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## IndexA |B |C |D |E |F |G |H |I |K |L |M |N |O |P |Q |R |S |T |U |V |W |Z

A
absolute value
3.3 | 6.1
absolute value (derivative of)
11.1
acceleration
15.2
acceleration due to gravity
15.2
addition law
9.1 | 9.1
addition of points
4.1
addition rule for area
5.2
addition theorem for area
B.
additivity of area
5.1
almost disjoint sets
5.2
Analyst
10.1
and (logical) operator
3.1
antiderivative
12.4 | 17.1
antiderivative theorem
12.4
antidifferentiation, Maple commands
17.1
Apollonius (c 260-170 B.C.)
10.1
approachable point
10.2
approximation
6.2
approximation (strong approximation theorem)
6.2
approximation to decimals
6.2
arc length
9.1
arccos
14.6
arccot
14.6
Archimedes(287-212 B.C.)
0.1 | 2.2 | 2.3 | 2.4 | 9.1 | 9.2 | 9.2
Archimedes and 0.3
Archimedes and 9.3
Archimedes and 0.3
Archimedes and area of parabolic segment
2.3
arcsin
14.6
arctan
14.6
area = integral
8.6
area as a number
1.
area (assumptions about)
5.1
area between graphs
8.6
area function
5.1 | 5.2
area of box
1.
area of circle
8.5
area of circular sector
17.5
area of ellipse
8.5
area of parabola
2.1 | 2.3
area of parabolic segment
2.3
area of snowflake
2.6
area of triangle
5.3
area under power function
7.2
area, basic assumptions
5.1
Aristotle(384-322 B.C.)
1. | 10.1 | 10.3
Aryabhata (circa 510)
9.1
associative law for points
4.1
assumptions about area
5.1
assumptions: additivity of area
5.1
assumptions: symmetry invariance of area
5.1
assumptions: normalization of area
5.1
assumptions: translation invariance of area
5.1
average velocity
10.3
B
Babylonians
2.2 | 2.2 | 2.4 | 4.3
Babylonians 0.3
Banach, Stefan(1892-1945)
5.1
Berkeley, George (1685-1753)
10.1
Bernoulli, Jacob (1654-1705)
2.2 | 6.3 | 6.7
Bernoulli, Daniel(1700-1782)
14.6
between, is between and .
14.1
bijective
14.3
Bolzano, Bernard (1781-1848)
10.3 | 14.1
bound for a function
5.1
bounded function
5.1
bounded set
5.1
box
1.
box (circumscribed)
2.1
Brouncker, William(1620-1684)
5.5
C
Cantor, Georg (1845-1918)
1.
Cartesian product.
3.2
Cauchy, Augustin (1789-1857)
3.4 | 10.3
Cavalieri, Bonaventura (1598-1647)
2.5
chain rule
11.3
change of scale for integrals
8.5
chord of an arc
9.1
circle (area of)
8.5
circle (definition of)
4.3
circle (unit)
4.3
circular sector (area of)
17.5
circumscribed box
2.1
circumscribed hexagon for snowflake
2.6
clockwise
9.1
closed interval
1.
codomain
3.3
commutative law for points
4.1
composition of continuous functions
12.1
composition of functions
11.3
composition problem
11.3
compound interest
6.7
computer calculation of area
5.6
congruence problem
5.1
conic section
10.1
conservation of energy
15.2
constant sequence
6.4
constructivists
3.1
continuity defined
12.1
continuity on a set
12.1
contrapositive
3.1
convergent sequence
6.3 | 6.3
convex downward (spills water)
15.3
convex upward (holds water)
15.3
cosh
14.6
cosine defined
9.1
cosine, integral of
9.3 | 9.3
cot
11.2
counterclockwise
9.1
critical point
12.3
critical point theorem I
12.3
critical point theorem II
12.3
critical set
12.3
csc
11.2
D
decreasing function
5.3
derivative
0.1 | 0.1
derivative defined
10.3
derivative (fractional)
15.1
derivative (higher order)
15.1
derivative of absolute value
11.1
derivative of 14.6
derivative of arccot
14.6
derivative of 14.6
derivative of 14.6
derivative of 14.6
derivative of 14.6
derivative of exponential
14.6
derivative of logarithm
11.1
derivative of order 0
15.1
derivative of powers
11.1
derivative of reciprocal
11.2
derivative of and 11.1
derivative of 14.6
derivative of trigonometric functions
11.2
derivative of 14.6
derivative (second)
15.1
derived function
0.1
Descartes, Rene (1596-1660)
10.1
difference of sets
1.
