<div class="mw-parser-output"><table class="vertical-navbox nowraplinks plainlist" style="float:right;clear:right;width:22.0em;margin:0 0 1.0em 1.0em;background:#f9f9f9;border:1px solid #aaa;padding:0.2em;border-spacing:0.4em 0;text-align:center;line-height:1.4em;font-size:88%"><tr><td style="padding-top:0.4em;line-height:1.2em">Part of a series of articles about</td></tr><tr><th style="padding:0.2em 0.4em 0.2em;padding-top:0;font-size:145%;line-height:1.2em;padding-bottom:0.25em;"><a href="/wiki/Calculus" title="Calculus">Calculus</a></th></tr><tr><td style="padding:0.3em 0.4em 0.3em;font-weight:bold;border-top: 1px solid #aaa; border-bottom: 1px solid #aaa;padding:0.15em 0.25em 0.3em;font-weight:normal;"> <ul><li> <a href="/wiki/Fundamental_theorem_of_calculus" title="Fundamental theorem of calculus">Fundamental theorem</a></li></ul> <div class="hlist"> <ul><li> <a href="/wiki/Limit_of_a_function" title="Limit of a function">Limits of functions</a></li> <li> <a href="/wiki/Continuous_function" title="Continuous function">Continuity</a></li></ul> </div><div class="hlist"> <ul><li> <a href="/wiki/Mean_value_theorem" title="Mean value theorem">Mean value theorem</a></li> <li> <a href="/wiki/Rolle%27s_theorem" title="Rolle's theorem">Rolle's theorem</a></li></ul> </div></td></tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame collapsed" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:transparent;text-align:left;text-align:center;;display:block;margin-top:0.65em;"><span style="font-size:110%;"><a href="/wiki/Differential_calculus" title="Differential calculus">Differential</a></span></div><div class="NavContent" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center;border-top:1px solid #aaa;padding-top:0.15em;border-bottom:1px solid #aaa;"><table class="vertical-navbox nowraplinks" style="float:right;clear:right;width:22.0em;margin:0 0 1.0em 1.0em;background:#f9f9f9;border:1px solid #aaa;padding:0.2em;border-spacing:0.4em 0;text-align:center;line-height:1.4em;font-size:88%;border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none"><tr><th style="padding:0.1em"> Definitions</th></tr><tr><td class="hlist" style="padding:0 0.1em 0.4em"> <ul><li> <a href="/wiki/Derivative" title="Derivative">Derivative</a> (<a href="/wiki/Generalizations_of_the_derivative" title="Generalizations of the derivative">generalizations</a>)</li></ul> <div class="hlist" style="padding:0.1em 0;line-height:1.2em;"> <ul><li> <a href="/wiki/Differential_(mathematics)" title="Differential (mathematics)">Differential</a> <ul><li> <a href="/wiki/Differential_(infinitesimal)" title="Differential (infinitesimal)">infinitesimal</a></li> <li> <a href="/wiki/Differential_of_a_function" title="Differential of a function">of a function</a></li> <li> <a href="/wiki/Total_differential" class="mw-redirect" title="Total differential">total</a></li></ul></li></ul> </div></td> </tr><tr><th style="padding:0.1em"> Concepts</th></tr><tr><td class="hlist" style="padding:0 0.1em 0.4em"> <div class="hlist"> <ul><li> <a href="/wiki/Notation_for_differentiation" title="Notation for differentiation">Differentiation notation</a></li> <li> <a href="/wiki/Second_derivative" title="Second derivative">Second derivative</a></li> <li> <a href="/wiki/Third_derivative" title="Third derivative">Third derivative</a></li> <li> <a href="/wiki/Change_of_variables" title="Change of variables">Change of variables</a></li> <li> <a href="/wiki/Implicit_function" title="Implicit function">Implicit differentiation</a></li> <li> <a href="/wiki/Related_rates" title="Related rates">Related rates</a></li> <li> <a href="/wiki/Taylor%27s_theorem" title="Taylor's theorem">Taylor's theorem</a></li></ul> </div></td> </tr><tr><th style="padding:0.1em"> <a href="/wiki/Differentiation_rules" title="Differentiation rules">Rules and identities</a></th></tr><tr><td class="hlist" style="padding:0 0.1em 0.4em"> <div