Difference between revisions of "Template:Intmath/doc"

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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>
  
[[Gauss's law]]
+
[[Maxwell's equations]]
  
:{{intmath|oiint|∂''V''}} '''E''' ∙ ''d'''''x''' = {{sfrac|1|''ε''<sub>0</sub>}}{{intmath|iiint|''V''}} ''ρ'' ''dV''
+
:{{intmath|oiint|∂''V''}} '''E''' ∙ ''d'''''S''' = {{sfrac|1|''ε''<sub>0</sub>}}{{intmath|iiint|''V''}} ''ρ'' ''dV''
  
:<code><nowiki>{{intmath|oiint|∂''V''}} '''E''' ∙ ''d'''''x''' = {{sfrac|1|''ε''<sub>0</sub>}}{{intmath|iiint|''V''}} ''ρ'' ''dV''</nowiki></code>
+
:{{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>
  
[[Gauss's law]]
+
[[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''}} '''E''' ∙ ''d'''''x''' {{=}} {{sfrac|1|''ε''<sub>0</sub>}}{{intmath|iiint|∂''V''}} ''ρ'' ''dV''}}
+
:<code><nowiki>{{math|{{intmath|oiint|∂''V''}} '''B''' ∙ ''d'''''S''' {{=}} 0}}</nowiki></code>
  
:<code><nowiki>{{math|{{intmath|oiint|∂''V''}} '''E''' ∙ ''d'''''x''' {{=}} {{sfrac|1|''ε''<sub>0</sub>}}{{intmath|iiint|∂''V''}} ''ρ'' ''dV''}}</nowiki></code>
+
:<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:

  1. Integral sign: Choose one of: These match the LaTeX definitions exactly: please do not modify them for something more "convenient", thank you.
  2. Subscript: Enter the subscript (symbol or short expression), for the lower limit or denoting an n-dimensional space or the (n − 1)- dimensional boundary.
  3. 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}}

Gamma function

Γ(z) =
0
ettz − 1dt
Γ(''z'') = {{intmath|int|0|∞}} ''e''<sup>−''t''</sup>''t''<sup>''z'' − 1</sup>''dt''

Line integral


C
F(x) ∙ dx = −
C
F(x) ∙ dx
{{intmath|varointclockwise|''C''}} ''F''('''x''') ∙ ''d'''''x''' = −{{intmath|ointctrclockwise|''C''}} ''F''('''x''') ∙ ''d'''''x'''

Maxwell's equations


V
EdS = Template:Sfrac
V
ρ dV

V
BdS = 0

S
Edx = −
S
Template:SfracdS

S
Bdx =
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}}

Gamma function

Γ(z) =
0
ettz − 1dt
{{math|Γ(''z'') {{=}} {{intmath|int|0|∞}} ''e''<sup>−''t''</sup>''t''<sup>''z'' − 1</sup>''dt''}}

Line integral


C
F(x) ∙ dx = −
C
F(x) ∙ dx
{{math|{{intmath|varointclockwise|''C''}} ''F''('''x''') ∙ ''d'''''x''' {{=}} −{{intmath|ointctrclockwise|''C''}} ''F''('''x''') ∙ ''d'''''x'''}}

Maxwell's equations


V
EdS = Template:Sfrac
V
ρ dV

V
BdS = 0

S
Edx = −
S
Template:SfracdS

S
Bdx =
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