Difference between revisions of "Template:Calculus"

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imported>Oleg Alexandrov
(rm Simpson. That's numerical integration. Rm surfaces of revoution and so on. Integration by disks and Shell integration should be enough. Let us keep this representative, not exhaustive.)
imported>Newone
 
(187 intermediate revisions by 86 users not shown)
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{| align="right" id="toc" style="width: 200px; margin: 0 0 1em 1em"
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<includeonly>{{#invoke:sidebar|collapsible
|- style="background:#ccccff" align="center"
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| class = plainlist
| style="border-bottom: 2px solid #303060"" | '''Topics in [[calculus]]'''
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| titlestyle = padding-bottom:0.25em;
|-  
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| pretitle = Part of a series of articles about
|
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| title = [[Calculus]]
[[Fundamental theorem of calculus|Fundamental theorem]] | [[Function (mathematics)|Function]] | [[Limit of a function|Limits of functions]] | [[Continuous function|Continuity]] | [[Mean value theorem]] | [[Vector calculus]] | [[Tensor|Tensor calculus]]
+
| image =
|- style="background:#ccccff" align="center"
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| listtitlestyle = text-align:center;
| [[Derivative|'''Differentiation''']]
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| liststyle = border-top:1px solid #aaa;padding-top:0.15em;border-bottom:1px solid #aaa;
|-
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| expanded = {{{expanded|{{lc:{{{selected|{{{1|}}}}}}}}}}}
|
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[[Product rule|Product rule]] | [[Quotient rule|Quotient rule]] | [[Chain rule]] | [[Implicit function|Implicit differentiation]] | [[Taylor's theorem]] | [[Related rates]]  
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| abovestyle = padding:0.15em 0.25em 0.3em;font-weight:normal;
|- style="background:#ccccff" align="center"
+
| above =
| [[Integral|'''Integration''']]
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* [[Fundamental theorem of calculus|Fundamental theorem]]
|-
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* [[Leibniz integral rule]]
|
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{{startflatlist}}
[[Substitution rule|Integration by substitution]] | [[Integration by parts|Integration by parts]] | [[Trigonometric substitution|Integration by trigonometric substitution]] | [[Disk integration|Integration by disks]] | [[Shell integration|Integration by cylindrical shells]] | [[Improper integral|Improper integrals]] | [[Lists of integrals]]  
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* [[Limit of a function|Limits of functions]]
|}
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* [[Continuous function|Continuity]]
 +
{{endflatlist}}{{startflatlist}}
 +
* [[Mean value theorem]]
 +
* [[Rolle's theorem]]
 +
{{endflatlist}}
 +
 
 +
| list2name = differential
 +
| list2titlestyle = display:block;margin-top:0.65em;
 +
| list2title = {{bigger|[[Differential calculus|Differential]]}}<!--resized here rather than via listtitlestyle otherwise [show/hide] link also resized-->
 +
| list2 =
 +
{{Sidebar |bodystyle={{subsidebar bodystyle}} |navbar=off
 +
  |contentclass=hlist
 +
  | heading1 = Definitions
 +
  | content1 =
 +
* [[Derivative]]&nbsp;([[Generalizations of the derivative|generalizations]])
 +
{{startflatlist|style=padding:0.1em 0;line-height:1.2em;<!--(longitem)-->}}
 +
* [[Differential (mathematics)|Differential]]
 +
** [[Differential (infinitesimal)|infinitesimal]]
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** [[Differential of a function|of a function]]
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** [[Differential of a function#Differentials in several variables|total]]
 +
{{endflatlist}}
 +
  | heading2 = Concepts
 +
  | content2 = {{startflatlist}}
 +
* [[Notation for differentiation|Differentiation notation]]
 +
* [[Second derivative]]
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* [[Implicit function|Implicit differentiation]]
 +
* [[Logarithmic differentiation]]
 +
* [[Related rates]]
 +
* [[Taylor's theorem]]
 +
{{endflatlist}}
 +
  | heading3 = [[Differentiation rules|Rules and identities]]
 +
  | content3 = {{startflatlist}}
 +
* [[Sum rule in differentiation|Sum]]
 +
* [[Product rule|Product]]
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* [[Chain rule|Chain]]
 +
* [[Power rule|Power]]
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* [[Quotient rule|Quotient]]
 +
* [[L'Hôpital's rule]]
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* [[Inverse functions and differentiation|Inverse]]
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* [[General Leibniz rule|General Leibniz]]
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* [[Faà di Bruno's formula]]
 +
{{endflatlist}}
 +
}}
 +
 
 +
| list3name = integral
 +
| list3title = {{bigger|[[Integral<!--|Integral calculus-->]]}}<!--(as above, etc)-->
 +
| list3 =
 +
{{Sidebar |bodystyle={{subsidebar bodystyle}} |navbar=off
 +
  |contentclass=hlist
 +
  | content1 =
 +
* [[Lists of integrals]]
 +
* [[Integral transform]]
 +
  | heading2 = Definitions
 +
  | content2 =
 +
* [[Antiderivative]]
 +
* [[Integral]]&nbsp;([[Improper integral|improper]])
 +
* [[Riemann integral]]
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* [[Lebesgue integration]]
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* [[Contour integration]]
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* [[Integral of inverse functions]]
 +
  | heading3 = Integration by
 +
  | content3 =
 +
* [[Integration by parts|Parts]]
 +
* [[Disc integration|Discs]]
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* [[Shell integration|Cylindrical shells]]
 +
* [[Integration by substitution|Substitution]]&nbsp;([[Trigonometric substitution|trigonometric]], [[Weierstrass substitution|Weierstrass]], [[Euler substitution|Euler]])
 +
* [[Integration using Euler's formula|Euler's formula]]
 +
* [[Partial fractions in integration|Partial fractions]]
 +
* [[Order of integration (calculus)|Changing order]]
 +
* [[Integration by reduction formulae|Reduction formulae]]
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* [[Leibniz integral rule#Evaluating definite integrals|Differentiating under the integral sign]]
 +
}}
 +
 
