Sometimes, as in the case of the natural logarithm , it is impossible to analytically continue a holomorphic function to a non-simply connected domain in the complex plane but it is possible to extend it to a holomorphic function on a closely related surface known as a Riemann surface.

### Navigation menu

All this refers to complex analysis in one variable. There is also a very rich theory of complex analysis in more than one complex dimension in which the analytic properties such as power series expansion carry over whereas most of the geometric properties of holomorphic functions in one complex dimension such as conformality do not carry over. The Riemann mapping theorem about the conformal relationship of certain domains in the complex plane, which may be the most important result in the one-dimensional theory, fails dramatically in higher dimensions.

A major use of certain complex spaces is in quantum mechanics as wave functions.

### Introduction to Complex Analysis

From Wikipedia, the free encyclopedia. Branch of mathematics studying functions of a complex variable. For the class of functions often called "complex analytic", see Holomorphic function.

- An Introduction to Complex Analysis: Classical and Modern Approaches.
- My First Ladies: Twenty-Five Years As the White House Chief Floral Designer.
- Haitian Revolutionary Studies (Blacks in the Diaspora).
- An Introduction to Complex Analysis: Classical and Modern Approaches - CRC Press Book;

Not to be confused with Complexity theory. Main article: Holomorphic function. Complex analysis at Wikipedia's sister projects. Categories : Complex analysis.

Hidden categories: Articles with short description All articles with unsourced statements Articles with unsourced statements from June Namespaces Article Talk. Views Read Edit View history. In other projects Wikimedia Commons Wikibooks Wikiquote.

- An Introduction to Complex Analysis in Several Variables, Volume 7.
- Book Details.
- Math Introduction to Complex Analysis - MathWiki!
- Against Socialist Illusion: A Radical Argument.
- Table of Contents.
- Children of the Matrix: How an Interdimensional Race has Controlled the World for Thousands of Years-and Still Does!
- Games in Economic Development.

By using this site, you agree to the Terms of Use and Privacy Policy. Real number Imaginary number Complex plane Complex conjugate Unit complex number. Complex-valued function Analytic function Holomorphic function Cauchy—Riemann equations Formal power series.

## Complex Analysis

Zeros and poles Cauchy's integral theorem Local primitive Cauchy's integral formula Winding number Laurent series Isolated singularity Residue theorem Conformal map Schwarz lemma Harmonic function Laplace's equation. Mathematics portal. Article no.

Introduction to Complex Analysis. Not available. This value doesn't have the right number of decimals.

## Introduction to Complex Analysis

This value is too small. This value is too large. This is required. Invalid value. Get notified when the product is in stock.

## Introduction to Complex Analysis

As a result it is essential that ALL required learning objectives be covered. Jump to: navigation , search. Category : Courses.

Navigation menu Personal tools Log in. Namespaces Page Discussion. Views Read View source View history. Navigation Main page Recent changes Random page Help.