CALCULUS GLOSSARY

Mr. X is glad to provide video presentations of hundreds of calculus glossary terms. The calculus glossary is part of a complete math glossary available free of charge on the website. All calculus glossary terms are provided free of charge to all users.

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  

Title Description
Absolute Maximum The highest point on a graph, especially over a specified domain.
It is the greatest value of f(x) over a defined interval of x, provided y=f(x).
Play_video
Absolute Minimum The lowest point on a graph, especially over a specified domain.
It is the least value of f(x) over a defined interval of x, provided y=f(x).
Play_video
Antiderivative Given a function with a derivative, the antiderivative of that derivative function returns the original function. Play_video
Area Under a Curve If we have limits of integration, it is most simply the definite integral of the function defined between those limits of integration. Play_video
Asymptote A line (or curve) that a function approaches without actually reaching the line as the domain either grows unbounded or approaches a limit. Play_video
Beta Beta is the second letter of the Greek alphabet. Play_video
Boundary Some functions are bounded, some are not.
Some regions are bounded, some are not.
To be bounded means to have a limit; its extent only goes so far, and then it stops or ends.
Play_video
Bounded Function A bounded function approaches or reaches a limit.
If a function goes toward infinity it is generally considered unbounded.
Play_video
Calculus Calculus is the branch of mathematics concerned with the rates of changes between variables (derivatives) as well as areas under curves that represent functions (integrals). Play_video
Chain Rule The Chain Rule is a basic rule in calculus to find the derivative of a composite function. Play_video
Continuous A function is considered Continuous if its graph has no gaps, no holes, no steps, and no cusps or discontinuities. Play_video
Continuous Function When the graph of a function has no holes, no gaps, no steps, or no discontinuities, then it is considered Continuous.
It may have cusps.
Play_video
Continuously Differentiable When a function is Continuously Differentiable it is both continuous and smooth. Play_video
Convergence To approach a limit is to experience Convergence.
Mathematical series experience convergence when the sum of their expanded terms reaches a boundary or limit.
Play_video
Convergent Series A series is said to be Convergent when its sum approaches a limit. Play_video
Critical Number While there are many ways to define Critical Numbers, depending on the circumstances, most generally we're interested in places where a function generates either an extreme value or a discontinuity. Play_video
Curve Beware that mathematicians consider straight lines to be Curves! Play_video
Cusp When the graph of a function comes to a sharp point, we say that point on the graph is a Cusp. Play_video
Cylindrical Shell A method for volumetric calculations especially for rotated bodies around an axis.
The small thickness of the shell is typically the differential "dx" (or dy or whatever differential represents the incremental thickness of the cylinder).
Play_video
Definite Integral An integral evaluated between limits of integration is termed a Definite Integral. Play_video
Delta Delta is the fourth letter of the Greek alphabet.
Upper-case Delta looks like a triangle and is used to mean "the change in..."
Play_video
Derivative A first Derivative is the slope of the line tangent to a function.
A Derivative provides an instantaneous rate of change between variables.
Play_video
Differentiable If a function is smooth and continuous it is differentiable. Play_video
Differential Equation A Differential Equation employs derivatives and algebra to solve for variables that represent functions. Play_video
Discontinuity When a function is literally not continuous because of a gap, a step, a hole, or any kind of "break" it is considered discontinuous. Play_video
Dot Product A product of vector multiplication, the Dot Product is a scalar, which means it has magnitude only and not an associated direction.
The Dot Product does not result in another vector.
Play_video
Extreme Value Theorem On any continuous function graphed on a closed interval from a domain, we are guaranteed to have a maximum and a minimum value if the range of the function is not constant. Play_video
Finite The common meaning of Finite and its meaning to mathematicians are not quite the same.
In everyday language, Finite means countable within a reasonable time.
To math people, Finite means not infinite; it means, simply, having a bound.
Play_video
First Derivative The First Derivative of a typical function, say, y = f(x), is the slope of the line tangent to a point on the graph of the original function f(x). Play_video
