3: COMPLEX VARIABLES

The following sections are included:

• Complex Numbers

• Functions of a Complex Variable

• Integration in the Complex Plane

• Cauchy's Theorem

• Cauchy's Integral Formula

• Taylor's Theorem

• Laurent's Expansion

• Poles and Essential Singularities

• Cauchy's Residue Theorem

• Applications of the Residue Theorem to Evaluate Real Integrals

• Contour Integration Applied to the Summation of Series

• Conformal Representation

• Laplace's Equation in Two Dimensions

• Applications to Hydrodynamics