A strange attractor arising from a differential equation. Differential equations are an important area of mathematical analysis with many applications in science and engineering.
Archimedes used the method of exhaustion to calculate the area under a parabola.
The limit as: x → x0+ ≠ x → x0−. Therefore, the limit as x → x0 does not exist.
Archimedes used the method of exhaustion to compute the area inside a circle by finding the area of regular polygons with more and more sides. This was an early but informal example of a limit, one of the most basic concepts in mathematical analysis.
Alhazen, 11th-century Arab mathematician and physicist
The function without a limit, at an essential discontinuity
Isaac Newton developed the use of calculus in his laws of motion and gravitation.
The limit of this function at infinity exists.
Gottfried Wilhelm Leibniz was the first to state clearly the rules of calculus.
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Maria Gaetana Agnesi
The logarithmic spiral of the Nautilus shell is a classical image used to depict the growth and change related to calculus.

Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis.

- Mathematical analysis

In mathematics, the limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular input.

- Limit of a function

In mathematics education, calculus denotes courses of elementary mathematical analysis, which are mainly devoted to the study of functions and limits.

- Calculus

The last third of the century saw the arithmetization of analysis by Weierstrass, who thought that geometric reasoning was inherently misleading, and introduced the "epsilon-delta" definition of limit.

- Mathematical analysis

In his work Weierstrass formalized the concept of limit and eliminated infinitesimals (although his definition can actually validate nilsquare infinitesimals).

- Calculus
A strange attractor arising from a differential equation. Differential equations are an important area of mathematical analysis with many applications in science and engineering.

2 related topics with Alpha

Overall

The failure of a function to be continuous at a point is quantified by its oscillation.

Continuous function

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Function such that a continuous variation of the argument induces a continuous variation of the value of the function.

Function such that a continuous variation of the argument induces a continuous variation of the value of the function.

The failure of a function to be continuous at a point is quantified by its oscillation.
The graph of a cubic function has no jumps or holes. The function is continuous.
For a Lipschitz continuous function, there is a double cone (shown in white) whose vertex can be translated along the graph, so that the graph always remains entirely outside the cone.
A right-continuous function
A left-continuous function

Continuity is one of the core concepts of calculus and mathematical analysis, where arguments and values of functions are real and complex numbers.

of its domain if the limit of

Cauchy around 1840. Lithography by Zéphirin Belliard after a painting by Jean Roller.

Augustin-Louis Cauchy

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Cauchy around 1840. Lithography by Zéphirin Belliard after a painting by Jean Roller.
Cauchy in later life
The title page of a textbook by Cauchy.
Leçons sur le calcul différentiel, 1829

Baron Augustin-Louis Cauchy (, ; ; 21 August 1789 – 23 May 1857) was a French mathematician, engineer, and physicist who made pioneering contributions to several branches of mathematics, including mathematical analysis and continuum mechanics.

He was one of the first to state and rigorously prove theorems of calculus, rejecting the heuristic principle of the generality of algebra of earlier authors.

In this book he gave the necessary and sufficient condition for the existence of a limit in the form that is still taught.