Provides a detailed, self-contained textbook on the theory and applications of complex analysis
Discusses topics with a relevant historical background of the subject to motivate students
Includes complete definitions, proofs, and a wealth of solved examples and end-of-chapter problems
Is a valuable asset for undergraduate and graduate students of mathematics and engineering
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Table of contents (15 chapters)
About this book
To benefit most from the book, students should have some prior knowledge of complex numbers. However, the essential prerequisites are quite minimal, and include basic calculus with some knowledge of partial derivatives, definite integrals, and topics in advanced calculus such as Leibniz’s rule for differentiating under the integral sign and to some extent analysis of infinite series. The book offers a valuable asset for undergraduate and graduate students of mathematics and engineering, as well as students with no background in topological properties.
- Complex number
- Riemann sphere
- Analytic function
- Power series
- Bilinear transformation
- Conformal mapping
- Entire function
- Analytic continuation
- Function theory
- Canonical product
- Univalent function
Authors and Affiliations
School of Studies in Mathematics, Pt. Ravishankar Shukla University, Raipur, India
Hemant Kumar Pathak
About the author
Hemant Kumar Pathak is Professor and Head of the School of Studies in Mathematics at the Pt. Ravishankar Shukla University, Raipur, India. He also is the dean of science, member of the standing committee, director of the Center for Basic Sciences, and director of the Human Resource Development Centre at the same university. He has previously worked at Kalyan Mahavidyalaya, Bhilai Nagar, and the Government Postgraduate College, Dhamtari, India. He earned his Ph.D. from Pt. Ravishankar Shukla University in 1988.
Professor Pathak was awarded the “Distinguished Service Award 2011” by the Vijnana Parishad of India. With over 40 years of teaching and research experience, he has published a book, An Introduction to Nonlinear Analysis and Fixed Point Theory (Springer Nature), and more than 200 research papers in leading international journals of repute on approximation theory, operator theory, integration theory, fixed point theory, number theory, cryptography, summability theory, and fuzzy set theory.
Professor Pathak currently serves on the editorial boards of the American Journal of Computational and Applied Mathematics, Fixed Point Theory and Applications (Springer Nature), and the Journal of Modern Methods in Numerical Mathematics; and as a reviewer for the Mathematical Review of the American Mathematical Society. In addition, he is a life member of the Allahabad Mathematical Society, Bharata Ganita Parishad, the Vijnana Parishad of India, Calcutta Mathematical Society, and National Academy of Mathematics.
Book Title: Complex Analysis and Applications
Authors: Hemant Kumar Pathak
Publisher: Springer Singapore
Copyright Information: Springer Nature Singapore Pte Ltd. 2019
Hardcover ISBN: 978-981-13-9733-2Published: 02 September 2019
eBook ISBN: 978-981-13-9734-9Published: 19 August 2019
Edition Number: 1
Number of Pages: XXV, 928
Number of Illustrations: 261 b/w illustrations