 # APEX Calculus

## IndexIndex

aa@$$"!$$
Absolute Convergence Theorem
absolute maximum
absolute minimum
Absolute Value Theorem
acceleration
accumulated error
using Euler’s method
Alternating Harmonic Series
Alternating Series Test
an@$$a_\text{N}$$
analytic function
angle of elevation
antiderivative
of vector-valued function
approximation
linear
tangent line
arc length
arc length parameter
asymptote
horizontal, Item
vertical
at@$$a_\text{T}$$
average rate of change
average value of a function
average value of function
average velocity
bacterial growth
Binomial Series
Bisection Method
boundary point
bounded
interval
bounded sequence
convergence
bounded set
carrying capacity
center of mass
Chain Rule
multivariable
notation
circle of curvature
circulation
closed
closed disk
concave down
concave up
concavity
inflection point
test for
conic sections
degenerate
ellipse
hyperbola
parabola
connected
simply
conservative field
Constant Multiple Rule
of derivatives, Item
of integration, Item
of series, Item
constrained optimization
continuity
of exponential functions
of logarithmic functions
of polynomial functions
of rational functions
of trigonometric functions
continuous
at a point, Item
everywhere, Item
on an interval, Item
continuous function
properties
vector-valued
contour lines
convergence
absolute
Alternating Series Test
conditional, Item
Direct Comparison Test
Direct Comparison Test!for integration, Item
Integral Test
interval of, Item
Limit Comparison Test
Limit Comparison Test!for integration
nth@$$n$$th-term test
of geometric series, Item
of improper int.
of monotonic sequences, Item
of p@of $$p$$-series
of power series
of sequence
of series, Item
Ratio Comparison Test
Root Comparison Test
coordinates
cylindrical
polar
spherical
critical number
critical point
cross product
and derivatives
applications
applications!area of parallelogram
applications!torque
applications!volume of parallelepiped
definition
properties
curl
of conservative fields
curvature
and motion
equations for
of circle
curve
parametrically defined
rectangular equation
smooth
curve sketching
cusp
cycloid
cylinder
cylindrical coordinates
decreasing function
finding intervals
definite integral
and substitution
of vector-valued function
properties
del operator
derivative
acceleration
as a function
at a point
basic rules
Chain Rule
Constant Multiple Rule, Item
Constant Rule, Item
differential
directional
exponential functions
First Deriv. Test
Generalized Power Rule
higher order
higher order!interpretation
hyperbolic funct., Item
implicit
interpretation
inverse function
inverse hyper., Item
inverse trig.
logarithmic
Mean Value Theorem
mixed partial
motion
multivariable differentiability
normal line
notation
parametric equations
partial
Power Rule
power series
Product Rule
Quotient Rule
Second Deriv. Test
Sum/Difference Rule, Item
tangent line
trigonometric functions
vector-valued functions
velocity
difference quotient
differentiable
on a closed interval
differential
notation
differential equation
definition
first order linear
general solution
graphical solution
implicit soution
integrating factor
logistic
modeling
numerical solution
order of
particular solution
separable
Direct Comparison Test
for integration, Item
for series
direction field. See slope field
directional derivative
directrix
discontinuity
infinite, Item
jump, Item
removable, Item
Disk Method
displacement
distance
between lines, Item
between point and line, Item
between point and plane
between points in space
traveled
divergence
Alternating Series Test
Direct Comparison Test
Direct Comparison Test!for integration, Item
Integral Test
Limit Comparison Test
Limit Comparison Test!for integration
nth@$$n$$th-term test
of geometric series, Item
of improper int.
