Complex Analysis

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Can you name the concepts and theorems from complex analysis?

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Mathemtics
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ConceptName of Concept or TheoremNumber of words
Term used to describe a complex function that is differentiable at every point in a region1
If a complex function is analytic at all finite points of the complex plane, that function is said to be _________.1
If a function is analytic in a region, then in that region it satisfies these equations2
If f(z)=u+iv is analytic in region, then u and v satisfy what famous differential equation?2
This theorem says that the contour integral around a closed curve of an analytic function is zero 2
A point at which a function is not analytic1
In any neighborhood of an essential singularity, however small, an analytic function assumes every value in the complex plane with at most one exception2
An analytic function f is said to have a ______ of order n at a point z=a if all terms in the Laurent series for which m is less than -n vanish & the -n term does not equal zero1
ConceptName of Concept or TheoremNumber of words
A function whose only singularities, other than the point at infinity, are poles is called_________.1
A unique series expansion of a complex function in positive and negative powers2
The coefficent of the 1/(z-a) term in the Laurent series of a function f(z) is called the _______.1
This powerful theorem allows one to evaluate contour integrals of functions which are analytic except at a finite number of poles2
This theorem says that any bounded entire function must be constant 2
A point in the complex plane whose complex argument can be mapped from a single point in the domain to multiple points in the range2
A transformation in the complex plane that preserves local angles is said to be1

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