Category: Calculus

Uniform convergence
In the mathematical field of analysis, uniform convergence is a mode of convergence of functions stronger than pointwise convergence. A sequence of functions converges uniformly to a limiting function
Hudde's rules
In mathematics, Hudde's rules are two properties of polynomial roots described by Johann Hudde. 1. If r is a double root of the polynomial equation and if are numbers in arithmetic progression, then r
Cours d'Analyse
Cours d'Analyse de l’École Royale Polytechnique; Partie. Analyse algébrique is a seminal textbook in infinitesimal calculus published by Augustin-Louis Cauchy in 1821. The article follows the tra
Tensor calculus
In mathematics, tensor calculus, tensor analysis, or Ricci calculus is an extension of vector calculus to tensor fields (tensors that may vary over a manifold, e.g. in spacetime). Developed by Gregori
Elementary Calculus: An Infinitesimal Approach
Elementary Calculus: An Infinitesimal approach is a textbook by H. Jerome Keisler. The subtitle alludes to the infinitesimal numbers of the hyperreal number system of Abraham Robinson and is sometimes
Slope field
Slope fields (also called direction fields) are a graphical representation of the solutions to a first-order differential equation of a scalar function. Solutions to a slope field are functions drawn
Differential calculus
In mathematics, differential calculus is a subfield of calculus that studies the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calc
Continuous function
In mathematics, a continuous function is a function such that a continuous variation (that is a change without jump) of the argument induces a continuous variation of the value of the function. This m
AP Calculus
Advanced Placement (AP) Calculus (also known as AP Calc, Calc AB / Calc BC or simply AB / BC) is a set of two distinct Advanced Placement calculus courses and exams offered by the American nonprofit o
In nonstandard analysis, a hyperinteger n is a hyperreal number that is equal to its own integer part. A hyperinteger may be either finite or infinite. A finite hyperinteger is an ordinary integer. An
Geometric calculus
In mathematics, geometric calculus extends the geometric algebra to include differentiation and integration. The formalism is powerful and can be shown to encompass other mathematical theories includi
Reflection formula
In mathematics, a reflection formula or reflection relation for a function f is a relationship between f(a − x) and f(x). It is a special case of a functional equation, and it is very common in the li
Euler spiral
An Euler spiral is a curve whose curvature changes linearly with its curve length (the curvature of a circular curve is equal to the reciprocal of the radius). Euler spirals are also commonly referred
Periodic function
A periodic function is a function that repeats its values at regular intervals. For example, the trigonometric functions, which repeat at intervals of radians, are periodic functions. Periodic functio
Ximera is a massive open online course by Ohio State University on Coursera and YouTube. The system was originally known as MOOCulus and Calculus One. The course features over 25 hours of video and ex
Donald Kreider
Donald Lester Kreider (December 5, 1931 — December 7, 2006) was an American mathematician and educator who served as President of the Mathematical Association of America (1993–1994).
Dirichlet average
Dirichlet averages are averages of functions under the Dirichlet distribution. An important one are dirichlet averages that have a certain argument structure, namely where and is the Dirichlet measure
List of types of functions
Functions can be identified according to the properties they have. These properties describe the functions' behaviour under certain conditions. A parabola is a specific type of function.
Variable (mathematics)
In mathematics, a variable (from Latin variabilis, "changeable") is a symbol and placeholder for any mathematical object. In particular, a variable may represent a number, a vector, a matrix, a functi
List of mathematical functions
In mathematics, some functions or groups of functions are important enough to deserve their own names. This is a listing of articles which explain some of these functions in more detail. There is a la
List of calculus topics
This is a list of calculus topics.