First Order Differential Equation This type of equation includes first derivatives and employs algebra to treat those derivative functions as variables. Play_video
Indefinite Integral An integral with no limits of integration, an Indefinite Integral, can be thought of an an antiderivative.
Play_video
Indeterminate Often a resultant fraction like 0/0 is an Indeterminate form that requires more analysis to determine its true nature, depending on the functions involved.
Play_video
Infinite In common language, not countable in any practical manner.
In math, having no bounds or boundary.
Play_video
Infinite Series Any series of terms whose progression has an unlimited (limitless) number of terms is an Infinite Series.
Play_video
Infinitesimal Infinitely small is Infinitesimal, so tiny that it occupies no space.
While in human terms anything really small (a molecule) is Infinitesimal, in math the term means approaching zero in size.
Play_video
Infinity That without bound; limitless.
Play_video
Inflection On the graph of a function, a point of Inflection is where the curve begins to "bend the other way." Play_video
Instantaneous Rate of Change The value of the first derivative of a standard function of the form y = f(x).
Play_video
Instantaneous Velocity The reading at any instant on a speedometer gives an Instantaneous Velocity.
To be precise, the speedometer gives an instant snapshot of speed (only) with no direction; physical velocity has both magnitude and direction, as a vector.
Play_video
Integral A specific function in calculus.
Or, simply related to integers.
Integral might also mean "important" in common language.
Play_video
Integrand The function that undergoes integration is the Integrand.
Play_video
Integration A process, or function, in calculus to sum an infinite number of infinitesimal increments.
Play_video
Intermediate Value Theorem The IVT basically says that between two different values is an intermediate value somewhere between the extremes.
Play_video
Inverse Function For most functions in Cartesian coordinates, the inverse function is the mirror image around the x=y line.
Play_video
Inverse, Matrix When two matrices multiply to produce the identity matrix, each is said to be the Inverse Matrix of the other.
Play_video
Lambda Lambda is the eleventh letter of the Greek alphabet and is used for wavelength in physics.
Play_video
Limit Some functions have a Limit, a bound beyond which they may not realize.
Play_video
Lower Bound As the name suggests, some functions are limited on the low side.
Play_video
Magnitude, Vectors The Magnitude of a vector is the length of the vector.
We may apply a Pythagorean relation to the perpendicular components of the vector to find the length.
Play_video
Mean Value Theorem Essentially, between any two extremes is an average value.
Play_video
Modulus Most typically it is the length of a vector.
Play_video
Moment Moment takes on many meanings in statistics and physics.
Play_video
Moment of Inertia Each shape or body has an associated Moment of Inertia related to mass distribution and the choice of the axis around which the body is rotated.
Play_video
Multivariable Having more than one variable.
Also multivariate.
Play_video
Multivariate Having more than one variable.
Also multivariable.
Play_video
Newton's Method An iterative method for finding roots of polynomials.
Play_video
Normalize We might Normalize data by culling errors.
Or we might Normalize a vector by assigning a unit vector in its direction.
Play_video
Octant As we have four quadrants in the rectangular plane, we have eight Octants in rectangular space.
In three dimensions the three axes divide space into eight sections, each termed an Octant.
Play_video
Odd Function An Odd Function adheres to this property: f(-x) = -f(x).
The standard sine function is an odd function.
Play_video
Order, Matrix The Order of a Matrix is its size, expressed as "rows by columns." Play_video
Ordered Triple Three coordinates are required to label a point in space, typically (x, y, z).
Play_video
Ordinary Differential Equation A Differential Equation with no partial derivatives is considered an Ordinary Differential Equation.
Play_video
Partial Derivative The derivative with respect to a single variable is a Partial Derivative.
Play_video
Partial Differential Equation A Differential Equation with a Partial derivative.
Play_video
Partial Fraction A Fraction built from the decomposition of other terms.
Play_video
Partial Sum A Partial Sum occurs when we sum only a finite number of terms from a larger or infinite series of terms.
Play_video
Power Rule A simple device in calculus to determine the derivative of a monomial.
Play_video
Product Rule An algorithm within the calculus to find the derivative of the Product of two functions.
Play_video
Projectile Motion Projectile Motion is a parabolic arc caused by gravity.
Play_video
Psi The 23rd letter (next-to-last) of the Greek alphabet.
Play_video
Pure Imaginary Number Given a complex number of the form a + bi, when a = 0 we say that the number is a Pure (or purely) Imaginary Number. Play_video
