Template:Calculus: Difference between revisions
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{{Sidebar | {{Sidebar | ||
| name = Calculus | | name = Calculus | ||
| title = [http://en.wikipedia.org/wiki/ Calculus] | | title = [http://en.wikipedia.org/wiki/Calculus]] | ||
| listtitlestyle = text-align: center | | listtitlestyle = text-align: center | ||
| listclass = hlist | | listclass = hlist | ||
| expanded = {{{expanded | | expanded = {{{expanded {{{1 }}}}}} | ||
| aboveclass = plainlist | | aboveclass = plainlist | ||
| above = | | above = | ||
* [http://en.wikipedia.org/wiki/ Fundamental theorem of calculus | * [http://en.wikipedia.org/wiki/Fundamental theorem of calculus Fundamental theorem]] | ||
* [http://en.wikipedia.org/wiki/ Limit of a function | * [http://en.wikipedia.org/wiki/Limit of a function Limits of functions]] | ||
* [http://en.wikipedia.org/wiki/ Continuous function | * [http://en.wikipedia.org/wiki/Continuous function Continuity]] | ||
* [http://en.wikipedia.org/wiki/ Mean value theorem] | * [http://en.wikipedia.org/wiki/Mean value theorem]] | ||
* [http://en.wikipedia.org/wiki/ Rolle's theorem] | * [http://en.wikipedia.org/wiki/Rolle's theorem]] | ||
| list2name = Differential | | list2name = Differential | ||
| list2title = [http://en.wikipedia.org/wiki/ Differential calculus] | | list2title = [http://en.wikipedia.org/wiki/Differential calculus]] | ||
| list2 = | | list2 = | ||
; Definitions: | ; Definitions: | ||
* [http://en.wikipedia.org/wiki/ Derivative] | * [http://en.wikipedia.org/wiki/Derivative]] | ||
* [http://en.wikipedia.org/wiki/ Differential (infinitesimal)] | * [http://en.wikipedia.org/wiki/Differential (infinitesimal)]] | ||
* [http://en.wikipedia.org/wiki/ Differential of a function] | * [http://en.wikipedia.org/wiki/Differential of a function]] | ||
* [http://en.wikipedia.org/wiki/ Generalizations of the derivative] | * [http://en.wikipedia.org/wiki/Generalizations of the derivative]] | ||
; Concepts: | ; Concepts: | ||
* [http://en.wikipedia.org/wiki/ Notation for differentiation] | * [http://en.wikipedia.org/wiki/Notation for differentiation]] | ||
* [http://en.wikipedia.org/wiki/ Second derivative] | * [http://en.wikipedia.org/wiki/Second derivative]] | ||
* [http://en.wikipedia.org/wiki/ Third derivative] | * [http://en.wikipedia.org/wiki/Third derivative]] | ||
* [http://en.wikipedia.org/wiki/ Change of variables] | * [http://en.wikipedia.org/wiki/Change of variables]] | ||
* [http://en.wikipedia.org/wiki/ Implicit function | * [http://en.wikipedia.org/wiki/Implicit function Implicit differentiation]] | ||
* [http://en.wikipedia.org/wiki/ Related rates] | * [http://en.wikipedia.org/wiki/Related rates]] | ||
* [http://en.wikipedia.org/wiki/ Taylor's theorem] | * [http://en.wikipedia.org/wiki/Taylor's theorem]] | ||
; [http://en.wikipedia.org/wiki/ Differentiation rules | ; [http://en.wikipedia.org/wiki/Differentiation rules Rules and identities]]: | ||
* [http://en.wikipedia.org/wiki/ Sum rule in differentiation | * [http://en.wikipedia.org/wiki/Sum rule in differentiation Sums]] | ||
* [http://en.wikipedia.org/wiki/ Product rule | * [http://en.wikipedia.org/wiki/Product rule Products]] | ||
* [http://en.wikipedia.org/wiki/ Chain rule] | * [http://en.wikipedia.org/wiki/Chain rule]] | ||
* [http://en.wikipedia.org/wiki/ Power rule | * [http://en.wikipedia.org/wiki/Power rule Powers]] | ||
* [http://en.wikipedia.org/wiki/ Quotient rule | * [http://en.wikipedia.org/wiki/Quotient rule Quotients]] | ||
* [http://en.wikipedia.org/wiki/ Faà di Bruno's formula] | * [http://en.wikipedia.org/wiki/Faà di Bruno's formula]] | ||
| list3name = Integral | | list3name = Integral | ||
| list3title = Integral calculus | | list3title = Integral calculus | ||
| list3 = | | list3 = | ||
* [http://en.wikipedia.org/wiki/ Lists of integrals] | * [http://en.wikipedia.org/wiki/Lists of integrals]] | ||
