Mathematical analysis

Mathematical analysis is a branch of mathematics that studies continuous change and includes the theories of differentiation, integration, measure, limits, infinite series, and analytic functions.

These theories are usually studied in the context of real and complex numbers and functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis. Analysis may be distinguished from geometry; however, it can be applied to any space of mathematical objects that has a definition of nearness (a topological space) or specific distances between objects (a metric space).

History

Mathematical analysis formally developed in the 17th century during the Scientific Revolution, but many of its ideas can be traced back to earlier mathematicians. Early results in analysis were implicitly present in the early days of ancient Greek mathematics. For instance, an infinite geometric sum is implicit in Zeno's paradox of the dichotomy. Later, 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. The explicit use of infinitesimals appears in Archimedes' The Method of Mechanical Theorems, a work rediscovered in the 20th century. In Asia, the Chinese mathematician Liu Hui used the method of exhaustion in the 3rd century AD to find the area of a circle.Zu Chongzhi established a method that would later be called Cavalieri's principle to find the volume of a sphere in the 5th century. The Indian mathematician Bhāskara II gave examples of the derivative and used what is now known as Rolle's theorem in the 12th century.

Analysis (disambiguation)

Analysis is the process of observing and breaking down a complex topic or substance into smaller parts to gain a better understanding of it.

Analysis may also refer to:

See also

Homeric scholarship

Homeric scholarship is the study of any Homeric topic, especially the two large surviving epics, the Iliad and Odyssey. It is currently part of the academic discipline of classical studies. The subject is one of the oldest in scholarship. For the purpose of the present article, Homeric scholarship is divided into three main phases: antiquity; the 18th and 19th centuries; and the 20th century and later.

Ancient scholarship

Scholia

Scholia are ancient commentaries, initially written in the margins of manuscripts, not necessarily at the bottom, as are their modern equivalents, the notes. The term marginalia includes them. Some are interlinear, written in very small characters. Over time the scholia were copied along with the work. When the copyist ran out of free text space, he listed them on separate pages or in separate works. Today’s equivalents are the chapter notes or the notes section at the end of the book. Notes are merely a continuation of the practice of creating or copying scholia in printed works, although the incunabula, the first printed works, duplicated some scholia. The works of Homer have been heavily annotated from their written beginnings. The total number of notes on manuscripts and printed editions of the Iliad and Odyssey are for practical purposes innumerable.

Anna

Anna may refer to:

People

Anna (Disney)

Princess Anna of Arendelle is a fictional character who appears in Walt Disney Animation Studios' 53rd animated film Frozen. She is voiced by Kristen Bell as an adult. At the beginning of the film, Livvy Stubenrauch and Katie Lopez provided her speaking and singing voice as a young child, respectively. Agatha Lee Monn portrayed her as a nine-year-old (singing).

Created by co-directors Jennifer Lee and Chris Buck, Anna is loosely based on Gerda, a character of the Danish fairytale The Snow Queen by Hans Christian Andersen. In the Disney film adaptation, Anna is depicted as the princess of Arendelle, a fictional Scandinavian kingdom and the younger sister of Princess Elsa (Idina Menzel), who is the heiress to the throne and possesses the elemental ability to create and control ice and snow. When Elsa exiles herself from the kingdom after inadvertently sending Arendelle into an eternal winter on the evening of her coronation, fearless and faithful Anna is determined to set out on a dangerous adventure to bring her sister back and save both her kingdom and her family.

Anna (singer)

Anna (born Anna Cote-Wursler on July 9, 1987) is a singer of the group Bon-Bon Blanco. She has five brothers and is the youngest sibling in the family. She uses Anna in her solo efforts, but she uses her real name when part of the band. She was born in Tokyo, Japan, but she has American citizenship.

Her husband is Japanese baseball player Manabu Mima.

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