Riemann Sum Effectively the definite integral in calculus.
Play_video
Rolle's Theorem A principle from first-semester calculus that asserts a first derivative of zero exists on a smooth, continuous, differentiable function between constant range values.
Play_video
Scalar Product A Product of vector multiplication, such as a dot product, that results in a value that is Scalar with size (magnitude) but no associated direction.
Play_video
Second Derivative A Derivative taken of a first Derivative is termed a Second Derivative.
Play_video
Second-order Differential Equation An ordinary Differential Equation in which the highest derivative is a second derivative is called a Second-Order Differential Equation.
Play_video
Sequence Informally, any series is a Sequence.
More formally, any series of terms that adheres or conforms to a pattern.
Play_video
Series Most often a sequence of terms to be summed.
Informally, any sequence of terms may be a Series.
Play_video
Shell Method A method in calculus to calculate volumetric values from functions having been rotated about an axis.
Play_video
Simpson's Rule In calculus we may use three points of a parabola to approximate the function's range of values to determine the area of each partition of the integral.
Play_video
Solid of Revolution When a function is rotated around an axis (of Revolution) it generates a Solid of Revolution.
Play_video
Solution Too often in math class, "the answer." More directly, a Solution is a value (or set of values) that makes a mathematical statement true.
Play_video
Spherical Geometry Unlike plane Geometry, Spherical Geometry is not based on the parallel postulate.
Many of our accepted geometric theorems, principles, and tenets (from plane Geometry) simply do not hold in Spherical Geometry.
Play_video
Spherical Trigonometry Unlike plane Trigonometry, elementary Spherical Trigonometry is three dimensional.
If based in spherical geometry, the math of Spherical Trig gets downright grisly.
Play_video
Tangent A line that touches a function curve at a single point is said to be Tangent to the function.
Tangent is also one of the six basic trigonometric functions; it is the ratio of the opposite side (from a specified angle) of a right triangle to the adjacent side.
Play_video
Tangent Line A Line is said to be Tangent to a function when it touches the graph of the function at a single point.
Play_video
Taylor Series Many common functions can be written as an expansion of the function about a point in a form known as a Taylor Series.
Play_video
Tetrahedron A polyhedron with four faces.
Play_video
Three Dimensions The Dimensions of space or volume are Three Dimensions, typically labeled with rectangular, spherical, or cylindrical coordinates.
Play_video
Three-Dimensional Coordinates Three-Dimensional Coordinates require an ordered triple to label a point in space.
Play_video
Transcendental Number A Transcendental Number will not be the root of a polynomial with integer coefficients; it is an irrational number.
Play_video
Transpose (Matrix) When we interchange the rows and columns of a matrix we Transpose the Matrix.
Play_video
Trapezoidal Rule When approximating an integral in calculus we may treat each partition as a Trapezoid to determine the area under the curve.
Play_video
Triple Product (Scalar) Effectively, a Scalar Triple Product is akin to the determinant of a 3x3 matrix.
Play_video
Unit Vector A vector of length one directed along one of the coordinate axes.
Play_video
Upper Bound The greatest permissible value of a function may be termed its Upper Bound.
Play_video
Vector Often represented with an arrow, a Vector is a quantity with both magnitude (size) and direction.
Play_video
Vector Calculus A piece of multivariable (or multivariate) Calculus, Vector Calculus concerns itself with Vector fields, their derivatives and integrals, most often in three-dimensional space.
Play_video
Velocity Formally a vector in physics, Velocity has both magnitude (speed) and direction.
Play_video
Verify To confirm is to Verify.
When we Verify, we prove or establish some assertion to a dependable conclusion independent from bias.
There is wisdom in these words: "Trust, but Verify."
Play_video
Volume The extent to which an object fills units of three-dimensional space is its Volume.
Play_video
Washer Essentially the same as a cylinder, the Washer method for integrating a volume of revolution in calculus employs a thin, hollow disk as the partition of integration.
Play_video
Xi The 14th letter of the Greek alphabet.
Play_video
Zero Vector A Vector of length Zero. Play_video

Please send us an email with your suggestions for this glossary. We at Mr. X want this site to be as helpful as possible.
 
Sample Arithmetic Problems | Math Glossary | Solving Algebra Problems | Trig Homework | Homework Help with Algebra | Learn Trigonometry | Math Glossary Geometry | Calculus Glossary