Index of Math Terms

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


1 -1 function

3 by 3 systems

3 dimensional coordinates 

abel's theorem for a system of differential equations

abel's theorem for higher order differential equations

abel's theorem for second order linear differential equations

absolute value

absolute value equation

absolute value function

absolute value inequalities

absolutely convergent

AC method

acceleration (normal and tangential components)

acceleration (with vectors)

access (r-stages)

addition of complex numbers

addition of matrices

addition of matrices (Properties)

Addition of Polynomials

addition of power series

addition of rational expressions

Addition Rule (for exponents)

adjacency matrix

adjoint of a matrix

affine transformation

algebra of vectors

algebraic expression

alternating series test

amplitude modulation


analytic function


angle between two planes

angle between two vectors

angle between vectors

angle of inclination


arc length

arc length of a parametrically defined curve

arc length of a polar curve

arc length parameterization


arcsin x


area (with a double integral)

area (with Green's theorem)

area between 2 curves

area of a parametric surface

area of a polar region

Area of a rectangle

area of a surface

Area of a triangle

arithmetic of functions

arithmetic of radical expressions

arithmetic sequence

arithmetic series

Associative Property

asymptotes of a hyperbola

augmented matrix

autonomous differential equations

average cost

average difference representation

average value

average velocity

average velocity


axis of symmetry of a parabola



basis for a uc-set



best fitting curve

binomial expansion

boundary point


Boyle's law and work

Cauchy Schwartz inequality

center of mass

center of mass (double integration)

Chain Rule

chain rule (several variables)

change of base formula

change of basis

changing order of integration

characteristic equations for higher order differential equations

characteristic polynomial of a matrix

circle (osculating)


circles (parametric equations)

circles in polar coordinates

circuits (electrical)


circumference on an ellipse

classification of first order differential equations


closed region

closure properties of a vector space



column rank

column space of a matrix

common difference

common logarithm

Commutative Property

completing the square

completing the square

complex conjugate

complex eigenvalues of a system of differential equations

complex fractions

complex numbers

complex roots for euler equations

complex roots to the characteristic equation of a second order differential equation

component form of a vector

component of u perpendicular to v

composition of functions

compound inequality

compound interest

computer graphics and 2x2 matrices

concave down

concave up

conditional equation

conditionally convergent

conic sections in polar coordinates

conic sections with matrices

connected (strongly)

conservative vector field


constant function

constant function

Constant Rule

constant term (of a polynomial)


continuity for a function of several variables

continuity of the inverse function

continuous compound interest

continuous vector valued function


convergence of series solutions to differential equations

converges (series)

converges to a limit

coordinate on a number line

coordinates with respect to a basis

corresponding linear operator

cos limit

cosh x


cosx (derivative)

Cramer's rule

critical number

critically damped free motion

cross product

cross product

cubes and factoring


current law (Krichhoff)


curvature for a plane curve

curve fitting


cylindrical coordinates

cylindrical coordinates for triple integration

cylindrical shells method for volume

d neighborhood

d neighborhood


damped free motion

dashed line (for linear inequalities)

definite integral

degree (of a polynomial)

derivative (limit definition)

derivative of a vector valued function

derivative of ex

derivative of parametric equations

derivative of the inverse function

derivatives in polar coordinates

derivatives of arctrigonometric functions

detail coefficients for wavelets

determinant (permutation definition)

determinant (Properties)

diagonal matrix

diagonalizable matrix

diagonalize a matrix (steps to)


difference equations

difference of squares

Difference of Squares

difference quotient

difference to quotient rule for logarithms

differences between linear and nonlinear differential equations

differentiable for a function of several variables

differential equation

differential form of a line integral


differentiation of power series


dimension of a vector space

direct comparison test

directed graph

directed line segment

direction cosines

directional derivative


discontinuous forcing functions



disk method for volume

distance = rate times time

distance between a point and a plane

distance between vectors

distance formula

distance formula in 3D

Distributive Property

Distributive Rule (for exponents)


divergence theorem


diverges (series)

