CALCULUS Understanding Its Concepts and Methods

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  A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

A   

Absolute value

Absolutely convergent series

Acceleration

Acceleration vector

Algebraic function

Alternating series

Altitude of a triangle

Angle measure

Angle between vectors

Angle bisector

Antiderivative

Approximate derivative

Approximate integral

Archimedes

Archimedes' principle

Arc length

Area

function

of a circle

of a parallelogram

of a surface

Arithmetic progression

Argument

Asymptotes

Average

cost

rate of change

velocity

B

Berkeley, George, Bishop of Cloyne

Bernoulli differential equation

Bernoulli, Johann

Bertrand, Joseph L. F.

Bézier curve

Bézier, Pierre

Binomial coefficient

Bounded interval

Bowditch, Nathaniel

C      A B C D E F G H I J K L M N O P Q R S T U V W X Y Z    top of page

Cauchy, Augustin Louis

Cauchy's mean value theorem

Cauchy test

Cavalieri, Francesco Bonaventura

Celsius

Ceiling

Centroid

Chain rule

Change of variable

Change order of integration

Chuquet, Nicolas

Circle

Circumcenter

Circumference

Closed interval

Comparison test

Complex

argument

number

Compound interest

Concave

Cone

Conic section

Conditionally convergent series

Conservative vector field

Continuous

Continuously compounded interest

Contour plot

Convergent series

Coordinates

cylindrical coordinates

polar coordinates

rectangular coordinates

spherical coordinates

Cosine

Cost

Cotes, Roger

Critical point

Cross product

Cross section method for volumes

Curl

Curtain

Curvature

Curve

Cylinder

Cylindrical coordinates

Cylindrical shell method

D       A B C D E F G H I J K L M N O P Q R S T U V W X Y Z    top of page

de Moivre, Abraham

Decay

Decreasing function

Definite integral

Degree

Del

Dependent variable

Derivative

definition

directional

notation

partial

rules

second

vector

Determinant

Difference quotient

Differentiable function

Differential

Differential equation

Differential operators

Direction

Directional derivative

Disc method for volumes

Discontinuity

Discriminant

Distance between two points

Distance from a point to a line

Divergence theorem

Divergent series

Divided differences

Domain

Doppler effect

Dot product

Double integral

polar coordinates

rectangular coordinates

Doubling time

E       A B C D E F G H I J K L M N O P Q R S T U V W X Y Z    top of page

e = 2.71828...

Ellipse

Ellipsoid

Equilateral triangle

Eratosthenes

Error bound

Essential discontinuity

Euclidean norm

Euler, Leonhard

Euler's method

Even function

Event

Exact differential equation

Expected value

Exponential functions

Exponential growth and decay

Extreme values

F       A B C D E F G H I J K L M N O P Q R S T U V W X Y Z    top of page

Factorial

Fahrenheit

Fermat, Pierre de

Finite interval

Floor

Fluid pressure

Force

Formulas for functions

Fourier polynomials

Fractional part

Fresnel sine function

Frustum

Fubini, Guido

Fubini's theorem

Function

algebraic

continuous

decreasing

definition

differentiable

even

exponential

hyperbolic

inverse

implicit

increasing

logarithmic

odd

one-to-one

piecewise-defined

rational

transcendental

trigonometric

Fundamental theorem of calculus

Fundamental theorem for conservative fields

G

Galileo Galilei

Gauss, Carl Friedrich

Gaussian quadrature

Generalized power rule

Generic function

Geometric progression

Geometric series

Gradient

definition

field

Graph

Gravitation

Greatest integer function

Green, George

Green's theorem

Gregory, James

Gregory of St. Vincent

Growth models

H

Half life

Half-open interval

Harmonic series

Heron of Alexandria (Hero)