; Definitions: | ; Definitions: | ||
* [http://en.wikipedia.org/wiki/ Antiderivative] | * [http://en.wikipedia.org/wiki/Antiderivative]] | ||
* [http://en.wikipedia.org/wiki/ Integral] | * [http://en.wikipedia.org/wiki/Integral]] | ||
* [http://en.wikipedia.org/wiki/ Improper integral] | * [http://en.wikipedia.org/wiki/Improper integral]] | ||
* [http://en.wikipedia.org/wiki/ Riemann integral] | * [http://en.wikipedia.org/wiki/Riemann integral]] | ||
* [http://en.wikipedia.org/wiki/ Lebesgue integration] | * [http://en.wikipedia.org/wiki/Lebesgue integration]] | ||
* [http://en.wikipedia.org/wiki/ Methods of contour integration | * [http://en.wikipedia.org/wiki/Methods of contour integration Contour integral]] | ||
; Integration by: | ; Integration by: | ||
* [http://en.wikipedia.org/wiki/ Integration by parts | * [http://en.wikipedia.org/wiki/Integration by parts parts]] | ||
* [http://en.wikipedia.org/wiki/ Disc integration | * [http://en.wikipedia.org/wiki/Disc integration discs]] | ||
* [http://en.wikipedia.org/wiki/ Shell integration | * [http://en.wikipedia.org/wiki/Shell integration cylindrical shells]] | ||
* [http://en.wikipedia.org/wiki/ Integration by substitution | * [http://en.wikipedia.org/wiki/Integration by substitution substitution]] | ||
* [http://en.wikipedia.org/wiki/ trigonometric substitution] | * [http://en.wikipedia.org/wiki/trigonometric substitution]] | ||
* [http://en.wikipedia.org/wiki/ Partial fractions in integration | * [http://en.wikipedia.org/wiki/Partial fractions in integration partial fractions]] | ||
* [http://en.wikipedia.org/wiki/ Order of integration (calculus) | * [http://en.wikipedia.org/wiki/Order of integration (calculus) changing order]] | ||
* [http://en.wikipedia.org/wiki/ Integration by reduction formulae | * [http://en.wikipedia.org/wiki/Integration by reduction formulae reduction formulae]] | ||
| list4name = Series | | list4name = Series | ||
| list4title = [http://en.wikipedia.org/wiki/ Series (mathematics) | | list4title = [http://en.wikipedia.org/wiki/Series (mathematics) Series]] | ||
| list4 = | | list4 = | ||
* [http://en.wikipedia.org/wiki/ Geometric series | * [http://en.wikipedia.org/wiki/Geometric series Geometric]] | ||
* [http://en.wikipedia.org/wiki/ Arithmetico-geometric sequence | * [http://en.wikipedia.org/wiki/Arithmetico-geometric sequence Arithmetico-geometric]] | ||
* [http://en.wikipedia.org/wiki/ Harmonic series (mathematics) | * [http://en.wikipedia.org/wiki/Harmonic series (mathematics) Harmonic]] | ||
* [http://en.wikipedia.org/wiki/ Alternating series | * [http://en.wikipedia.org/wiki/Alternating series Alternating]] | ||
* [http://en.wikipedia.org/wiki/ Power series | * [http://en.wikipedia.org/wiki/Power series Power]] | ||
* [http://en.wikipedia.org/wiki/ Binomial series | * [http://en.wikipedia.org/wiki/Binomial series Binomial]] | ||
* [http://en.wikipedia.org/wiki/ Taylor series | * [http://en.wikipedia.org/wiki/Taylor series Taylor]] | ||
; [http://en.wikipedia.org/wiki/ Convergence tests]: | ; [http://en.wikipedia.org/wiki/Convergence tests]]: | ||
* [http://en.wikipedia.org/wiki/ Term test | * [http://en.wikipedia.org/wiki/Term test Summand limit (Term test)]] | ||
* [http://en.wikipedia.org/wiki/ Ratio test | * [http://en.wikipedia.org/wiki/Ratio test Ratio]] | ||
* [http://en.wikipedia.org/wiki/ Root test | * [http://en.wikipedia.org/wiki/Root test Root]] | ||
* [http://en.wikipedia.org/wiki/ Integral test for convergence | * [http://en.wikipedia.org/wiki/Integral test for convergence Integral]] | ||
* [http://en.wikipedia.org/wiki/ Direct comparison test | * [http://en.wikipedia.org/wiki/Direct comparison test Direct comparison]] | ||
* [http://en.wikipedia.org/wiki/ Limit comparison test | * [http://en.wikipedia.org/wiki/Limit comparison test Limit comparison]] | ||
* [http://en.wikipedia.org/wiki/ Alternating series test | * [http://en.wikipedia.org/wiki/Alternating series test Alternating series]] | ||
