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Complex Analysis and Special Functions: Cauchy Formula, Elliptic Functions and Laplace’s Method (De Gruyter Textbook)

Serov, Valery; Harju, Markus

 
9783111632117: Complex Analysis and Special Functions: Cauchy Formula, Elliptic Functions and Laplace’s Method (De Gruyter Textbook)
ISBN 10: 3111632113 ISBN 13: 9783111632117
Verlag: De Gruyter, 2025

Inhaltsangabe

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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Über die Autorin bzw. den Autor

Dr. Valery Serov is professor emeritus of applied mathematics at University of Oulu, Finland. He is highly experienced scholar who has taught extensively many courses on partial differential equations, Fourier analysis, spectral theory, complex analysis and more. His research interests are mostly devoted to inverse scattering and inverse spectral problems. He has authored two textbooks earlier and his extensive list of publications contains more than 100 papers.

PhD Markus Harju holds a docentship on applied mathematics at University of Oulu, Finland. He is an experienced educator who is currently teaching engineering mathematics at the undergraduate level. His research interest fall under inverse scattering problems but he also works on numerical and applied mathematics met in engineering and medical disciplines.

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Verlag
De Gruyter
Erscheinungsdatum
2025
Sprache
Englisch
ISBN 10 
3111632113
ISBN 13 
9783111632117
Einband
Broschiert
Auflage
1
Anzahl der Seiten
362
Kontakt zum Hersteller
preigu GmbH & Co. KG
mail@preigu.de

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