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Book synopsis

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.

Book details

Book category Books in English Mathematics & science Mathematics Calculus & mathematical analysis

• Full title: Complex Analysis and Special Functions
• Subtitle: Cauchy Formula, Elliptic Functions and Laplace's Method
• Author: Valery Serov, Markus Harju
• Language: English
• Binding: Paperback
• Number of pages: 350
• EAN: 9783111632117
• ID: 46875035
• Publisher: De Gruyter
• Weight: 611 g
• Dimensions: 240 × 170 mm
• Date of publishing: 21. April 2025

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