Heron's formula

Higher derivatives

Hilbert, David

Historical sketches

Homogeneous differential equation

Horizontal

asymptote

line test

tangent line

Hydrostatic pressure

Hyperbola

Hyperbolic functions

Hyperboloid

Hypotenuse

I       A B C D E F G H I J K L M N O P Q R S T U V W X Y Z    top of page

i = − 1 ​

Implicit functions

Improper integral

Incenter

Income tax

Increasing function

Independent variable

Indeterminate forms

Infinite series

Inflection point

Initial value problem

Inner product

Instantaneous

rate of change

velocity

Integral

definite

double

iterated

line

Riemann sum

rules

surface

tables

test

Integrating factor

Integration methods

change of variable

partial fractions

parts

substitution

trig substitution

Intercepts

Interest

Intermediate value theorem

Interpolating polynomials

Interval

bounded

of convergence

unbounded

Inverse function

Irreducible quadratic polynomial

Isosceles triangle

Iterated integrals

J

Joule

Jump discontinuity

K

Kepler, Johannes

Kepler's laws

Kilogram

Kinetic energy

L       A B C D E F G H I J K L M N O P Q R S T U V W X Y Z    top of page

Lagrange form of the remainder

Lagrange interpolating polynomial

Lagrange, Joseph-Louis

Lambert, Johann Heinrich

Law of cosines and law of sines

Left-hand limit

Left sum

Leibniz, Gottfried

Leibniz notation

Length

of a vector

of a curve

Level curve

Level surface

l'Hôpital's rule

l'Hôpital, Marquis de

Limit

definition

one-sided

rules

Lindemann, Ferdinand von

Line

distance to a point

equations for a line

integral

Linear

differential equation

functions

Linearization

Lissajous, Jules Antoine

Local

linearity

maximum

Logarithms

Logistic growth

Lower sum

M       A B C D E F G H I J K L M N O P Q R S T U V W X Y Z    top of page

Maclaurin

polynomials

series

Maclaurin, Colin

Magnitude

Marginal cost

Matrix

addition

definition

determinant

Maximum

Mean value theorem

Median of a triangle

Menger, Karl

Mengoli, Pietro

Meter

Middle sum

Minimum

Moivre, Abraham de

Moment of inertia

Monotone

convergence theorem

function

sequence

Motion

Multiple integrals

N

Net area

Neville's polynomial interpolation algorithm

Newton

force

interpolating polynomial

iteration

law of cooling

law of gravitation

method

Newton-Cotes formulas

Newton, Isaac

Norm of a vector

Normal

Notation for vectors

Numerical integration

Gaussian quadrature

left sum

middle sum

Newton-Cotes formulas

right sum

Simpson's rule

trapezoidal rule

O

Odd functions

One-to-one function

Order of integration

Open interval

Optimization

Operators

Orthocenter

Orthogonal

Osculating circle

P       A B C D E F G H I J K L M N O P Q R S T U V W X Y Z    top of page

Padé, Henri

Pappus theorem

Parabola

Paraboloid

Parallelepiped

Parallelogram

Parametric

Partial

derivative

fractions

sums

Parts

Pascal, Blaise

Pascal's law

Pascal's triangle

Peano, Giuseppe

Periodic function

Perpendicular

Perpendicular bisector

Pi ( π ​)

Piecewise-defined function

Piecewise smooth curve

Pinching theorem

Pitch of a roof

Plane in space

Plane curve

Polar coordinates

Polynomial

functions

interpolation

Population

Position function

Power

rule

series

series tables

Pressure

Probability

definition

density function

Product

cross

dot

rule

Profit

Projection

Proportion

p-series

Pyramid

Pythagorean theorem

Q

Quadric surfaces

Quotient rule

R       A B C D E F G H I J K L M N O P Q R S T U V W X Y Z    top of page

Radian measure

Radius

of circle

of convergence

of curvature

of gyration

Random variable

Rate of change

Ratio

definition

test

Rational functions

Reciprocal rule

Rectangle

Rectangular coordinates

Recursive definition

Related rates

Relative maximum

Removable discontinuity

Revenue

Revolution

solid of revolution

surface of revolution

Riemann, Bernhard

Riemann sum

Right-hand limit

Right sum

Rolle's theorem

Rolle, Michel

Rotations

Rules

for derivatives

for integrals

for limits

S       A B C D E F G H I J K L M N O P Q R S T U V W X Y Z    top of page

Saddle point

Sample space

Sandwich theorem

Scalar

multiple

projection

triple product

Secant line

Second derivative

Second derivative test

Separable differential equation

Separation of variables

Sequence

Sequence of partial sums

Series

absolutely convergent series

alternating series

comparison test

conditionally convergent series

geometric series

harmonic series

infinite series

interval of convergence

Maclaurin series

p-series

power series

radius of convergence

ratio test

Taylor series

Shape of a graph

Shell method

Sigmoidal functions

Similar triangles

Simple closed curve

Simpson's rule

Simpson, Thomas

Sine

Slope

definition

field

Smooth curve

Solid of revolution

Solution to a differential equation

Space curve

Speed

Spherical

coordinates

integration

Sphere

Splines

Square

Squeeze theorem

Standard unit vectors

Step function

Stokes, George

Stokes' theorem

Substitution

Sum rule

Surface

area

definition

integral

level

parametric

quadric

of revolution

Symmetric difference quotient

T       A B C D E F G H I J K L M N O P Q R S T U V W X Y Z    top of page

Table

of integrals

of power series

of trigonometric identities

of values

Tangent

function

horizontal

lines

planes

vertical

Taylor

polynomials

theorem

series

Taylor, Brook

Temperature

Temperature scales

Tests for extreme values

Tests for convergence of series

absolute convergence

alternating series

comparison

divergent series

integral

limit comparison

p-series

ratio

Tetrahedron

Transcendental functions

Transformations

Translation of a graph

Trapezoidal rule

Triangle

Trigonometric

functions

identities

polynomials

substitution

Triple integral

in cylindrical coordinates

in rectangular coordinates

in spherical coordinates

U

Unbounded interval

Units

Upper sum

V

Variable

Vector

arithmetic

cross product

definition

derivative

direction

dot product

inner product

magnitude

notation

projection

velocity

Vector field

Velocity

Velocity vector

Vertex

Vertical line test

Vertical tangent

Volume

of a cone

by cross section

of a parallelepiped

by shell method

of revolution

of sphere

of a tetrahedron

by triple integration

under z = f(x,y)

W

Weierstrass, Karl

Work

X

x-coordinate

x-intercept

Y

y-coordinate

y-intercept

Z

z-coordinate

Index   A B C D E F G H I J K L M N O P Q R S T U V W X Y Z    top of page