Complex Analysis and Special Functions

Cauchy Formula, Elliptic Functions and Laplace’s Method
1. Auflage 2025
ISBN: 978-3-11-163211-7
Verlag: De Gruyter

Buch, Englisch, 354 Seiten, Format (B × H): 170 mm x 240 mm, Gewicht: 611 g

Reihe: De Gruyter Textbook

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.

Zielgruppe

Graduate and advanced undergraduate math students interested in m

Autoren/Hrsg.

Serov, Valery

Harju, Markus

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis
• Mathematik | Informatik Mathematik Mathematik Interdisziplinär Systemtheorie
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Kybernetik, Systemtheorie, Komplexe Systeme
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Geometrie

Über Autor(innen)

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.