## Cauchy's integral theorem

In mathematics , the **Cauchy** integral theorem (also known as the **Cauchy** -Goursat theorem ) in complex analysis , named after **Augustin** -Louis **Cauchy** , is an important statement about line integrals for holomorphic functions in the complex plane . Essentially, it says that if two different

**wikipedia.org**| 2011/7/8 11:00:11

## List of topics named after Augustin-Louis Cauchy

Many things are named after the 19th-century French mathematician **Augustin** -Louis **Cauchy** : Binet– **Cauchy** identity **Cauchy–Binet** formula **Cauchy** boundary condition **Cauchy** condensation test **Cauchy** 's convergence test **Cauchy** (crater) **Cauchy** determinant **Cauchy** distribution **Cauchy**

**wikipedia.org**| 2011/4/18 6:06:03

## Cauchy theorem

Several theorems are named after **Augustin** -Louis **Cauchy** . **Cauchy** theorem may mean: **Cauchy** 's integral theorem in complex analysis, also **Cauchy** 's integral formula **Cauchy** 's mean value theorem in real analysis, an extended form of the mean value theorem **Cauchy** 's theorem (group theory

**wikipedia.org**| 2010/9/26 19:59:37

## Differential calculus

In mathematics , "differential calculus" is a subfield of calculus concerned with the study of the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus . The primary objects of study in differential calculus are the derivative

**wikipedia.org**| 2011/7/30 0:20:29

## Cauchy's integral formula

In mathematics , **Cauchy** 's integral formula , named after **Augustin** -Louis **Cauchy** , is a central statement in complex analysis . It expresses the fact that a holomorphic function defined on a disk is completely determined by its values on the boundary of the disk, and it provides integral

**wikipedia.org**| 2011/9/23 8:19:25

## Cauchy–Riemann equations

In mathematics , the **Cauchy–Riemann** differential equations in complex analysis , named after **Augustin Cauchy** and Bernhard Riemann , consist of a system of two partial differential equations which must be satisfied in order for a differentiable function to be holomorphic in an open

**wikipedia.org**| 2011/7/12 16:09:53

## Cauchy–Kowalevski theorem

In mathematics , the **Cauchy–Kowalevski** theorem is the main local existence and uniqueness theorem for analytic partial differential equations associated with **Cauchy** initial value problems . A special case was proved by **Augustin Cauchy** ( 1842 ), and the full result by Sophie Kowalevski

**wikipedia.org**| 2010/9/24 23:15:26

## Cauchy–Schwarz inequality

In mathematics , the **Cauchy–Schwarz** inequality (also known as the Bunyakovsky inequality , the Schwarz inequality , or the **Cauchy–Bunyakovsky–Schwarz** inequality ), is a useful inequality encountered in many different settings, such as linear algebra , analysis , probability theory

**wikipedia.org**| 2011/8/12 20:52:53

## Cauchy sequence

In mathematics , a **Cauchy** sequence (pronounced [koˈʃi] ), named after **Augustin** -Louis **Cauchy** , is a sequence whose elements become arbitrarily close to each other as the sequence progresses. To be more precise, given any positive number, we can always drop some terms from the start of

**wikipedia.org**| 2011/2/27 1:22:09