Search results
Results from the WOW.Com Content Network
The Cauchy integral theorem may be used to equate the line integral of an analytic function to the same integral over a more convenient curve. It also implies that over a closed curve enclosing a region where f ( z ) is analytic without singularities , the value of the integral is simply zero, or in case the region includes singularities, the ...
The theorem is a generalization of the second fundamental theorem of calculus to any curve in a plane or space (generally n-dimensional) rather than just the real line. If φ : U ⊆ R n → R is a differentiable function and γ a differentiable curve in U which starts at a point p and ends at a point q , then
In calculus, the Leibniz integral rule for differentiation under the integral sign, named after Gottfried Wilhelm Leibniz, states that for an integral of the form () (,), where < (), < and the integrands are functions dependent on , the derivative of this integral is expressible as (() (,)) = (, ()) (, ()) + () (,) where the partial derivative indicates that inside the integral, only the ...
Fundamental theorem of calculus for line integrals. Add languages. Add links. Article; ... Download as PDF; Printable version; ... Redirect page. Redirect to ...
In complex analysis, the residue theorem, sometimes called Cauchy's residue theorem, is a powerful tool to evaluate line integrals of analytic functions over closed curves; it can often be used to compute real integrals and infinite series as well. It generalizes the Cauchy integral theorem and Cauchy's integral formula.
In mathematics, the Cauchy integral theorem (also known as the Cauchy–Goursat theorem) in complex analysis, named after Augustin-Louis Cauchy (and Édouard Goursat), is an important statement about line integrals for holomorphic functions in the complex plane.
Download as PDF; Printable version; In other projects ... clockwise sense is the negative of the same line integral in the ... of a vector integral theorem may be ...
Then the gradient theorem (also called fundamental theorem of calculus for line integrals) states that = (). This holds as a consequence of the definition of a line integral, the chain rule, and the second fundamental theorem of calculus.