Difference between revisions of "Template:Intmath/doc"

From blackwiki
Jump to navigation Jump to search
({{Unicode|∫}}'' doesn't have the same font-face as the others, furthermore it doesn't have the same vertical alignment.)
(whereas it does have an effect on all the other integral symbols)
Line 30: Line 30:
 
<ol>
 
<ol>
 
<li>'''''Integral sign:''''' Choose one of:
 
<li>'''''Integral sign:''''' Choose one of:
*''int'' for {{Unicode|∫}} symbol is U+222B,*  
+
*<tt>int</tt> for {{Unicode|∫}} symbol is U+222B,*  
*''iint'' for {{Unicode|∬}} ([[double integral]], U+222C),  
+
*<tt>iint</tt> for {{Unicode|∬}} ([[double integral]], U+222C),  
*''iiint'' for {{Unicode|∭}} ([[triple integral]], U+222D),  
+
*<tt>iiint</tt> for {{Unicode|∭}} ([[triple integral]], U+222D),  
*''oint'' for {{Unicode|∮}} ([[contour integral]], U+222E),  
+
*<tt>oint</tt> for {{Unicode|∮}} ([[contour integral]], U+222E),  
*''varointclockwise'' for {{Unicode|∲}} ([[clockwise]] contour integral, U+2232)  
+
*<tt>varointclockwise</tt> for {{Unicode|∲}} ([[clockwise]] contour integral, U+2232)  
*''ointctrclockwise'' for {{Unicode|∳}} ([[anticlockwise]] contour integral, U+2233),  
+
*<tt>ointctrclockwise</tt> for {{Unicode|∳}} ([[anticlockwise]] contour integral, U+2233),  
*''oiint'' for {{Unicode|∯}} ([[closed manifold|closed]] [[surface integral]], U+222F),  
+
*<tt>oiint</tt> for {{Unicode|∯}} ([[closed manifold|closed]] [[surface integral]], U+222F),  
*''oiiint'' for {{Unicode|∰}} (closed [[volume integral]], U+2230).
+
*<tt>oiiint</tt> for {{Unicode|∰}} (closed [[volume integral]], U+2230).
 
These match the LaTeX definitions exactly: <span style="color:red;">'''''please do not modify them for something more "convenient", thank you'''''</span>.</li>
 
These match the LaTeX definitions exactly: <span style="color:red;">'''''please do not modify them for something more "convenient", thank you'''''</span>.</li>
 
''*{{nbsp}}{{nbsp}}''{{Unicode|∫}}'' doesn't have the same font-face as the others, furthermore it doesn't have the same vertical alignment.''   
 
''*{{nbsp}}{{nbsp}}''{{Unicode|∫}}'' doesn't have the same font-face as the others, furthermore it doesn't have the same vertical alignment.''   
<li>'''''Subscript:''''' Enter the subscript (symbol or short expression), for the lower limit or denoting an ''n''-[[Dimension (mathematics and physics)|dimension]]al space or the (''n'' − 1)- dimensional [[boundary (topology)|boundary]].</li>
+
<li>'''''Subscript:''''' Enter the subscript (symbol or short expression), for the lower limit or denoting an {{math|''n''}}-[[Dimension (mathematics and physics)|dimension]]al space or the {{math|(''n'' − 1)}}- dimensional [[boundary (topology)|boundary]].</li>
 
<li>'''''Superscript:''''' Enter the superscript (symbol or short expression) for the upper limit.</li>
 
<li>'''''Superscript:''''' Enter the superscript (symbol or short expression) for the upper limit.</li>
 
</ol>
 
</ol>
  
 
'''NB:'''  
 
'''NB:'''  
*Applying {{code|font-style: italic;}} or {{code|font-style: oblique;}} to the integral symbol has no effect in Firefox, it remains upright. E.g.  
+
*Applying {{code|font-style: italic;}} or {{code|font-style: oblique;}} to the <tt>int</tt> symbol {{Unicode|∫}} has no effect in Firefox, it remains upright (whereas it does have an effect on all the other integral symbols), e.g.  
*:{{code|<span style{{=}}"font-style: italic;">∫</span>}} yields <span style="font-style: italic;">∫</span>;
+
*:{{code|<span style{{=}}"font-style: italic;">∫ ∬ ∭ ∮ ∲ ∳ ∯ ∰</span>}} yields <span style="font-style: italic;">∫ ∬ ∭ ∮ ∲ ∳ ∯ ∰</span>;
*:{{code|<span style{{=}}"font-style: oblique;">∫</span>}} yields <span style="font-style: oblique;">∫</span>.
+
*:{{code|<span style{{=}}"font-style: oblique;">∫ ∬ ∭ ∮ ∲ ∳ ∯ ∰</span>}} yields <span style="font-style: oblique;">∫ ∬ ∭ ∮ ∲ ∳ ∯ ∰</span>.
 
*This template already includes {{tl|su}}.
 
*This template already includes {{tl|su}}.
  
Line 117: Line 117:
 
==See also==
 
==See also==
 
*{{tl|Intorient}}
 
*{{tl|Intorient}}
 +
*{{tl|oiint}}
 
*{{tl|oiiint}}
 
*{{tl|oiiint}}
*{{tl|oiint}}
 
 
*[[Wikipedia:«math»]]
 
*[[Wikipedia:«math»]]
 
{{Math templates|notation}}
 
{{Math templates|notation}}

Revision as of 18:40, 12 March 2016

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