differential
0.1 | 0.1 | 11.1
differentiation
0.1
differentiation, logarithmic
11.3
Dirichlet,P.G.Lejenue(1805-1859)
8.3
discontinuous function
12.1
disjoint sets
5.1
disjoint (almost disjoint sets)
5.2
distance between numbers
6.1
distance between points
4.3
distributive law for points
4.1
divergent sequence
6.3
domain
3.3
double angle formulas
9.1
dummy index
1.
dummy variable
3.4 | 8.2 | 10.2
E
e
5.4
e (numerical calculatioin of)
6.7
ellipse (area of)
8.5
Emperor Yu(c. 21st century B.C.)
4.3
end points of interval
1.
entertainment 6.7
entertainment (Calculation of sines)
9.1
entertainment (Discontinuous derivative problem)
15.3
entertainment (Falling bodies problem)
10.1
entertainment (Archimedes sine integral)
9.3
entertainment (Calculate )
5.4
entertainment (Composition problem)
11.3
entertainment (Area of a triangle)
5.3
entertainment (Square root problem)
0.3
entertainment (Calculate )
5.4
entertainment (Pine Tree problem)
2.4
entertainment (Snowflake problem)
2.6
entertainment (Bernoulli's problem)
2.2
entertainment (Calculation of )
0.3
entertainment (Congruence problem)
5.1
equal functions
3.3
equal propositions
3.1
equivalent proposition
3.1
error function
17.1
etymology of corollary
5.2
etymology of sine
9.1
Euclid ( fl. c. 300 B.C.)
1. | 2.4 | 10.1 | 10.3
Euler, Leonard (1707-1783)
3.3 | 6.3
Euler (summation notation)
3.4
even function
12.4
exponential function
14.3 | 14.4
exponential function (derivative of)
14.6
exponential function (properties of)
14.4
extreme point
12.3
extreme point (local)
12.3
extreme value property
12.3
F
fluxion
0.1 | 11.1
Fourier, Joseph (1768-1830)
8.1 | 15.1
fractional derivatives
15.1
function
0.1
function (bounded)
5.1
function (defined)
3.3
function (Euler's definition)
3.3
function (increasing)
5.3
functions equal
3.3
functions (operations on)
8.2
fundamental theorem of the calculus
0.1
fundamental theorem of calculus I
16.
fundamental theorem of calculus II
16.
Fundamental theorem of calculus (Leibniz statement of)
16.
G
Galileo (1564-1642)
10.1 | 10.1
geometric series
6.6
geometric series (finite)
2.4
Gougu
4.3
graph
3.3
graphs (area between)
8.6
gravity (acceleration due to)
15.2
H
half angle formulas
9.1
Hausdorff, Felix (1868-1942)
5.1
height of box
1.
Heine, Heinrich Eduard (1821-1881)
10.3
Heron (sometime between 250B.C and 150 A.D.)
13.3
higher order derivatives
15.1
hyperbolic functions
14.6
I
Ibn-al-Haitham (circa 1000 A.D.)
