Difference between revisions of "Template:Intmath/doc"
Jump to navigation
Jump to search
imported>Salix alba |
imported>Maschen (full set of Maxwell's eqns) |
||
| Line 40: | Line 40: | ||
:<code><nowiki>{{intmath|varointclockwise|''C''}} ''F''('''x''') ∙ ''d'''''x''' = −{{intmath|ointctrclockwise|''C''}} ''F''('''x''') ∙ ''d'''''x'''</nowiki></code> | :<code><nowiki>{{intmath|varointclockwise|''C''}} ''F''('''x''') ∙ ''d'''''x''' = −{{intmath|ointctrclockwise|''C''}} ''F''('''x''') ∙ ''d'''''x'''</nowiki></code> | ||
| − | [[ | + | [[Maxwell's equations]] |
| − | :{{intmath|oiint|∂''V''}} '''E''' ∙ ''d''''' | + | :{{intmath|oiint|∂''V''}} '''E''' ∙ ''d'''''S''' = {{sfrac|1|''ε''<sub>0</sub>}}{{intmath|iiint|''V''}} ''ρ'' ''dV'' |
| − | :<code><nowiki>{{intmath|oiint|∂''V''}} '''E''' ∙ ''d''''' | + | :{{intmath|oiint|∂''V''}} '''B''' ∙ ''d'''''S''' = 0 |
| + | |||
| + | :{{intmath|oint|∂''S''}} '''E''' ∙ ''d'''''x''' = −{{intmath|iint|''S''}} {{sfrac|∂'''B'''|∂''t''}} ∙ ''d'''''S''' | ||
| + | |||
| + | :{{intmath|oint|∂''S''}} '''B''' ∙ ''d'''''x''' = {{intmath|iint|''S''}} (''μ''<sub>0</sub>'''J''' + {{sfrac|1|''c''<sup>2</sup>}}{{sfrac|∂'''E'''|∂''t''}}) ∙ ''d'''''S''' | ||
| + | |||
| + | :<code><nowiki>{{intmath|oiint|∂''V''}} '''E''' ∙ ''d'''''S''' = {{sfrac|1|''ε''<sub>0</sub>}}{{intmath|iiint|''V''}} ''ρ'' ''dV''</nowiki></code> | ||
| + | |||
| + | :<code><nowiki>{{intmath|oiint|∂''V''}} '''B''' ∙ ''d'''''S''' = 0</nowiki></code> | ||
| + | |||
| + | :<code><nowiki>{{intmath|oint|∂''S''}} '''E''' ∙ ''d'''''x''' = −{{intmath|iint|''S''}} {{sfrac|∂'''B'''|∂''t''}} ∙ ''d'''''S'''</nowiki></code> | ||
| + | |||
| + | :<code><nowiki>{{intmath|oint|∂''S''}} '''B''' ∙ ''d'''''x''' = {{intmath|iint|''S''}} (''μ''<sub>0</sub>'''J''' + {{sfrac|1|''c''<sup>2</sup>}}{{sfrac|∂'''E'''|∂''t''}}) ∙ ''d'''''S''' | ||
| + | </nowiki></code> | ||
==={{tl|math}}=== | ==={{tl|math}}=== | ||
| Line 60: | Line 73: | ||
:<code><nowiki>{{math|{{intmath|varointclockwise|''C''}} ''F''('''x''') ∙ ''d'''''x''' {{=}} −{{intmath|ointctrclockwise|''C''}} ''F''('''x''') ∙ ''d'''''x'''}}</nowiki></code> | :<code><nowiki>{{math|{{intmath|varointclockwise|''C''}} ''F''('''x''') ∙ ''d'''''x''' {{=}} −{{intmath|ointctrclockwise|''C''}} ''F''('''x''') ∙ ''d'''''x'''}}</nowiki></code> | ||
| − | [[ | + | [[Maxwell's equations]] |
| + | |||
| + | :{{math|{{intmath|oiint|∂''V''}} '''E''' ∙ ''d'''''S''' {{=}} {{sfrac|1|''ε''<sub>0</sub>}}{{intmath|iiint|''V''}} ''ρ'' ''dV''}} | ||
| + | |||
| + | :{{math|{{intmath|oiint|∂''V''}} '''B''' ∙ ''d'''''S''' {{=}} 0}} | ||
| + | |||
| + | :{{math|{{intmath|oint|∂''S''}} '''E''' ∙ ''d'''''x''' {{=}} −{{intmath|iint|''S''}} {{sfrac|∂'''B'''|∂''t''}} ∙ ''d'''''S'''}} | ||
| + | |||
| + | :{{math|{{intmath|oint|∂''S''}} '''B''' ∙ ''d'''''x''' {{=}} {{intmath|iint|''S''}} (''μ''<sub>0</sub>'''J''' + {{sfrac|1|''c''<sup>2</sup>}}{{sfrac|∂'''E'''|∂''t''}}) ∙ ''d'''''S'''}} | ||
| + | |||
| + | :<code><nowiki>{{math|{{intmath|oiint|∂''V''}} '''E''' ∙ ''d'''''S''' {{=}} {{sfrac|1|''ε''<sub>0</sub>}}{{intmath|iiint|''V''}} ''ρ'' ''dV''}}</nowiki></code> | ||
| − | :{{math|{{intmath|oiint|∂''V''}} ''' | + | :<code><nowiki>{{math|{{intmath|oiint|∂''V''}} '''B''' ∙ ''d'''''S''' {{=}} 0}}</nowiki></code> |
| − | :<code><nowiki>{{math|{{intmath| | + | :<code><nowiki>{{math|{{intmath|oint|∂''S''}} '''E''' ∙ ''d'''''x''' {{=}} −{{intmath|iint|''S''}} {{sfrac|∂'''B'''|∂''t''}} ∙ ''d'''''S'''}}</nowiki></code> |
| + | :<code><nowiki>{{math|{{intmath|oint|∂''S''}} '''B''' ∙ ''d'''''x''' {{=}} {{intmath|iint|''S''}} (''μ''<sub>0</sub>'''J''' + {{sfrac|1|''c''<sup>2</sup>}}{{sfrac|∂'''E'''|∂''t''}}) ∙ ''d'''''S'''}} | ||
| + | </nowiki></code> | ||
==See also== | ==See also== | ||
Revision as of 09:28, 16 March 2013
This template generates integral symbols using unicode, for inline {{math}} formulae as an alternative to LaTeX generated in <math>.
