Serov V Complex Analysis and Special Functions 2025
General:
Name: Serov V Complex Analysis and Special Functions 2025
Format: pdf
Size: 2.97 MB
Book:
Title: Complex Analysis and Special Functions: Cauchy Formula, Elliptic Functions and Laplace’s Method
Author: Valery Serov, Markus Harju
Language: angielski
Year: 2025
Subjects: Science & Technology, Mathematics, Theories of Science, Geometry, Mathematical Analysis, Geometry – General & Miscellaneous, Mathematical Analysis – Complex Analysis, Mathematical Analysis – Functional Analysis, Mathematical Analysis – General & Miscellaneous, Mathematics – Applied, Mathematics – Sets, General Topology, & Categories, System Theory
Publisher: De Gruyter
ISBN: 9783111632322
Total pages: 363
Description:
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.
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