Complex Analysis and Special Functions: Cauchy Formula, Elliptic Functions and Laplace’s Method

The  first two parts of this book focus on developing standard analysis  concepts in the extended complex plane. We cover differentiation and  integration of functions of one complex variable. Famous Cauchy formulas  are established and applied in the frame of residue theory. Taylor  series is used to investigate analytic functions, and they are connected  to harmonic functions. Laurent series theory is developed. 

The  third part of the book finds applications of the earlier chapter in  conformal mappings and the Laplace transform. Special functions solving  ordinary differential equations are studied extensively, along with  their asymptotic behavior. A highlight of the book is the elliptic  function of Weierstrass and Jacobi. Finally, we present Laplace’s  method, which is applied to find large arguments asymptotic of some  special functions. 

The book is filled with  examples, exercises, and problems of varying degrees of difficulty. This  makes it useful to all students in mathematics, physics, and related  fields.