Dividing by a Monomial

dividing rational expressions

division of complex numbers

division of power series



domain of a function of several variables

dot product

dot product of vectors

dot product properties

double integral

double integration for polar coordinates

double riemann sums




ed definition

ed game

edges of a graph







electrical and mechanical vibrations

electrical circuits

electrical circuits

eliminating the parameter


elimination (3 by 3 systems)



empty set

equation of a line (Point-Slope form)

equations with rational expressions


equilibrium solutions for difference equations

equipotential lines

equivalence relationship

error and differentials

euler equations

euler's formula

even permutation


exact differential equations

exchange of stability for difference equations

existence and uniqueness for first order linear differential equations

existence and uniqueness for first order nonlinear differential equations

existence and uniqueness for second order linear differential equations

existence and uniqueness theorem for systems of differential equations

explicit function



exponential equations

exponential graph


exponentials with other bases

exponents (Integer)


Extreme Value Theorem

Extreme Value Theorem


factoring by grouping

factoring strategies

Fibonacci sequence with matrices

fields (vector fields)

First Derivative Test

First Fundamental Theorem of Calculus

first order difference equation

first order linear differential equations

fit (best fitting curve)

fluid force on a submerged rectangular sheet

fluid force on a vertical surface

fluid pressure




forced response

forced vibrations


Fourier coefficient

Fourier series


fubini's theorem


function (vector valued)

function arithmetic 

function composition

function notation

function of several variables

functions (definition)

functions (parametric equations)

fundamental theorem of algebra

fundamental theorem of line integrals

general linear transformation matrix

geometric power series

geometric sequence

geometric series

geometric series

geometric series test

geometry of a 2x2 matrix

Geometry Problems


gradient field

Gram Schmidt process


graph of an exponential function

graphing inverses

graphing with calculus

greater than (>)

greater than or equal to (<)

greatest common factor

green's theorem

harmonic series

heaviside functions


hidden quadratics

higher order differential equations

higher order partial derivative

homogeneous differential equations

homogeneous second order differential equations

homogeneous system (Matrices)

homogeneous systems of differential equations

homogeneous systems of differential equations (solutions)

Hook's law

hook's law

horizontal asymptote

horizontal line

horizontal line test

horizontal line test and Rolle's Theorem

horizontal shift


hyperbolic trigonometric functions

hyperboloid of one sheet

hyperboloid of two sheets

identifying conics

identity (for equations)

identity permutation

Identity Property

ijth entry of a matrix

implicit differentiation

implicit differentiation (several variables)

implicit function

improper integrals

independence of path

index of summation



inequalities (quadratic)

inequalities (rational)

inertia (moment of inertial with double integration)

inertia (moment of inertial with triple integration)

infinity table

inflection point

initial value problems

initial value problems with Laplace transforms

inner product

inner product space

instantaneous velocity


integral (double)

integral equations

integral of a vector valued function

integral test

integral transforms

integrals (line integrals)

integrating factors (for first order linear differential equations)

integrating involving inverse trigonometric functions

integrating powers of sin and cos

integrating powers of tan and sec

integrating powers of trigonometric functions

integration by parts

integration of power series

interest (compound)

interior point

Intermediate Value Theorem

Intermediate Value Theorem


intersections of parametrically defined curves

interval of convergence


inverse (graph)

inverse functions

inverse hyperbolic derivatives

inverse of a matrix

inverse of a matrix (Properties)

Inverse Property

inverse property of logarithms

inverse trigonometric functions

inverse with cofactors

inversely proportional to 

inverses and linear systems

Irrational Number

irregular singular point





iterated integral


Kepler's laws

kernel of a general linear transformation

kernel of an integral transform

Krichhoff's current law

Krichhoff's voltage law

Kronecker delta symbol

Lagrange multipliers

laplace transform (definition)

Laplace transform solution to differential equations with discontinuous forcing

Laplace transform solution to initial value problems

leading coefficient

least squares regression line

least squares regression line with matrices

least squares solution

left Riemann sum

length between vectors

length of a vector

less than (<)

less than or equal to (<)

level curves

L'Hopital's rule

like terms

limit at infinity

limit comparison test

limit for a function of several variables

limit of a sequence

limit of a vector valued function

limit test

limits (graphical)

limits (tabular)

limits using power series

line (general algebraic equation)

line (slope definition)

line integrals

line integrals (fundamental theorem)

linear algebra review

linear approximation

linear combination

linear difference equations

Linear Equations

linear first order differential equations

linear functions

linear independence

linear inequality

linear inequality (one variable)

linear inequality (two variable)

linear system of equations

linear systems and inverses

linear systems and matrices

linear transformation (definition for Rn)

linear transformation matrix (for Rn)

linear transformation of general vector spaces

linear transformation on general vector spaces (Properties)

