Term used to describe a complex function that is differentiable at every point in a region

1

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 equations

2

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 analytic

1

In any neighborhood of an essential singularity, however small, an analytic function assumes every value in the complex plane with at most one exception

2

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 zero

1

Concept

Name of Concept or Theorem

Number 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 powers

2

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 poles

2

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 range

2

A transformation in the complex plane that preserves local angles is said to be