Maxima and minima
In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest valu
Evolution of the human oral microbiome
The evolution of the human oral microbiome is the study of microorganisms in the oral cavity and how they have adapted over time. There are recent advancements in ancient dental research that have giv
Reduction (mathematics)
In mathematics, reduction refers to the rewriting of an expression into a simpler form. For example, the process of rewriting a fraction into one with the smallest whole-number denominator possible (w
Regiomontanus' angle maximization problem
In mathematics, the Regiomontanus's angle maximization problem, is a famous optimization problem posed by the 15th-century German mathematician Johannes Müller (also known as Regiomontanus). The probl
Standard part function
In nonstandard analysis, the standard part function is a function from the limited (finite) hyperreal numbers to the real numbers. Briefly, the standard part function "rounds off" a finite hyperreal t
Quasi-continuous function
In mathematics, the notion of a quasi-continuous function is similar to, but weaker than, the notion of a continuous function. All continuous functions are quasi-continuous but the converse is not tru
Uniform continuity
In mathematics, a real function of real numbers is said to be uniformly continuous if there is a positive real number such that function values over any function domain interval of the size are as clo
Undefined (mathematics)
In mathematics, the term undefined is often used to refer to an expression which is not assigned an interpretation or a value (such as an indeterminate form, which has the propensity of assuming diffe
Visual calculus
Visual calculus, invented by Mamikon Mnatsakanian (known as Mamikon), is an approach to solving a variety of integral calculus problems. Many problems that would otherwise seem quite difficult yield t
Even and odd functions
In mathematics, even functions and odd functions are functions which satisfy particular symmetry relations, with respect to taking additive inverses. They are important in many areas of mathematical a
Hermitian function
In mathematical analysis, a Hermitian function is a complex function with the property that its complex conjugate is equal to the original function with the variable changed in sign: (where the indica
Voorhoeve index
In mathematics, the Voorhoeve index is a non-negative real number associated with certain functions on the complex numbers, named after Marc Voorhoeve. It may be used to extend Rolle's theorem from re
Mean of a function
In calculus, and especially multivariable calculus, the mean of a function is loosely defined as the average value of the function over its domain. In one variable, the mean of a function f(x) over th
Outline of calculus
Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of contemporary mathematics education. Calculus has
Cubic function
In mathematics, a cubic function is a function of the form where the coefficients a, b, c, and d are complex numbers, and the variable x takes real values, and . In other words, it is both a polynomia
Increment theorem
In nonstandard analysis, a field of mathematics, the increment theorem states the following: Suppose a function y = f(x) is differentiable at x and that Δx is infinitesimal. Then for some infinitesima
Discrete calculus
Discrete calculus or the calculus of discrete functions, is the mathematical study of incremental change, in the same way that geometry is the study of shape and algebra is the study of generalization
Series (mathematics)
In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity. The study of series is a major pa
Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra
In mathematics, an infinitesimal number is a quantity that is closer to zero than any standard real number, but that is not zero. The word infinitesimal comes from a 17th-century Modern Latin coinage
Calculus on finite weighted graphs
In mathematics, calculus on finite weighted graphs is a discrete calculus for functions whose domain is the vertex set of a graph with a finite number of vertices and weights associated to the edges.
Proper integral
Proper integral is a kind of integral in Integral calculus , a branch of Mathematics in Calculus .
Differential (mathematics)
In mathematics, differential refers to several related notions derived from the early days of calculus, put on a rigorous footing, such as infinitesimal differences and the derivatives of functions. T
Ricci calculus
In mathematics, Ricci calculus constitutes the rules of index notation and manipulation for tensors and tensor fields on a differentiable manifold, with or without a metric tensor or connection. It is
Exterior calculus identities
This article summarizes several identities in exterior calculus.
John Wallis
John Wallis (/ˈwɒlɪs/; Latin: Wallisius; 3 December [O.S. 23 November] 1616 – 8 November [O.S. 28 October] 1703) was an English clergyman and mathematician who is given partial credit for the developm
Ruler function
In number theory, the ruler function of an integer can be either of two closely-related functions. One of these functions counts the number of times can be evenly divided by two, which for the numbers
Linear function (calculus)
In calculus and related areas of mathematics, a linear function from the real numbers to the real numbers is a function whose graph (in Cartesian coordinates) is a non-vertical line in the plane. The
Binary logarithm
In mathematics, the binary logarithm (log2 n) is the power to which the number 2 must be raised to obtain the value n. That is, for any real number x, For example, the binary logarithm of 1 is 0, the
Calculus of moving surfaces
The calculus of moving surfaces (CMS) is an extension of the classical tensor calculus to deforming manifolds. Central to the CMS is the Tensorial Time Derivative whose original definition was put for
Perron's formula
In mathematics, and more particularly in analytic number theory, Perron's formula is a formula due to Oskar Perron to calculate the sum of an arithmetic function, by means of an inverse Mellin transfo
Nova Methodus pro Maximis et Minimis
"Nova Methodus pro Maximis et Minimis" is the first published work on the subject of calculus. It was published by Gottfried Leibniz in the Acta Eruditorum in October 1684. It is considered to be the
Gabriel's horn
Gabriel's horn (also called Torricelli's trumpet) is a particular geometric figure that has infinite surface area but finite volume. The name refers to the Christian tradition that (albeit not strictl
Thomae's function
Thomae's function is a real-valued function of a real variable that can be defined as: It is named after Carl Johannes Thomae, but has many other names: the popcorn function, the raindrop function, th
Time-scale calculus
In mathematics, time-scale calculus is a unification of the theory of difference equations with that of differential equations, unifying integral and differential calculus with the calculus of finite
Calculus on Euclidean space
In mathematics, calculus on Euclidean space is a generalization of calculus of functions in one or several variables to calculus of functions on Euclidean space as well as a finite-dimensional real ve
Nonstandard calculus
In mathematics, nonstandard calculus is the modern application of infinitesimals, in the sense of nonstandard analysis, to infinitesimal calculus. It provides a rigorous justification for some argumen
Integral of inverse functions
In mathematics, integrals of inverse functions can be computed by means of a formula that expresses the antiderivatives of the inverse of a continuous and invertible function , in terms of and an anti