linear transformation properties (for Rn)

linearly dependent functions

linearly independent function (higher order)

linearly independent functions

lines (parametric equations)

lines in 3D

lines in polar coordinates

ln x (properties)

log equations

log x

logarithm (definition)


logarithms and integrals

logarithms with other bases

logistics equations

logistics equations

logistics growth

loop in an electrical circuit


magnitude of a vector


marginal cost

mass (and center of mass with triple integration)

mass (center of mass with double integration)

mass (double integration)


matrix addition

matrix multiplication

matrix of a general linear transformation

matrix of a linear transformation (for Rn)

matrix subtraction


maximum (relative)

maximum and minimum problems involving parabolas

McLaurin polynomial

McLaurin series

Mean Value Theorem

Mean Value Theorem For Integrals

mechanical and electrical vibrations

Midpoint Approximation

midpoint approximation

midpoint formula


minimum (relative)

minor (of a matrix)

mixed angle formulas

Mixture Problems

Mmxn as a vector space

modeling with differential equations


moment of inertia with double integration

moment of inertia with triple integration

moments (double integration)

Money Problems



Monte Carlo Method

Motion Problems

multiplication of a matrix and a scalar (Properties)

multiplication of complex numbers

multiplication of matrices

multiplication of matrices (Properties)

Multiplication of Polynomials

multiplication of power series

multiplying rational expressions

natural logarithm (definition)

Natural Number

negatively oriented curve

newton's law

Newton's method


node in an electrical circuit

nonhomogeneous second order differential equations

nonhomogeneous systems (matrices)

nonhomogeneous systems of differential equations

nonlinear systems

nonsingular equivalences

nonsingular matrix

nontrivial solution to the homogeneous system (Matrices)


normal component of acceleration

normal distribution 

normal line

normal vector (principle unit)

normal vector to a parametric surface

normal vector to a plane

notation (function)

nth partial sum

nth root

null space

null space (finding it)

nullity of a general linear transformation

nullity of a matrix

Number Problems

odd permutation


one sided limits

one to one function

one to one linear transformation

onto for a general linear transformation

open region



order of integration

order of operations

ordered pair

ordinary differential equations

ordinary point

oriented curve

oriented surface



orthogonal basis

orthogonal complement

orthogonal for general vectors

orthogonal matrix

orthogonal vectors

orthonormal basis

orthonormal basis for general vector space

osculating circle

other bases

overdamped free motion

Pappus' Theorem




parallel vectors


parameterization by arc length

parametric equation of a function

parametric equations

parametric equations of a circle

parametric equations of a line

parametric surface

partial derivative

partial differential equations

partial fractions

partial sum

parts (integration by parts)

Pascal's principle

Pascal's triangle

path independence

percent error

Percent Problems




phase plane

phase portrait

planes (equation)

Pn as a vector space

Point Slope equation of a line

polar coordinates

polar coordinates for double integration


polynomial (characteristic) for a matrix

Polynomial Division


pond (a differential equation model)

positively oriented curve

potential function


Power Rule

Power Rule (for exponents)

power rule for logarithms

power series

power series review

pressure (fluid)

principle unit normal vector


problem solving (More that one variable)

problem solving (One Variable)


Product Rule

product rule for radicals

product to sum rule for logarithms


projectile motion (with vectors)

projection of u onto v

projection of v onto w

properties of a linear transformation (for Rn)

properties of addition and subtraction of vectors

properties of linear transformations on general vector spaces

properties of ln x

properties of matrix addition

properties of matrix multiplication

properties of scalar multiplication and matrices

properties of the determinant

properties of the dot product

properties of the inverse of a matrix

properties of the transpose

properties of vector spaces

properties of vectors

proportional to

p-series test

Pythagorean theorem

Pythagorean theorem


quadratic approximation

quadratic formula

quadratic formula

quadratic functions

quadratic inequalities

quadric surface

quasi frequency

quasi period


Quotient Rule

quotient rule for radicals

Quotient to Difference Rule (for exponents)

quotient to difference rule for logarithms

radical equations

radical equations

radioactive dating

radioactive decay

radius of convergence



range of a matrix

rank of a general linear transformation

rank of a matrix

rate = rate in - rate out

ratio test

rational expression

rational expressions

rational inequalities

Rational Number

rational roots

rationalizing the denominator

real distinct roots for euler equations

Real Number

real roots of the characteristic equation of a second order differential equation

rearrangement theorem

reduced row echelon form

reduction of order

reflecting about the x-axis

reflecting about the y-axis

reflection (2x2 matrices)

regression line (least squares with matrices)

regular singular point

Reimann sum

Related Rates



relative error

relative extrema

relative maximum

relative maximum

relative minimum

relative minimum

remainder theorem

repeated roots for euler equations

repeated roots to the characteristic equation of a second order differential equation




