Complex Analysis and Special Functions: Cauchy Formula, Elliptic Functions and Laplace’s Method, 1st Edition eBook

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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.

This is a digital product.

Complex Analysis and Special Functions: Cauchy Formula, Elliptic Functions and Laplace’s Method 1st Edition is written by Valery Serov; Markus Harju and published by De Gruyter. The Digital and eTextbook ISBNs for Complex Analysis and Special Functions are 9783111632322, 3111632326 and the print ISBNs are 9783111632117, 3111632113. Additional ISBNs for this eTextbook include 9783111632278.