of p@of $$p$$-series
of sequence
of series, Item
Ratio Comparison Test
Root Comparison Test
Divergence Theorem
in space
in the plane
dot product
and derivatives
definition
properties
double integral
in polar
properties
eccentricity
elementary function
ellipse
definition
eccentricity
parametric equations, Item
reflective property
standard equation
Euler’s Method
Euler’s method
accumulated error
everywhere continuous, Item
exponential function
continuity of
extrema
absolute
and First Deriv. Test
and Second Deriv. Test
finding
relative
Extreme Value Theorem
extreme values
factorial
First Derivative Test
first octant
floor function
flow
fluid pressure/force
focus
Fubini’s Theorem
function
continuous
floor
of three variables
of two variables
vector-valued
Fundamental Theorem of Calculus
and Chain Rule
Fundamental Theorem of Line Integrals
Gabriel’s Horn
Gauss’s Law
general solution
of a differential equation
Generalized Power Rule
geometric series
and level curves, Item
and level surfaces
Green’s Theorem
half life
Harmonic Series, Item
Hooke’s Law
hyperbola
definition
eccentricity
parametric equations, Item
reflective property
standard equation
hyperbolic function
definition, Item
derivatives, Item
identities, Item
integrals, Item
inverse
inverse!derivative, Item
inverse!integration
inverse!logarithmic def., Item
implicit differentiation
improper integration
incompressible vector field
increasing function
finding intervals
indefinite integral
of vector-valued function
indeterminate form
inflection point
initial condition
initial point
initial value problem
for differential equations
Integral Test
integration
arc length
area
area between curves
average value
by parts
by substitution
definite
definite!and substitution
definite!properties
definite!Riemann Sums
displacement
distance traveled
double
fluid force
Fun. Thm. of Calc.
general application technique
hyperbolic funct., Item
improper
indefinite
inverse hyperbolic
iterated
Mean Value Theorem
multiple
notation
numerical
numerical!Left/Right Hand Rule
numerical!Simpson’s Rule
numerical!Trapezoidal Rule
of multivariable functions
of power series
of trig. functions
of trig. powers
of vector-valued function
of vector-valued functions
partial fraction decomp.
Power Rule, Item
Sum/Difference Rule, Item
surface area
trig. subst., Item
triple
volume!cross-sectional area
volume!Disk Method
volume!Shell Method
volume!Washer Method
with cylindrical coordinates
with spherical coordinates
work
interior point
Intermediate Value Theorem
interval of convergence, Item
iterated integration
changing order
properties
lamina
Left Hand Rule
Left/Right Hand Rule
level curves
level surface
limit
Absolute Value Theorem
at infinity, Item
definition
difference quotient
does not exist
indeterminate form
left-handed, Item
l’Hospital’s Rule
of exponential functions
of infinity
of logarithmic functions
of multivariable function
of polynomial functions
of rational functions
of sequence
of trigonometric functions
of vector-valued functions
one-sided
properties
pseudo-definition
right-handed, Item
Squeeze Theorem
Limit Comparison Test
for integration
for series
line integral
Fundamental Theorem
over scalar field
over vector field
path independent
properties over a scalar field, Item
properties over a vector field, Item
linearization
lines
distances between, Item
equations for
intersecting
parallel
skew
logarithmic differentiation
logarithmic function
continuity of
l’Hospital’s Rule
infinity over infinity, Item
zero over zero
Maclaurin Polynomial
definition
Maclaurin Polynomial|see{Taylor Polynomial}
Maclaurin Series
definition
Maclaurin Series|see{Taylor Series}
magnitude of vector
center of
maximum
absolute
and First Deriv. Test
and Second Deriv. Test
relative/local
Mean Value Theorem
of differentiation
of integration
Midpoint Rule
minimum
absolute
and First Deriv. Test
relative/local
moment
monotonic sequence, Item
multiple integration|see{iterated integration}
multivariable function
continuity
differentiability
domain
level curves
level surface
limit
range
Möbius band
Newton’s Law of Cooling
Newton’s Method
norm
normal line
normal vector
nth@$$n$$th-term test
numerical integration
Left/Right Hand Rule
Simpson’s Rule
Simpson’s Rule!error bounds
Trapezoidal Rule
Trapezoidal Rule!error bounds
octant
first
one to one
open