Revenue equation

riemann sums (for double integration)

right Riemann sum


Rolle's Theorem

root method

root test

rotation (2x2 matrices)

row echelon form

row equivalent

row operation

row rank

row space of a matrix


r-stage access

rules of exponents

scalar matrix

scalar multiplication and matrices (Properties)

scalar multiplication of vectors

scalar product

Scientific Notation

second derivative of parametric equations

Second Derivative Test

second derivative test for a function of two variables

Second Fundamental Theorem of Calculus

semi-stable equilibrium point

separable differential equations

separable differential equations



sequence (arithmetic)

sequence (geometric)


series (arithmetic)

series (definition)

series (geometric)

series solutions to differential equations


shear (2x2 matrices)

shift (horizontal)

shift (vertical)

sigma notation

similar matrices

simple curve

simply connected

Simpson's Estimate

Simpson's estimate

Simpson's Estimate

Simpson's Estimate (error)

Simpson's estimate (error)

Simpson's Estimate (error)

singular point

sinh x

sinx (derivative)




solid line (for linear inequalities)

solution set

solution to an equation

solutions to higher order homogeneous differential equations

solve for a variable x

solved for a variable x

span (vectors span a space)

span of a set of vectors

special products

speed (with vectors)

spherical coordinates

spherical coordinates for triple coordinates

spiral node

spring (work and Hook's law)

square matrix

square of a difference

Square of a Difference

Square of a Sum

square root function

square root method

squeeze theorem

Squeeze Theorem

stable equilibrium point

stage (r-stage access)

standard basis

standard basis

standard form of a circle

standard form of the ellipse

steady-state solution

step functions

stokes theorem

strongly connected


subspace definition


subtraction of matrices

Subtraction of Polynomials

subtraction of power series

subtraction of rational expressions

sum and product of roots

sum of vectors

sum to product rule for logarithms

surface (parametric)

surface area

surface area of revolution

surface area of revolution (parametric)

surface area of revolution of a polar curve

surface integral

surface of revolution

symmetric matrix

system of differential equations (theory)

system of equations

T (transpose)

T Table

tangent line

tangent line to a curve

tangent plane

tangent plane to a parametric surface

tangent vector (unit)

tangential component of acceleration

tanh x

Taylor polynomial

Taylor series

Taylor's remainder theorem

telescoping series

test value

TFAE nonsingular equivalences

three by three systems

three dimensional coordinates

threshold level

threshold number for wavelets

threshold value for wavelets



total differential

transient solution

transition matrix



transpose of a matrix (Properties)

transposition of a permutation

Trapezoidal Rule

Trapezoidal Rule

triangle inequality


trigonometric substitution

triple integral

triple integration in cylindrical coordinates

triple integration in spherical coordinates

trivial solution to the homogeneous system (Matrices)


undamped free vibrations

undetermined coefficients

undetermined coefficients for higher order differential equations


uniqueness and existence for first order linear differential equations

uniqueness and existence for first order nonlinear differential equations

uniqueness and existence for second order linear differential equations

uniqueness and existence theorem for systems of differential equations

Unit Calculations

unit normal vector

unit step functions

unit tangent vector

unit vector

unit vector

unstable equilibrium point

unstable equilibrium point for a system of differential equations



variation of parameters

variation of parameters for higher order differential equations

varies jointly as


vector (n-dimensional)

vector fields

vector space definition

vector space properties

vector valued function

vectors (properties)

velocity (with vectors)

vertex of a parabola

vertical asymptotes

vertical line

vertical line test

Vertical Line Test

vertical shift

vertices of a graph

vertices of the ellipse

voltage law (Kirchhoff)

volume (with double integration)

volume of revolution

washer method for volume


Whole Number



work (vectors)

work (with line integrals)

work in emptying a tank

work in lifting a chain

work in sending a rocket into orbit

work on a spring

work problems

wronskian for higher order differential equations

wronskian of a a system of differential equations

wronskian of a second order differential equation






zero product rule

zero product theorem