basic_tools:vector_calculus
Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision | Next revision Both sides next revision | ||
|
basic_tools:vector_calculus [2017/12/16 15:38] jakobadmin |
basic_tools:vector_calculus [2018/03/28 12:22] jakobadmin |
||
|---|---|---|---|
| Line 1: | Line 1: | ||
| ====== Vector Calculus ====== | ====== Vector Calculus ====== | ||
| - | <tabbox Why is it interesting?> | ||
| - | |||
| - | Vector calculus is an important tool, whenever we want to understand systems where directions play a role. A vector is an arrow that points in some direction. Thus, a vector is a tool to denote a direction. | ||
| - | |||
| - | This is needed, for example, to describe in which spatial direction a ball moves or how a fluid flows. | ||
| - | |||
| - | <blockquote>A vector is the mathematical representation of a physical entity that may be | ||
| - | characterized by size (or “magnitude”) and direction. In keeping with this definition, speed (how fast an object is going) is not represented by a vector, but velocity (how fast and in which direction an object is | ||
| - | going) does qualify as a vector quantity. Another example of a vector quantity | ||
| - | is force, which describes how strongly and in what direction something is being | ||
| - | pushed or pulled. But temperature, which has magnitude but no direction, is not | ||
| - | a vector quantity<cite>A Student's Guide to Vectors and Tensors by Daniel A. Fleisch | ||
| - | </cite></blockquote> | ||
| - | |||
| - | ---- | ||
| - | |||
| - | **Important Vector Calculus Concepts:** | ||
| - | * [[basic_tools:vector_calculus:curl]] | ||
| - | * [[basic_tools:vector_calculus:gradient]] | ||
| - | * [[basic_tools:vector_calculus:flux]] | ||
| - | * [[basic_tools:vector_calculus:divergence]] | ||
| - | * [[basic_tools:vector_calculus:dot_product]] | ||
| - | * [[basic_tools:vector_calculus:cross_product]] | ||
| - | * [[basic_tools:vector_calculus:gauss_theorem]] | ||
| - | * [[basic_tools:vector_calculus:stokes_theorem]] | ||
| - | <tabbox Layman> | + | <tabbox Intuitive> |
| <note tip> | <note tip> | ||
| Line 35: | Line 10: | ||
| </note> | </note> | ||
| | | ||
| - | <tabbox Student> | + | <tabbox Concrete> |
| * [[http://www2.eng.cam.ac.uk/~alj3/vc.pdf|A Survival Guide to Vector Calculus]] by Aylmer Johnson | * [[http://www2.eng.cam.ac.uk/~alj3/vc.pdf|A Survival Guide to Vector Calculus]] by Aylmer Johnson | ||
| Line 46: | Line 21: | ||
| * DIV, Grad, Curl, and All That: An Informal Text on Vector Calculus by H. M Schey | * DIV, Grad, Curl, and All That: An Informal Text on Vector Calculus by H. M Schey | ||
| * [[http://www.physics.miami.edu/~nearing/mathmethods/|Mathematical Tools for Physics]] by James Nearing | * [[http://www.physics.miami.edu/~nearing/mathmethods/|Mathematical Tools for Physics]] by James Nearing | ||
| - | <tabbox Researcher> | + | <tabbox Abstract> |
| <note tip> | <note tip> | ||
| Line 53: | Line 28: | ||
| | | ||
| - | <tabbox Examples> | + | <tabbox Why is it interesting?> |
| - | --> Example1# | + | Vector calculus is an important tool, whenever we want to understand systems where directions play a role. A vector is an arrow that points in some direction. Thus, a vector is a tool to denote a direction. |
| - | + | This is needed, for example, to describe in which spatial direction a ball moves or how a fluid flows. | |
| - | <-- | + | |
| - | --> Example2:# | + | <blockquote>A vector is the mathematical representation of a physical entity that may be |
| + | characterized by size (or “magnitude”) and direction. In keeping with this definition, speed (how fast an object is going) is not represented by a vector, but velocity (how fast and in which direction an object is | ||
| + | going) does qualify as a vector quantity. Another example of a vector quantity | ||
| + | is force, which describes how strongly and in what direction something is being | ||
| + | pushed or pulled. But temperature, which has magnitude but no direction, is not | ||
| + | a vector quantity<cite>A Student's Guide to Vectors and Tensors by Daniel A. Fleisch | ||
| + | </cite></blockquote> | ||
| - | |||
| - | <-- | ||
| - | <tabbox FAQ> | ||
| - | | ||
| <tabbox History> | <tabbox History> | ||
basic_tools/vector_calculus.txt · Last modified: 2022/09/07 01:15 by laserblue
Page Tools
Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 4.0 International