class="hlist"> <ul><li> <a href="/wiki/Sum_rule_in_differentiation" title="Sum rule in differentiation">Sum</a></li> <li> <a href="/wiki/Product_rule" title="Product rule">Product</a></li> <li> <a href="/wiki/Chain_rule" title="Chain rule">Chain</a></li> <li> <a href="/wiki/Power_rule" title="Power rule">Power</a></li> <li> <a href="/wiki/Quotient_rule" title="Quotient rule">Quotient</a></li> <li> <a href="/wiki/Inverse_functions_and_differentiation" title="Inverse functions and differentiation">Inverse</a></li> <li> <a href="/wiki/General_Leibniz_rule" title="General Leibniz rule">General Leibniz</a></li> <li> <a href="/wiki/Fa%C3%A0_di_Bruno%27s_formula" title="Faà di Bruno's formula">Faà di Bruno's formula</a></li></ul> </div></td> </tr></table></div></div></td> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame collapsed" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:transparent;text-align:left;text-align:center;"><span style="font-size:110%;"><a href="/wiki/Integral" title="Integral">Integral</a></span></div><div class="NavContent" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center;border-top:1px solid #aaa;padding-top:0.15em;border-bottom:1px solid #aaa;"><table class="vertical-navbox nowraplinks" style="float:right;clear:right;width:22.0em;margin:0 0 1.0em 1.0em;background:#f9f9f9;border:1px solid #aaa;padding:0.2em;border-spacing:0.4em 0;text-align:center;line-height:1.4em;font-size:88%;border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none"><tr><td class="hlist" style="padding:0 0.1em 0.4em"> <ul><li> <a href="/wiki/Lists_of_integrals" title="Lists of integrals">Lists of integrals</a></td></li></ul> </tr><tr><th style="padding:0.1em"> Definitions</th></tr><tr><td class="hlist" style="padding:0 0.1em 0.4em"> <ul><li> <a href="/wiki/Antiderivative" title="Antiderivative">Antiderivative</a></li> <li> <a href="/wiki/Integral" title="Integral">Integral</a> (<a href="/wiki/Improper_integral" title="Improper integral">improper</a>)</li> <li> <a href="/wiki/Riemann_integral" title="Riemann integral">Riemann integral</a></li> <li> <a href="/wiki/Lebesgue_integration" title="Lebesgue integration">Lebesgue integration</a></li> <li> <a href="/wiki/Methods_of_contour_integration" class="mw-redirect" title="Methods of contour integration">Contour integration</a></td></li></ul> </tr><tr><th style="padding:0.1em"> Integration by</th></tr><tr><td class="hlist" style="padding:0 0.1em 0.4em"> <ul><li> <a href="/wiki/Integration_by_parts" title="Integration by parts">Parts</a></li> <li> <a href="/wiki/Disc_integration" title="Disc integration">Discs</a></li> <li> <a href="/wiki/Shell_integration" title="Shell integration">Cylindrical shells</a></li> <li> <a href="/wiki/Integration_by_substitution" title="Integration by substitution">Substitution</a> (<a href="/wiki/Trigonometric_substitution" title="Trigonometric substitution">trigonometric</a>)</li> <li> <a href="/wiki/Partial_fractions_in_integration" class="mw-redirect" title="Partial fractions in integration">Partial fractions</a></li> <li> <a href="/wiki/Order_of_integration_(calculus)" title="Order of integration (calculus)">Order</a></li> <li> <a href="/wiki/Integration_by_reduction_formulae" title="Integration by reduction formulae">Reduction formulae</a></td></li></ul> </tr></table></div></div></td> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame collapsed" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:transparent;text-align:left;text-align:center;"><span style="font-size:110%;"><a href="/wiki/Series_(mathematics)" title="Series (mathematics)">Series</a></span></div><div class="NavContent" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center;border-top:1px solid #aaa;padding-top:0.15em;border-bottom:1px solid #aaa;"><table class="vertical-navbox nowraplinks" style="float:right;clear:right;width:22.0em;margin:0 0 1.0em 