2.2
image of under 3.3
image of 3.3
implies
3.1
increasing function
5.3
indefinite integral
9.4
induction
3.5
inequality rule for limits of functions
10.2
inequality rule for sequences
6.4
inequality theorem for integrals
8.2
inflection point
15.3
injective
14.3
inner snowflake
2.6
instantaneous velocity
10.3
integrable function
8.1
integral
8.1
integral (as area under a curve)
8.6
integral (Ei = exponential integral)
17.1
integral indefinite
9.4
integral of 9.3 | 9.3
integral of 9.3 | 9.3
integral (Si = sine integral)
17.1
integral (change of scale in)
8.5
integration
0.1
integration by parts
17.3
integration by substitution
17.4
integration of rational functions
17.7
interior point
10.2
intermediate value property
14.1 | 14.1 | 14.1
intersection of sets
1. | 2.6
interval
1.
inverse function
14.3
inverse function theorem
14.5
K
Katyayana (c. 600 BC or 500BC??)
4.3
kinetic energy
15.2
Koch, Helga von(1870-1924)
2.6 | 12.2
L
l'Hôpital,Guillaume François (1661-1701)
6.3
Lagrange, Joseph Louis(1736-1813)
0.1
11.1
Leibniz, Gottfried (1646-1716)
0.1 | 0.1 | 0.1 | 3.3 | 8.1 | 8.2 | 10.1 | 11.1 | 13.3 | 15.1 | 16.
Leibniz (notation for sums)
3.4
Leibniz (proof of product rule)
11.2
length of arc
9.1
limit of a sequence
6.3
limit (one-sided)
13.1
limits (infinite)
13.1
lines
4.1
Liouville, Joseph (1809-1882)
15.1
ln(2) calculation
5.6
ln(a)
0.1
local maximum
12.3
local minimum
12.3
localization rule
11.1
logarithm
5.4 | 5.4 | 7.2
logarithm (derivative of)
11.1
logarithmic differentiation
11.3
M
Maple
5.6 | 17.1 | 17.6
Maple leftsum
5.6
Maple rightsum
5.6
Maple average
5.6
Maple calculation of 6.7
Maple mypi
9.2
Maple routine
9.2
Maple sinsq
9.2
Maple, approximate integration
5.6
Maple, symbolic antidifferentiation
17.1
Maple: integration
9.4
maximum (local)
12.3
maximum of function
12.3
mean value theorem
12.4
mean value theorem for integrals
16.
Mercator, Nicolaus (1620-1687)
5.5
mesh of partition
5.3
minimum (local)
12.3
minimum of function
12.3
monotonic function
5.3
monotonic (piecewise)
8.2
monotonicity of area
5.2 | B.
N th root rule for sequences
6.4 th power theorem
6.5
Napier, John(1550-1632)
5.4
Newton, Isaac(1642-1727)
0.1 | 0.1 | 10.3 | 11.1
Newton's law (F=ma)
0.1
nice function
16.
non-integrable function
8.3
normalization property of area
5.1
not (logical) operator
3.1
nowhere differentiable function
12.2
Nullsequence rule
6.4
number as area
1.
O
objects in a set
1.
odd function
12.4
open interval
1.
operations on functions
8.2
optical illusion
9.1
optimization problems
13.2
or (logical) operator
3.1
ordered pair
3.2
outer snowflake
2.6
P
pair (ordered pair)
3.2
parabola (area of)
2.1 | 2.3
parabolic segment (area of)
2.3
parallelogram
4.1
partition
5.3
partition regular
5.3
partition-sample sequence
8.2
Pascal, Blaise (1623-1662)
2.2
peicewise monotonic function
8.2
piecewise monotonic (example of non-piecewise monotonic function)
12.2
pi
0.1 | 0.3 | 0.3 | 5.6 | 8.5
pi, computer calculation
5.6
point in plane
1.
point of inflection
15.3
points (in )
4.1
points in a set
1.
points (addition of)
4.1
potential energy
15.2
power function
14.4
power ( th power theorem)
6.5
power-sums (list of)
2.2
prerequisites
0.2
product rule for derivatives
11.2
product rule for limits
10.2
product rule for limits of functions
10.2
product rule for sequences
6.4
product (Cartesian)
3.2
proofs without words
2.2
proposition
3.1
proposition (set defined by)
3.2
proposition form
3.1
propositions (equality of)
3.1
propositions (equivalence of)
3.1
Ptolemy, Claudius (fl 127-151)
9.1
Pythagoras (f. 530-510 B.C.)
