculus Volume 3

# Index

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
F
focal parameter 1.5 Conic Sections
Fourier’s law of heat transfer 6.8 The Divergence Theorem
Frenet frame of reference 3.3 Arc Length and Curvature
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’s law for magnetism 6.5 Divergence and Curl
general bounded region 5.4 Triple Integrals
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
graph of a function of two variables 4.1 Functions of Several Variables
H
harmonic function 6.4 Green’s Theorem
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
Hyperboloid of One Sheet 2.6 Quadric Surfaces
Hyperboloid of Two Sheets 2.6 Quadric Surfaces
I
implicit differentiation 4.5 The Chain Rule
indefinite integral of a vector-valued function 3.2 Calculus of Vector-Valued Functions
independent random variables 5.2 Double Integrals over General Regions
independent variables 4.5 The Chain Rule
intermediate variables 4.5 The Chain Rule
inverse-square law 6.8 The Divergence Theorem
K
Kepler’s laws of planetary motion 3.4 Motion in Space
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
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
M
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
mixed partial derivatives 4.3 Partial Derivatives
N
nonhomogeneous linear equation 7.1 Second-Order Linear Equations
normal component of acceleration 3.4 Motion in Space
normal form of Green’s theorem 6.4 Green’s Theorem
Q
S
scalar line integral 6.2 Line Integrals
scalar multiplication 2.1 Vectors in the Plane
scalar projection 2.3 The Dot Product
simple harmonic motion 7.3 Applications
simply connected region 6.3 Conservative Vector Fields
space-filling curve 1.3 Polar Coordinates
space-filling curves 1.1 Parametric Equations
spring-mass system 7.3 Applications
standard equation of a sphere 2.2 Vectors in Three Dimensions
standard form 1.5 Conic Sections
standard unit vectors 2.1 Vectors in the Plane
standard-position vector 2.1 Vectors in the Plane
stream function 6.4 Green’s Theorem
superposition principle 7.1 Second-Order Linear Equations
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
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
transient solution 7.3 Applications
triangle inequality 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 scalar product 2.4 The Cross Product
U
unit vector field 6.1 Vector Fields
W
William Thomson (Lord Kelvin) 4.3 Partial Derivatives
work done by a vector field 6.2 Line Integrals
work done by the force 2.3 The Dot Product
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