Template:Intmath/doc

From blackwiki
< Template:Intmath
Revision as of 18:40, 12 March 2016 by 132.204.243.88 (talk) (whereas it does have an effect on all the other integral symbols)
Jump to navigation Jump to search

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:

int iint iiint oint varointclockwise ointctrclockwise oiint oiiint
  1. Integral sign: Choose one of: These match the LaTeX definitions exactly: please do not modify them for something more "convenient", thank you.
  2. *  Template:Unicode doesn't have the same font-face as the others, furthermore it doesn't have the same vertical alignment.
  3. Subscript: Enter the subscript (symbol or short expression), for the lower limit or denoting an n-dimensional space or the (n − 1)- dimensional boundary.
  4. Superscript: Enter the superscript (symbol or short expression) for the upper limit.

NB:

  • Applying font-style: italic; or font-style: oblique; to the int symbol Template:Unicode has no effect in Firefox, it remains upright (whereas it does have an effect on all the other integral symbols), e.g.
    <span style="font-style: italic;">∫ ∬ ∭ ∮ ∲ ∳ ∯ ∰</span> yields ∫ ∬ ∭ ∮ ∲ ∳ ∯ ∰;
    <span style="font-style: oblique;">∫ ∬ ∭ ∮ ∲ ∳ ∯ ∰</span> yields ∫ ∬ ∭ ∮ ∲ ∳ ∯ ∰.
  • 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