4.3
Pythagoreans
2.2
Q
quadratic formula
4.3
quotient rule for derivatives
11.2
quotient rule for limits
10.2
quotient rule for limits of functions
10.2
quotient rule for sequences
6.4
R
Ramanujan, Srinivasa (1887-1920)
0.3
rate of change
13.3
rational functions
17.7
rational number (definition)
1.
real number
0.1
reciprocal (derivative of)
11.2
reflection
2.3 | 4.2
reflection law for sin and cos
9.1
reflection theorem
14.3
regular partition
5.3
Rhind Papyrus
0.3
Riemann sum
7.1
Riemann, Bernhard (1826-1866)
8.1
right triangle
5.3
rituals for integration
17.4 | 17.4 | 17.5 | 17.6 | 17.6
Rolle, Michel (1652-1719)
12.4
Rolle's theorem
12.4
rotation
4.2
ruler function
8.4
S
Saint-Vincent, Grégoire de, (1584-1667)
6.6
sample
7.1
Sarasa, Alfons Anton de (1618-1667)
5.4
schizophrenia
3.1
sec 11.2
sector (circular)
17.5
segment
4.2
segments
4.1
sequence
3.3
sequence (constant sequence rule)
6.4
sequence (convergent)
6.3 | 6.3
sequence (divergent)
6.3
sequence (null sequence rule)
6.4
sequence (constant)
6.4
sequence (limit of)
6.3
sequence (product rule for)
6.4
sequence (sum rule for)
6.4
sequence (translate of)
6.4
sequence (translation rule for)
6.4
sequence ( th root rule for)
6.4
sequences (inequality rule for)
6.4
sequences (quotient rule for)
6.4
set
1.
set (bounded)
5.1
sets defined by propositions
3.2
sine (definition)
9.1
sine (etymology of)
9.1
sine (integral of)
9.3 | 9.3
sine integral (Si)
17.1
sinh
14.6
snowflake
2.6 | 12.2
snowflake (area of)
2.6
spike function
8.2 | 8.2 | 10.2
square root problem
0.3
squeezing rule for limits of functions
10.2
squeezing rule for sequences
6.4
stretch
8.5
Stringham, Irving
5.4
subadditivity of area
5.2
subinterval of a partition
5.3
subset
1.
substitution in integrals
17.6
substitution (trigonometric)
17.5
sum rule for derivatives
11.2
sum rule for limits
10.2
sum rule for limits of functions
10.2
sum rule for sequences
6.4
sum theorem for derivatives
17.2
sum theorem for indefinite integrals
9.4
sum theorem for integrals
8.2
summation formula
2.2 | 2.2 | 2.2 | 2.2 | 2.2
surjective
14.3
symmetric set
12.4
symmetry invariance
5.1
symmetry of square
4.2
T
tangent
10.1 | 10.1 | 10.3
tan 11.2
translate of a sequence
6.4
translate of set
4.2
translation invariance
5.1
translation rule for sequences
6.4
triangle inequality
6.1
triangle (area of)
5.3
triangle (right)
5.3
trick
6.5
trigonometric functions (definition)
9.1
trigonometric functions derivative of
11.1 | 11.2
trigonometric identities
9.1 | 9.1 | 9.1
trigonometric substitution
17.5
U
union of sets
1. | 2.6
uniqueness of inverses
14.3
Uniqueness theorem for convergence
6.3
unit circle
4.3
V
velocity
0.1 | 10.1 | 10.1
velocity (average)
10.3
velocity (instantaneous)
10.3
W
Weierstrass, Karl(1815-1897)
6.1 | 12.2
width of box
1.
work
0.1
Z
zero-area set
5.2 | 8.6
zeroth order derivative
15.1
Zu Chongzhi (429-500 A.D.)
0.3

Ray Mayer 2007-09-07