1.0em;background:#f9f9f9;border:1px solid #aaa;padding:0.2em;border-spacing:0.4em 0;text-align:center;line-height:1.4em;font-size:88%;border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none"><tr><td class="hlist" style="padding:0 0.1em 0.4em"> <ul><li> <a href="/wiki/Geometric_series" title="Geometric series">Geometric</a> (<a href="/wiki/Arithmetico-geometric_sequence" class="mw-redirect" title="Arithmetico-geometric sequence">arithmetico-geometric</a>)</li> <li> <a href="/wiki/Harmonic_series_(mathematics)" title="Harmonic series (mathematics)">Harmonic</a></li> <li> <a href="/wiki/Alternating_series" title="Alternating series">Alternating</a></li> <li> <a href="/wiki/Power_series" title="Power series">Power</a></li> <li> <a href="/wiki/Binomial_series" title="Binomial series">Binomial</a></li> <li> <a href="/wiki/Taylor_series" title="Taylor series">Taylor</a></td></li></ul> </tr><tr><th style="padding:0.1em"> <a href="/wiki/Convergence_tests" title="Convergence tests">Convergence tests</a></th></tr><tr><td class="hlist" style="padding:0 0.1em 0.4em"> <ul><li> <a href="/wiki/Term_test" title="Term test">Summand limit (term test)</a></li> <li> <a href="/wiki/Ratio_test" title="Ratio test">Ratio</a></li> <li> <a href="/wiki/Root_test" title="Root test">Root</a></li> <li> <a href="/wiki/Integral_test_for_convergence" title="Integral test for convergence">Integral</a></li> <li> <a href="/wiki/Direct_comparison_test" title="Direct comparison test">Direct comparison</a></li> <li> <br/><a href="/wiki/Limit_comparison_test" title="Limit comparison test">Limit comparison</a></li> <li> <a href="/wiki/Alternating_series_test" title="Alternating series test">Alternating series</a></li> <li> <a href="/wiki/Cauchy_condensation_test" title="Cauchy condensation test">Cauchy condensation</a></li> <li> <a href="/wiki/Dirichlet%27s_test" title="Dirichlet's test">Dirichlet</a></li> <li> <a href="/wiki/Abel%27s_test" title="Abel's test">Abel</a></td></li></ul> </tr></table></div></div></td> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame collapsed" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:transparent;text-align:left;text-align:center;"><span style="font-size:110%;"><a href="/wiki/Vector_calculus" title="Vector calculus">Vector</a></span></div><div class="NavContent" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center;border-top:1px solid #aaa;padding-top:0.15em;border-bottom:1px solid #aaa;"><table class="vertical-navbox nowraplinks" style="float:right;clear:right;width:22.0em;margin:0 0 1.0em 1.0em;background:#f9f9f9;border:1px solid #aaa;padding:0.2em;border-spacing:0.4em 0;text-align:center;line-height:1.4em;font-size:88%;border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none"><tr><td class="hlist" style="padding:0 0.1em 0.4em"> <ul><li> <a href="/wiki/Gradient" title="Gradient">Gradient</a></li> <li> <a href="/wiki/Divergence" title="Divergence">Divergence</a></li> <li> <a href="/wiki/Curl_(mathematics)" title="Curl (mathematics)">Curl</a></li> <li> <a href="/wiki/Laplace_operator" title="Laplace operator">Laplacian</a></li> <li> <a href="/wiki/Directional_derivative" title="Directional derivative">Directional derivative</a></li> <li> <a href="/wiki/Vector_calculus_identities" title="Vector calculus identities">Identities</a></td></li></ul> </tr><tr><th style="padding:0.1em"> Theorems</th></tr><tr><td class="hlist" style="padding:0 0.1em 0.4em"> <ul><li> <a href="/wiki/Divergence_theorem" title="Divergence theorem">Divergence</a></li> <li> <a href="/wiki/Gradient_theorem" title="Gradient theorem">Gradient</a></li> <li> <a href="/wiki/Green%27s_theorem" title="Green's theorem">Green's</a></li> <li> <a href="/wiki/Kelvin%E2%80%93Stokes_theorem" title="Kelvin–Stokes theorem">Kelvin–Stokes</a></li> <li> <a href="/wiki/Stokes%27_theorem" title="Stokes' theorem">Stokes</a></td></li></ul> </tr></table></div></div></td> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame