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| + | =Vector Identities and Operator Definitions= | ||
| + | Please feel free to add onto this table! And if you see a mistake, please correct it. If you are not sure if an equation/expression is right, please write a note or something next to it. | ||
| − | |||
| + | {| | ||
| + | ! colspan="2" style="background: #eee;" | Vector Identities | ||
| + | |- | ||
| + | | align="right" style="padding-right: 1em;" | place note here || <math>\bold{x}\cdot \left(\bold{y}\times \bold{z}\right)= \left(\bold{x}\times \bold{y}\right)\cdot \bold{z}</math> | ||
| + | |- | ||
| + | | align="right" style="padding-right: 1em;" | place note here || <math>\bold{x}\times \left(\bold{y}\times \bold{z} \right)=\bold{y}\left(\bold{x} \cdot \bold{z} \right)-\bold{z} \left( \bold{x}\cdot\bold{y}\right) </math> | ||
| + | |} | ||
| − | + | {| | |
| + | |- | ||
| + | ! colspan="2" style="background: #eee;" | Vector Operators in Rectangular Coordinates | ||
| + | |- | ||
| + | | align="right" style="padding-right: 1em;" | place note here || <math>\nabla f(x,y,z) = \bold{e}_1 \frac{\partial f}{\partial x}+\bold{e}_2 \frac{\partial f}{\partial y}+\bold{e}_3 \frac{\partial f}{\partial z}</math> | ||
| + | |- | ||
| + | |} | ||
| + | {| | ||
| + | |- | ||
| + | ! colspan="2" style="background: #eee;" | Vector Operators in Spherical Coordinates | ||
| + | |- | ||
| + | | align="right" style="padding-right: 1em;" | place note here || <math>\nabla f(x,y,z) = </math> | ||
| + | |- | ||
| + | |} | ||
| − | [[ MegaCollectiveTableTrial1|Back to | + | {| |
| + | |- | ||
| + | ! colspan="2" style="background: #eee;" | Vector Operators in Cylindrical Coordinates | ||
| + | |- | ||
| + | | align="right" style="padding-right: 1em;" | place note here || <math>\nabla f(x,y,z) = </math> | ||
| + | |- | ||
| + | |} | ||
| + | |||
| + | ---- | ||
| + | [[MegaCollectiveTableTrial1|Back to Collective Table]] | ||
Revision as of 05:21, 29 October 2009
Vector Identities and Operator Definitions
Please feel free to add onto this table! And if you see a mistake, please correct it. If you are not sure if an equation/expression is right, please write a note or something next to it.
| Vector Identities | |
|---|---|
| place note here | $ \bold{x}\cdot \left(\bold{y}\times \bold{z}\right)= \left(\bold{x}\times \bold{y}\right)\cdot \bold{z} $ |
| place note here | $ \bold{x}\times \left(\bold{y}\times \bold{z} \right)=\bold{y}\left(\bold{x} \cdot \bold{z} \right)-\bold{z} \left( \bold{x}\cdot\bold{y}\right) $ |
| Vector Operators in Rectangular Coordinates | |
|---|---|
| place note here | $ \nabla f(x,y,z) = \bold{e}_1 \frac{\partial f}{\partial x}+\bold{e}_2 \frac{\partial f}{\partial y}+\bold{e}_3 \frac{\partial f}{\partial z} $ |
| Vector Operators in Spherical Coordinates | |
|---|---|
| place note here | $ \nabla f(x,y,z) = $ |
| Vector Operators in Cylindrical Coordinates | |
|---|---|
| place note here | $ \nabla f(x,y,z) = $ |
