Comlex Analysis , Msc1 Sem
Cauchys Theorem, Cauchy Integral Formula , Moreras Theorem , Taylor Theorem, Laurent Theorem
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Complex analysis is the study of complex numbers together with their derivatives, manipulation, and other properties. Complex analysis is an extremely powerful tool with an unexpectedly large number of practical applications to the solution of physical problems. Contour integration, for example, provides a method of computing difficult integrals by investigating the singularities of the function in regions of the complex plane near and between the limits of integration.
The key result in complex analysis is the Cauchy integral theorem, which is the reason that single-variable complex analysis has so many nice results. A single example of the unexpected power of complex analysis is Picard's great theorem, which states that an analytic function assumes every complex number, with possibly one exception, infinitely often in any neighborhood of an essential singularity!
A fundamental result of complex analysis is the Cauchy-Riemann equations, which give the conditions a function must satisfy in order for a complex generalization of the derivative, the so-called complex derivative, to exist. When the complex derivative is defined "everywhere," the function is said to be analytic.
Analytic Continuation, Argument Principle, Branch Cut, Branch Point, Cauchy Integral Formula, Cauchy Integral Theorem, Cauchy Principal Value, Cauchy-Riemann Equations, Complex Number, Complex Residue, Conformal Mapping, Contour Integration, de Moivre's Identity, Euler Formula, Inside-Outside Theorem, Jordan's Lemma, Laurent Series, Liouville's Conformality Theorem, Monogenic Function, Morera's Theorem, Permanence of Algebraic Form, Picard's Great Theorem, Pole, Polygenic Function
Негізгі бет Cauchy's theorem, Cauchy's Integral Theorem
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