Complex Analysis and Applications

ISBN-13: 9789811397332 / Angielski / Twarda / 2019 / 928 str.

Hemant Kumar Pathak

Spis treści

1. Complex Numbers and Metric Topology of C.- 2. Analytic Functions,Power Series and Elementary Complex Functions.- 3. Complex Integrations.- 4. Singularities,Meromorphic Functions and Principle of Argument.- 5. Calculus of Residues.- 6. Bilinear Transformations.- 7. Conformal Mappings.- 8. Spaces of Analytic Functions.- 9. Entire Functions.- 10. Analytic Continuation.- 11. Harmonic Functions, Uniform Convergence and Integral Functions.- 12. Canonical Products and Convergence of Entire Functions.- 13. The Range of an Analytic Function.- 14. Univalent Functions.

O autorze

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.

Blurb

This book offers an essential textbook on complex analysis. After introducing the theory of complex analysis, it places special emphasis on the importance of Poincare theorem and Hartog’s theorem in the function theory of several complex variables. Further, it lays the groundwork for future study in analysis, linear algebra, numerical analysis, geometry, number theory, physics (including hydrodynamics and thermodynamics), and electrical engineering. 

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.