Calculus

Calculus is the mathematical study of continuous change, and the principal precursor of modern mathematical analysis. Originally called infinitesimal calculus or the calculus of infinitesimals, it has two major branches, differential calculus and integral calculus. Differential calculus analyses instantaneous rates of change and the slopes of curves; integral calculus analyses accumulation of quantities and areas under or between curves. These two branches are related to each other by the fundamental theorem of calculus. Calculus uses convergence of infinite sequences and infinite series to a

value that can change, usually with a context of an equation or operation

infinite sum

subfield of calculus

function such that the preimage of an open set is open

function that repeats its values in regular intervals or periods

largest and smallest value taken by a function in a given range

function whose graph is a straight line; polynomial function of degree at most one

English mathematician (*1616 – †1703)

class=skin-invert-image|450px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (ε = 1/ω)

types of mathematical functions

a polynomial function in a single variable where the highest exponent of the variable is 3

property limiting the "growth" of distances of outputs of a function uniformly across its domain

infinite surface of revolution with infinite surface area enclosing a finite volume, which contributed to 17th century debate on the nature of infinity

mathematical function

plane curve given by Fresnel integrals such that the curvature increases linearly with curve length

mode of convergence of a function sequence

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function that is discontinuous at rationals and continuous at irrationals

formula to calculate the sum of an arithmetic function in analytic number theory

visual representation of solutions to a differential equation

complex function with the property that its complex conjugate is equal to the original function with the variable changed in sign

rewriting of an expression into a simpler form

mathematical notion of infinitesimal difference

formula for the average value of a function over its domain

numerical computation of special functions

mathematical concept which does not have meaning and so which is not assigned an interpretation

famous textbook on calculus

famous mathematical optimization problem

In non-standard analysis, the standard part function is a function from the limited (finite) hyperreal numbers to the real numbers.

tensor index notation for tensor-based calculations

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mathematical formula

the unification of the theory of difference equations with differential equations