9474

The Geometry of Integrating a Power around the Origin

This Demonstration shows some geometric relationships between terms in the contour integral around the origin of , . Note in particular that the complete integral around the origin takes on a nonzero value only when . In this case the term (green) and the term (red) rotate in such in such a way that their product (green) points in a fixed direction. In all other cases, the product rotates an integer number of times along the complete contour, resulting in a zero value.
The term in the legend refers to the end-point of the (black) arc of integration.

THINGS TO TRY

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

Computing the integral of around the origin longhand provides a nice complement to this Demonstration. See details on pages 240–241 of the excellent book Complex Analysis with Mathematica by William T. Shaw.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+