# A report on Mathematical analysis, Calculus and Archimedes

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

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

- CalculusLater, Greek mathematicians such as Eudoxus and Archimedes made more explicit, but informal, use of the concepts of limits and convergence when they used the method of exhaustion to compute the area and volume of regions and solids.

- Mathematical analysisArchimedes anticipated modern calculus and analysis by applying the concept of the infinitely small and the method of exhaustion to derive and rigorously prove a range of geometrical theorems, including: the area of a circle; the surface area and volume of a sphere; area of an ellipse; the area under a parabola; the volume of a segment of a paraboloid of revolution; the volume of a segment of a hyperboloid of revolution; and the area of a spiral.

- ArchimedesDuring the Hellenistic period, this method was further developed by Archimedes, who combined it with a concept of the indivisibles—a precursor to infinitesimals—allowing him to solve several problems now treated by integral calculus.

- Calculus2 related topics with Alpha

## Geometry

0 linksGeometry is, with arithmetic, one of the oldest branches of mathematics.

Geometry is, with arithmetic, one of the oldest branches of mathematics.

Archimedes (c.

This was a necessary precursor to the development of calculus and a precise quantitative science of physics.

Two of the master geometers of the time were Bernhard Riemann (1826–1866), working primarily with tools from mathematical analysis, and introducing the Riemann surface, and Henri Poincaré, the founder of algebraic topology and the geometric theory of dynamical systems.

## Series (mathematics)

0 linksIn 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.

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 part of calculus and its generalization, mathematical analysis.

Greek mathematician Archimedes produced the first known summation of an infinite series with amethod that is still used in the area of calculus today.