 +
| list4name = series
 +
| list4title = {{bigger|[[Series (mathematics)|Series]]}}
 +
| list4 =
 +
{{Sidebar |bodystyle={{subsidebar bodystyle}} |navbar=off
 +
  |contentclass=hlist
 +
  | content1 =
 +
* [[Geometric series|Geometric]]&nbsp;([[Arithmetico–geometric sequence|arithmetico-geometric]])
 +
* [[Harmonic series (mathematics)|Harmonic]]
 +
* [[Alternating series|Alternating]]
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* [[Power series|Power]]
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* [[Binomial series|Binomial]]
 +
* [[Taylor series|Taylor]]
 +
  | heading2 = [[Convergence tests]]
 +
  | content2 =
 +
* [[Term test|Summand limit (term test)]]
 +
* [[Ratio test|Ratio]]
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* [[Root test|Root]]
 +
* [[Integral test for convergence|Integral]]
 +
* [[Direct comparison test|Direct comparison]]
 +
* <br/>[[Limit comparison test|Limit comparison]]
 +
* [[Alternating series test|Alternating series]]
 +
* [[Cauchy condensation test|Cauchy condensation]]
 +
* [[Dirichlet's test|Dirichlet]]
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* [[Abel's test|Abel]]
 +
}}
 +
 
 +
| list5name = vector
 +
| list5title = {{bigger|[[Vector calculus|Vector]]}}
 +
| list5 =
 +
{{Sidebar |bodystyle={{subsidebar bodystyle}} |navbar=off
 +
  |contentclass=hlist
 +
  | content1 =
 +
* [[Gradient]]
 +
* [[Divergence]]
 +
* [[Curl (mathematics)|Curl]]
 +
* [[Laplace operator|Laplacian]]
 +
* [[Directional derivative]]
 +
* [[Vector calculus identities|Identities]]
 +
  | heading2 = Theorems
 +
  | content2 =
 +
* [[Gradient theorem|Gradient]]
 +
* [[Green's theorem|Green's]]
 +
* [[Kelvin–Stokes theorem|Stokes']]
 +
* [[Divergence theorem|Divergence]]
 +
* [[Stokes' theorem|generalized Stokes]]
 +
}}
 +
 
 +
| list6name = multivariable
 +
| list6title = {{bigger|[[Multivariable calculus|Multivariable]]}}
 +
| list6 =
 +
{{Sidebar |bodystyle={{subsidebar bodystyle}} |navbar=off
 +
  |contentclass=hlist
 +
  | heading1 = Formalisms
 +
  | content1 =
 +
* [[Matrix calculus|Matrix]]
 +
* [[Tensor calculus|Tensor]]
 +
* [[Exterior derivative|Exterior]]
 +
* [[Geometric calculus|Geometric]]
 +
  | heading2 = Definitions
 +
  | content2 =
 +
* [[Partial derivative]]
 +
* [[Multiple integral]]
 +
* [[Line integral]]
 +
* [[Surface integral]]
 +
* [[Volume integral]]
 +
* [[Jacobian matrix and determinant|Jacobian]]
 +
* [[Hessian matrix|Hessian]]
 +
}}
 +
 
 +
| list7name = specialized
 +
| list7title = {{bigger|Specialized}}
 +
| list7 = {{startflatlist}}
 +
* [[Fractional calculus|Fractional]]
 +
* [[Malliavin calculus|Malliavin]]
 +
* [[Stochastic calculus|Stochastic]]
 +
* [[Calculus of variations|Variations]]
 +
{{endflatlist}}
 +
 
 +
| list8name = glossary
 +
| list8title = {{bigger|[[Glossary of calculus]]}}
 +
| list8 = {{startflatlist}}
 +
* [[Glossary of calculus]]
 +
* [[List of calculus topics]]
 +
{{endflatlist}}
 +
 
 +
}}</includeonly><noinclude>{{Documentation}}</noinclude>

Latest revision as of 03:41, 17 November 2020

Template documentation[view] [edit] [history] [purge]

Template:Calculus is used to give a brief outline of calculus topics (you can see an example on the right).

Collapsible lists

This template includes collapsible lists.

  • To set it to display all lists when it appears (i.e. all lists expanded), use:
  •  {{Calculus |expanded=all}} or, if enabled, {{Calculus |all}}  (i.e. omitting "expanded=").
  • To set it to display one particular list while keeping the remainder collapsed (i.e. hidden apart from their headings), use:
  •  {{Calculus |expanded=listname}} or, if enabled, {{Calculus |listname}}
  • …where listname is one of the following (do not include any quotemarks):
  • differential, integral, series, vector, multivariable, specialized

See also