open ball, Item
open disk
optimization
constrained
order
of a differential equation
orientable
orthogonal
decomposition
orthogonal decomposition of vectors
orthogonal projection
osculating circle
outer unit normal vector
p@$$p$$-series
parabola
definition
general equation
reflective property, Item
parallel vectors, Item
Parallelogram Law
parametric equations
arc length
concavity
definition
finding $$\frac{d^2y}{dx^2}$$
finding $$\frac{dy}{dx}$$
normal line
of a surface
surface area
tangent line
parametrized surface
partial derivative
high order
meaning
mixed
second derivative
total differential
partition
size of
path independent
perpendicular|see{orthogonal}
piecewise smooth curve
planes
coordinate plane
distance between point and plane
equations of
introduction
normal vector
tangent
point of inflection
polar
coordinates
function!arc length
function!gallery of graphs
function!surface area
functions
functions!area
functions!area between curves
functions!finding $$\frac{dy}{dx}$$
functions!graphing
polar coordinates
plotting points
polynomial function
continuity of
potential function
Power Rule
differentiation
integration, Item
power series
algebra of
convergence
derivatives and integrals
projectile motion
definition
ellipsoid
elliptic cone
elliptic paraboloid
gallery
hyperbolic paraboloid
hyperboloid of one sheet
hyperboloid of two sheets
sphere
trace
Quotient Rule
r@$$\mathbb{R}$$
Ratio Comparison Test
for series
rational function
continuity of
rearrangements of series
reduction formula
trigonometric integral
Related Rates
related rates
Riemann Sum
and definite integral
Right Hand Rule
right hand rule
of Cartesian coordinates
of the cross product
Rolle’s Theorem
Root Comparison Test
for series
Second Derivative Test
sensitivity analysis
separation of variables
sequence
Absolute Value Theorem
positive
sequences
boundedness
convergent
definition
divergent
limit
limit properties, Item
monotonic, Item
series
absolute convergence, Item
Absolute Convergence Theorem
alternating
Alternating Series Test
alternating!Approximation Theorem
Binomial
conditional convergence, Item
convergent, Item
definition, Item
Direct Comparison Test
divergent, Item
geometric
Integral Test
interval of convergence, Item
Limit Comparison Test
Maclaurin
nth@$$n$$th-term test
p@$$p$$-series
partial sums, Item
power
power!derivatives and integrals
properties, Item
Ratio Comparison Test
rearrangements
Root Comparison Test
Taylor
telescoping
Shell Method
signed area
signed volume
simple curve
simply connected
Simpson’s Rule
error bounds
slope field
smooth
curve
surface
smooth curve
piecewise
speed, Item
sphere
spherical coordinates
Squeeze Theorem
Stokes’ Theorem
Sum/Difference Rule
of derivatives, Item
of integration, Item
of series, Item
summation
notation
properties
surface
smooth
surface area
of parametrized surface
solid of revolution
surface integral
surface of revolution
tangent line
directional
tangent plane
to a graph
Taylor Polynomial
definition
Taylor’s Theorem, Item
Taylor Series
common series
definition
equality with generating function
Taylor’s Theorem, Item
telescoping series
terminal point
theorem
Intermediate Value
torque
total differential
sensitivity analysis
total signed area
trace
Trapezoidal Rule
error bounds
trigonometric function
continuity of
triple integral
properties
unbounded sequence
unbounded set
unit normal vector
an@$$a_\text{N}$$
and acceleration
and curvature
definition
in $$\mathbb{R}^2$$
unit tangent vector
and acceleration
and curvature
at@$$a_\text{T}$$
definition
in $$\mathbb{R}^2$$
unit vector
properties, Item
standard unit vector, Item
unit normal vector
unit tangent vector
vector field, Item
conservative
curl of
divergence of
over vector field
potential function of
vector-valued function
algebra of
arc length
average rate of change
continuity
definition
derivatives
describing motion, Item
displacement
distance traveled
graphing
integration
limits
of constant length
projectile motion
smooth
tangent line
vectors
algebra of, Item
algebraic properties
component form
cross product
definition
dot product
magnitude
norm
normal vector
orthogonal
orthogonal decomposition
orthogonal projection
parallel, Item
Parallelogram Law
resultant
standard unit vector, Item
unit vector
zero vector
velocity
average velocity
volume
Washer Method
work