Parameters
The template has three parameters, applicable one by one:
- Integral sign: Choose one of:
- int for Template:Unicode symbol is U+222B
- iint for Template:Unicode (double integral, U+222C),
- iiint for Template:Unicode (triple integral, U+222D),
- oint for Template:Unicode (contour integral, U+222E),
- varointclockwise for Template:Unicode (clockwise contour integral, U+2232)
- ointctrclockwise for Template:Unicode (anticlockwise contour integral, U+2233),
- oiint for Template:Unicode (closed surface integral, U+222F),
- oiiint for Template:Unicode (closed volume integral, U+2230).
- Subscript: Enter the subscript (symbol or short expression), for the lower limit or denoting an n-dimensional space or the (n − 1)- dimensional boundary.
- Superscript: Enter the superscript (symbol or short expression) for the upper limit.
NB:
- Applying italics to the integral symbol has no effect, it remains upright.
- This template already includes {{su}}.
Examples
No {{math}}
- Γ(z) = ∫∞
0 e−ttz − 1dt
Γ(''z'') = {{intmath|int|0|∞}} ''e''<sup>−''t''</sup>''t''<sup>''z'' − 1</sup>''dt''
- ∲
C F(x) ∙ dx = −∳
C F(x) ∙ dx
{{intmath|varointclockwise|''C''}} ''F''('''x''') ∙ ''d'''''x''' = −{{intmath|ointctrclockwise|''C''}} ''F''('''x''') ∙ ''d'''''x'''
- ∯
∂V E ∙ dS = Template:Sfrac∭
V ρ dV
- ∯
∂V B ∙ dS = 0
- ∮
∂S E ∙ dx = −∬
S Template:Sfrac ∙ dS
- ∮
∂S B ∙ dx = ∬
S (μ0J + Template:SfracTemplate:Sfrac) ∙ dS
{{intmath|oiint|∂''V''}} '''E''' ∙ ''d'''''S''' = {{sfrac|1|''ε''<sub>0</sub>}}{{intmath|iiint|''V''}} ''ρ'' ''dV''
{{intmath|oiint|∂''V''}} '''B''' ∙ ''d'''''S''' = 0
{{intmath|oint|∂''S''}} '''E''' ∙ ''d'''''x''' = −{{intmath|iint|''S''}} {{sfrac|∂'''B'''|∂''t''}} ∙ ''d'''''S'''
{{intmath|oint|∂''S''}} '''B''' ∙ ''d'''''x''' = {{intmath|iint|''S''}} (''μ''<sub>0</sub>'''J''' + {{sfrac|1|''c''<sup>2</sup>}}{{sfrac|∂'''E'''|∂''t''}}) ∙ ''d'''''S'''
{{math}}
- Γ(z) = ∫∞
0 e−ttz − 1dt
{{math|Γ(''z'') {{=}} {{intmath|int|0|∞}} ''e''<sup>−''t''</sup>''t''<sup>''z'' − 1</sup>''dt''}}
- ∲
CF(x) ∙ dx = −∳
C F(x) ∙ dx
{{math|{{intmath|varointclockwise|''C''}} ''F''('''x''') ∙ ''d'''''x''' {{=}} −{{intmath|ointctrclockwise|''C''}} ''F''('''x''') ∙ ''d'''''x'''}}
- ∯
∂V E ∙ dS = Template:Sfrac∭
V ρ dV
- ∯
∂V B ∙ dS = 0
- ∮
∂S E ∙ dx = −∬
S Template:Sfrac ∙ dS
- ∮
∂S B ∙ dx = ∬
S (μ0J + Template:SfracTemplate:Sfrac) ∙ dS
{{math|{{intmath|oiint|∂''V''}} '''E''' ∙ ''d'''''S''' {{=}} {{sfrac|1|''ε''<sub>0</sub>}}{{intmath|iiint|''V''}} ''ρ'' ''dV''}}
{{math|{{intmath|oiint|∂''V''}} '''B''' ∙ ''d'''''S''' {{=}} 0}}
{{math|{{intmath|oint|∂''S''}} '''E''' ∙ ''d'''''x''' {{=}} −{{intmath|iint|''S''}} {{sfrac|∂'''B'''|∂''t''}} ∙ ''d'''''S'''}}
{{math|{{intmath|oint|∂''S''}} '''B''' ∙ ''d'''''x''' {{=}} {{intmath|iint|''S''}} (''μ''<sub>0</sub>'''J''' + {{sfrac|1|''c''<sup>2</sup>}}{{sfrac|∂'''E'''|∂''t''}}) ∙ ''d'''''S'''}}
See also