collapsed" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:transparent;text-align:left;text-align:center;"><span style="font-size:110%;"><a href="/wiki/Multivariable_calculus" title="Multivariable calculus">Multivariable</a></span></div><div class="NavContent" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center;border-top:1px solid #aaa;padding-top:0.15em;border-bottom:1px solid #aaa;"><table class="vertical-navbox nowraplinks" style="float:right;clear:right;width:22.0em;margin:0 0 1.0em 1.0em;background:#f9f9f9;border:1px solid #aaa;padding:0.2em;border-spacing:0.4em 0;text-align:center;line-height:1.4em;font-size:88%;border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none"><tr><th style="padding:0.1em"> Formalisms</th></tr><tr><td class="hlist" style="padding:0 0.1em 0.4em"> <ul><li> <a href="/wiki/Matrix_calculus" title="Matrix calculus">Matrix</a></li> <li> <a href="/wiki/Tensor_calculus" title="Tensor calculus">Tensor</a></li> <li> <a href="/wiki/Exterior_derivative" title="Exterior derivative">Exterior</a></li> <li> <a href="/wiki/Geometric_calculus" title="Geometric calculus">Geometric</a></td></li></ul> </tr><tr><th style="padding:0.1em"> Definitions</th></tr><tr><td class="hlist" style="padding:0 0.1em 0.4em"> <ul><li> <a href="/wiki/Partial_derivative" title="Partial derivative">Partial derivative</a></li> <li> <a href="/wiki/Multiple_integral" title="Multiple integral">Multiple integral</a></li> <li> <a href="/wiki/Line_integral" title="Line integral">Line integral</a></li> <li> <a href="/wiki/Surface_integral" title="Surface integral">Surface integral</a></li> <li> <a href="/wiki/Volume_integral" title="Volume integral">Volume integral</a></li> <li> <a href="/wiki/Jacobian_matrix_and_determinant" title="Jacobian matrix and determinant">Jacobian</a></li> <li> <a href="/wiki/Hessian_matrix" title="Hessian matrix">Hessian matrix</a></td></li></ul> </tr></table></div></div></td> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame collapsed" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:transparent;text-align:left;text-align:center;"><span style="font-size:110%;">Specialized</span></div><div class="NavContent" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center;border-top:1px solid #aaa;padding-top:0.15em;border-bottom:1px solid #aaa;"><div class="hlist"> <ul><li> <a href="/wiki/Fractional_calculus" title="Fractional calculus">Fractional</a></li> <li> <a href="/wiki/Malliavin_calculus" title="Malliavin calculus">Malliavin</a></li> <li> <a href="/wiki/Stochastic_calculus" title="Stochastic calculus">Stochastic</a></li> <li> <a href="/wiki/Calculus_of_variations" title="Calculus of variations">Variations</a></div></div></td></li></ul> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame collapsed" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:transparent;text-align:left;text-align:center;"><span style="font-size:110%;"><a href="/wiki/Glossary_of_calculus" title="Glossary of calculus">Glossary of calculus</a></span></div><div class="NavContent" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center;border-top:1px solid #aaa;padding-top:0.15em;border-bottom:1px solid #aaa;"><div class="hlist"> <ul><li> <a href="/wiki/Glossary_of_calculus" title="Glossary of calculus">Glossary of calculus</a></li></ul> <p><br /> </p> </div></div></div></td> </tr><tr><td style="text-align:right;font-size:115%;padding-top: 0.6em;"><div class="plainlinks hlist navbar mini"><ul><li class="nv-view"><a href="/wiki/Template:Calculus" title="Template:Calculus"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Calculus" title="Template talk:Calculus"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a class="external text" href="//en.wikipedia.org/w/index.php?title=Template:Calculus&action=edit"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></table> </div>
