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 | ||
| Line 12: | Line 12: | ||
| aboveclass = plainlist | | aboveclass = plainlist | ||
| above = | | above = | ||
* [http://en.wikipedia.org/wiki/Fundamental theorem of calculus Fundamental theorem | * [http://en.wikipedia.org/wiki/Fundamental theorem of calculus Fundamental theorem] | ||
* [http://en.wikipedia.org/wiki/Limit of a function Limits of functions | * [http://en.wikipedia.org/wiki/Limit of a function Limits of functions] | ||
* [http://en.wikipedia.org/wiki/Continuous function Continuity | * [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 Implicit differentiation | * [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 Rules and identities | ; [http://en.wikipedia.org/wiki/Differentiation rules Rules and identities]: | ||
* [http://en.wikipedia.org/wiki/Sum rule in differentiation Sums | * [http://en.wikipedia.org/wiki/Sum rule in differentiation Sums] | ||
* [http://en.wikipedia.org/wiki/Product rule Products | * [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 Powers | * [http://en.wikipedia.org/wiki/Power rule Powers] | ||
* [http://en.wikipedia.org/wiki/Quotient rule Quotients | * [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 Contour integral | * [http://en.wikipedia.org/wiki/Methods of contour integration Contour integral] | ||
; Integration by: | ; Integration by: | ||
* [http://en.wikipedia.org/wiki/Integration by parts parts | * [http://en.wikipedia.org/wiki/Integration by parts parts] | ||
* [http://en.wikipedia.org/wiki/Disc integration discs | * [http://en.wikipedia.org/wiki/Disc integration discs] | ||
* [http://en.wikipedia.org/wiki/Shell integration cylindrical shells | * [http://en.wikipedia.org/wiki/Shell integration cylindrical shells] | ||
* [http://en.wikipedia.org/wiki/Integration by substitution 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 partial fractions | * [http://en.wikipedia.org/wiki/Partial fractions in integration partial fractions] | ||
* [http://en.wikipedia.org/wiki/Order of integration (calculus) changing order | * [http://en.wikipedia.org/wiki/Order of integration (calculus) changing order] | ||
* [http://en.wikipedia.org/wiki/Integration by reduction formulae 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) Series | | list4title = [http://en.wikipedia.org/wiki/Series (mathematics) Series] | ||
| list4 = | | list4 = | ||
* [http://en.wikipedia.org/wiki/Geometric series Geometric | * [http://en.wikipedia.org/wiki/Geometric series Geometric] | ||
* [http://en.wikipedia.org/wiki/Arithmetico-geometric sequence Arithmetico-geometric | * [http://en.wikipedia.org/wiki/Arithmetico-geometric sequence Arithmetico-geometric] | ||
* [http://en.wikipedia.org/wiki/Harmonic series (mathematics) Harmonic | * [http://en.wikipedia.org/wiki/Harmonic series (mathematics) Harmonic] | ||
* [http://en.wikipedia.org/wiki/Alternating series Alternating | * [http://en.wikipedia.org/wiki/Alternating series Alternating] | ||
* [http://en.wikipedia.org/wiki/Power series Power | * [http://en.wikipedia.org/wiki/Power series Power] | ||
* [http://en.wikipedia.org/wiki/Binomial series Binomial | * [http://en.wikipedia.org/wiki/Binomial series Binomial] | ||
* [http://en.wikipedia.org/wiki/Taylor series Taylor | * [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 Summand limit (Term test) | * [http://en.wikipedia.org/wiki/Term test Summand limit (Term test)] | ||
* [http://en.wikipedia.org/wiki/Ratio test Ratio | * [http://en.wikipedia.org/wiki/Ratio test Ratio] | ||
* [http://en.wikipedia.org/wiki/Root test Root | * [http://en.wikipedia.org/wiki/Root test Root] | ||
* [http://en.wikipedia.org/wiki/Integral test for convergence Integral | * [http://en.wikipedia.org/wiki/Integral test for convergence Integral] | ||
* [http://en.wikipedia.org/wiki/Direct comparison test Direct comparison | * [http://en.wikipedia.org/wiki/Direct comparison test Direct comparison] | ||
* [http://en.wikipedia.org/wiki/Limit comparison test Limit comparison | * [http://en.wikipedia.org/wiki/Limit comparison test Limit comparison] | ||
* [http://en.wikipedia.org/wiki/Alternating series test Alternating series | * [http://en.wikipedia.org/wiki/Alternating series test Alternating series] | ||
* [http://en.wikipedia.org/wiki/Cauchy condensation test Cauchy condensation | * [http://en.wikipedia.org/wiki/Cauchy condensation test Cauchy condensation] | ||
* [http://en.wikipedia.org/wiki/Dirichlet's test Dirichlet | * [http://en.wikipedia.org/wiki/Dirichlet's test Dirichlet] | ||
* [http://en.wikipedia.org/wiki/Abel's test Abel | * [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) Curl | * [http://en.wikipedia.org/wiki/Curl (mathematics) Curl] | ||
* [http://en.wikipedia.org/wiki/Laplace operator Laplacian | * [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 Matrix | * [http://en.wikipedia.org/wiki/Matrix calculus Matrix] | ||
* [http://en.wikipedia.org/wiki/Tensor calculus Tensor | * [http://en.wikipedia.org/wiki/Tensor calculus Tensor] | ||
* [http://en.wikipedia.org/wiki/Exterior derivative Exterior | * [http://en.wikipedia.org/wiki/Exterior derivative Exterior] | ||
* [http://en.wikipedia.org/wiki/Geometric calculus Geometric | * [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 Jacobian | * [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 Fractional | * [http://en.wikipedia.org/wiki/Fractional calculus Fractional] | ||
* [http://en.wikipedia.org/wiki/Malliavin calculus Malliavin | * [http://en.wikipedia.org/wiki/Malliavin calculus Malliavin] | ||
* [http://en.wikipedia.org/wiki/Stochastic calculus Stochastic | * [http://en.wikipedia.org/wiki/Stochastic calculus Stochastic] | ||
}}<noinclude>{{documentation}}</noinclude> | }}<noinclude>{{documentation}}</noinclude> | ||
Revision as of 17:19, 3 November 2013
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