Contour Integral Symbol ∮
The contour integral is a concept in complex analysis that involves integrating a complex-valued function along a curve or path in the complex plane. It plays a crucial role in the study of complex analysis and has applications in physics and engineering.
Definition
The contour integral is denoted by the symbol ∮ and is expressed as ∮ f(z) dz, where f(z) is a complex-valued function of a complex variable z, and dz represents the differential along the contour.
Representation in HTML
In HTML, the contour integral symbol can be represented using the HTML entity ∮.
Usage in Mathematics
Contour integrals are used to evaluate complex integrals and are especially powerful when applied to functions with singularities or complex paths in the complex plane. They are widely used in physics, particularly in the study of fluid dynamics and quantum mechanics.
Example
An example of a contour integral might involve integrating a function f(z) along a closed path in the complex plane, such as a circle or a square.
Understanding the contour integral is essential for mathematicians and scientists working in fields where complex analysis is applied. It provides a powerful tool for solving problems involving complex functions and integrals.
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Contour Integral Symbol Information
| Symbol Name | Contour Integral |
| Unicode Version | 1.1 (June 1993) |
| Unicode | U+222E |
| CSS Code | \222E |
| HTML Entity | ∮ |
Contour Integral Symbol Encoding
| UTF-8 | 0xE2 0x88 0xAE |
| UTF-16 | 0x222E |
| UTF-32 | 0x0000222E |
Table of contents
- Contour Integral PNG and SVG files
- How to type contour integral in latex
- How to type contour integral on Microsoft Word
- How to type contour integral on Microsoft Windows
- How to type contour integral on Mac OS
- How to type contour integral on Linux
- How to type contour integral on IOS and Android
- How to use contour integral in CSS
- How to use contour integral in HTML
- Contour Integral representation in programming languages
Contour Integral symbol's PNG and SVG files
How to type contour integral symbol in latex
\documentclass{article}
\begin{document}
\oint
\end{document}
How to add contour integral symbol via keyboard on different Operating systems
You can type the contour integral on most modern devices with the help of following methods:
How to type contour integral symbol on Microsoft Word
You can type the contour integral on microsoft Microsoft Word using steps mentioned below:
- Place your cursor in the text area where you need to insert the symbol and type 2 2 2 E
- Without moving the cursor press keys Alt + x together
- The original 2 2 2 E is now transformed into ∮
How to type contour integral symbol on Microsoft Windows
You can type the contour integral on Microsoft windows using following steps:
- Hold Alt and press to type contour integral on your windows machine.
How to type contour integral symbol on Mac OS
You can type the contour integral on Mac OS using following steps:
- Place your cursor in the text area where you need to insert the symbol
- Press Ctrl + ⌘ Command + ⎵ Space to bring up the Character Viewer. Alternatively, choose Edit ⇒ Emoji & Symbols
- Type “Contour Integral” in the search field at the top and press Enter
- The symbol should appear. Click on it to insert it into your text
How to type contour integral symbol on Linux
You can type the contour integral on Linux using following steps:
- Place your cursor in the text area where you need to insert the symbol
- Hold ⇧ Shift + Ctrl and press the letter + U
- Press keys 2 2 2 E consecutively
- And then press ↵ Enter , the desired symbol will be added to your document
How to type contour integral symbol on IOS and Android
The easiest way to type the contour integral on ios and android is to copy and paste it wherever you need it.
How to use contour integral in CSS
span {
content: "\222E";
}
How to type contour integral in HTML
<span>∮</span>
Contour Integral symbol representation in programming languages
contour integral's representation in different programming languages can be found in table below:
| Language | Representation |
| Rust | \u{222E} |
| Ruby | \u{222E} |
| Python | \u222E |
| PHP | \u{222E} |
| Perl | "\x{222E}" |
| Java | \u222E |
| Modern JavaScript - Since ES6 | \u{222E} |
| JavaScript | \u222E |
| Go | \u222E |
| C# | \u222E |
| C and C++ | \u222E |
| Bash and Zsh - inside echo -e | \u222E |
| RFC 5137 | \u'222E' |