* [http://en.wikipedia.org/wiki/ Cauchy condensation test | * [http://en.wikipedia.org/wiki/Cauchy condensation test Cauchy condensation]] | ||
* [http://en.wikipedia.org/wiki/ Dirichlet's test | * [http://en.wikipedia.org/wiki/Dirichlet's test Dirichlet]] | ||
* [http://en.wikipedia.org/wiki/ Abel's test | * [http://en.wikipedia.org/wiki/Abel's test Abel]] | ||
| list5name = Vector | | list5name = Vector | ||
| list5title = [http://en.wikipedia.org/wiki/ Vector calculus] | | list5title = [http://en.wikipedia.org/wiki/Vector calculus]] | ||
| list5 = | | list5 = | ||
* [http://en.wikipedia.org/wiki/ Gradient] | * [http://en.wikipedia.org/wiki/Gradient]] | ||
* [http://en.wikipedia.org/wiki/ Divergence] | * [http://en.wikipedia.org/wiki/Divergence]] | ||
* [http://en.wikipedia.org/wiki/ Curl (mathematics) | * [http://en.wikipedia.org/wiki/Curl (mathematics) Curl]] | ||
* [http://en.wikipedia.org/wiki/ Laplace operator | * [http://en.wikipedia.org/wiki/Laplace operator Laplacian]] | ||
* [http://en.wikipedia.org/wiki/ Gradient theorem] | * [http://en.wikipedia.org/wiki/Gradient theorem]] | ||
* [http://en.wikipedia.org/wiki/ Green's theorem] | * [http://en.wikipedia.org/wiki/Green's theorem]] | ||
* [http://en.wikipedia.org/wiki/ Stokes' theorem] | * [http://en.wikipedia.org/wiki/Stokes' theorem]] | ||
* [http://en.wikipedia.org/wiki/ Divergence theorem] | * [http://en.wikipedia.org/wiki/Divergence theorem]] | ||
* [http://en.wikipedia.org/wiki/ Directional derivative] | * [http://en.wikipedia.org/wiki/Directional derivative]] | ||
| list6name = Multivariable | | list6name = Multivariable | ||
| list6title = [http://en.wikipedia.org/wiki/ Multivariable calculus] | | list6title = [http://en.wikipedia.org/wiki/Multivariable calculus]] | ||
| list6 = | | list6 = | ||
; Formalisms: | ; Formalisms: | ||
* [http://en.wikipedia.org/wiki/ Matrix calculus | * [http://en.wikipedia.org/wiki/Matrix calculus Matrix]] | ||
* [http://en.wikipedia.org/wiki/ Tensor calculus | * [http://en.wikipedia.org/wiki/Tensor calculus Tensor]] | ||
* [http://en.wikipedia.org/wiki/ Exterior derivative | * [http://en.wikipedia.org/wiki/Exterior derivative Exterior]] | ||
* [http://en.wikipedia.org/wiki/ Geometric calculus | * [http://en.wikipedia.org/wiki/Geometric calculus Geometric]] | ||
; Definitions: | ; Definitions: | ||
* [http://en.wikipedia.org/wiki/ Partial derivative] | * [http://en.wikipedia.org/wiki/Partial derivative]] | ||
* [http://en.wikipedia.org/wiki/ Multiple integral] | * [http://en.wikipedia.org/wiki/Multiple integral]] | ||
* [http://en.wikipedia.org/wiki/ Line integral] | * [http://en.wikipedia.org/wiki/Line integral]] | ||
* [http://en.wikipedia.org/wiki/ Surface integral] | * [http://en.wikipedia.org/wiki/Surface integral]] | ||
* [http://en.wikipedia.org/wiki/ Volume integral] | * [http://en.wikipedia.org/wiki/Volume integral]] | ||
* [http://en.wikipedia.org/wiki/ Jacobian matrix and determinant | * [http://en.wikipedia.org/wiki/Jacobian matrix and determinant Jacobian]] | ||
| list7name = Specialized | | list7name = Specialized | ||
| list7title = Specialized calculi | | list7title = Specialized calculi | ||
| list7 = | | list7 = | ||
* [http://en.wikipedia.org/wiki/ Calculus of variations] | * [http://en.wikipedia.org/wiki/Calculus of variations]] | ||
* [http://en.wikipedia.org/wiki/ Fractional calculus | * [http://en.wikipedia.org/wiki/Fractional calculus Fractional]] | ||
* [http://en.wikipedia.org/wiki/ Malliavin calculus | * [http://en.wikipedia.org/wiki/Malliavin calculus Malliavin]] | ||
* [http://en.wikipedia.org/wiki/ Stochastic calculus | * [http://en.wikipedia.org/wiki/Stochastic calculus Stochastic]] | ||
}}<noinclude>{{documentation}}</noinclude> | }}<noinclude>{{documentation}}</noinclude> | ||
Revision as of 16:18, 3 November 2013
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