A report on Calculus and Mathematical analysis

Archimedes used the method of exhaustion to calculate the area under a parabola.
A strange attractor arising from a differential equation. Differential equations are an important area of mathematical analysis with many applications in science and engineering.
Alhazen, 11th-century Arab mathematician and physicist
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.
Isaac Newton developed the use of calculus in his laws of motion and gravitation.
Gottfried Wilhelm Leibniz was the first to state clearly the rules of calculus.
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 education, calculus denotes courses of elementary mathematical analysis, which are mainly devoted to the study of functions and limits.

- Calculus
Archimedes used the method of exhaustion to calculate the area under a parabola.

14 related topics with Alpha

Overall

Graphs like this are among the objects studied by discrete mathematics, for their interesting mathematical properties, their usefulness as models of real-world problems, and their importance in developing computer algorithms.

Discrete mathematics

1 links

Study of mathematical structures that can be considered "discrete" rather than "continuous" (analogously to continuous functions).

Study of mathematical structures that can be considered "discrete" rather than "continuous" (analogously to continuous functions).

Graphs like this are among the objects studied by discrete mathematics, for their interesting mathematical properties, their usefulness as models of real-world problems, and their importance in developing computer algorithms.
Much research in graph theory was motivated by attempts to prove that all maps, like this one, can be colored using only four colors so that no areas of the same color share an edge. Kenneth Appel and Wolfgang Haken proved this in 1976.
Complexity studies the time taken by algorithms, such as this sorting routine.
The ASCII codes for the word "Wikipedia", given here in binary, provide a way of representing the word in information theory, as well as for information-processing algorithms.
Graph theory has close links to group theory. This truncated tetrahedron graph is related to the alternating group A4.
The Ulam spiral of numbers, with black pixels showing prime numbers. This diagram hints at patterns in the distribution of prime numbers.
Computational geometry applies computer algorithms to representations of geometrical objects.
PERT charts like this provide a project management technique based on graph theory.

By contrast, discrete mathematics excludes topics in "continuous mathematics" such as real numbers, calculus or Euclidean geometry.

Although the main objects of study in discrete mathematics are discrete objects, analytic methods from "continuous" mathematics are often employed as well.

The dichotomy

Zeno's paradoxes

0 links

Zeno's paradoxes are a set of philosophical problems generally thought to have been devised by Greek philosopher Zeno of Elea (c.

Zeno's paradoxes are a set of philosophical problems generally thought to have been devised by Greek philosopher Zeno of Elea (c.

The dichotomy
Achilles and the tortoise
The arrow
The moving rows

Some mathematicians and historians, such as Carl Boyer, hold that Zeno's paradoxes are simply mathematical problems, for which modern calculus provides a mathematical solution.

Today's analysis achieves the same result, using limits (see convergent series).

Smooth infinitesimal analysis

0 links

Smooth infinitesimal analysis is a modern reformulation of the calculus in terms of infinitesimals.

Smooth infinitesimal analysis is like nonstandard analysis in that (1) it is meant to serve as a foundation for analysis, and (2) the infinitesimal quantities do not have concrete sizes (as opposed to the surreals, in which a typical infinitesimal is 1/ω, where ω is a von Neumann ordinal).

Rigour

0 links

Rigour (British English) or rigor (American English; see spelling differences) describes a condition of stiffness or strictness.

Rigour (British English) or rigor (American English; see spelling differences) describes a condition of stiffness or strictness.

During the 19th century, the term "rigorous" began to be used to describe increasing levels of abstraction when dealing with calculus which eventually became known as mathematical analysis.