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  • © 2019

Complex Analysis and Applications

  • 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

  • 31k Accesses

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-xxv
  2. Complex Integrations

    • Hemant Kumar Pathak
    Pages 191-305
  3. Bilinear Transformations and Applications

    • Hemant Kumar Pathak
    Pages 487-557
  4. Conformal Mappings and Applications

    • Hemant Kumar Pathak
    Pages 559-623
  5. Spaces of Analytic Functions

    • Hemant Kumar Pathak
    Pages 625-648
  6. Entire and Meromorphic Functions

    • Hemant Kumar Pathak
    Pages 649-713
  7. Analytic Continuation

    • Hemant Kumar Pathak
    Pages 715-752
  8. Harmonic Functions and Integral Functions

    • Hemant Kumar Pathak
    Pages 753-805
  9. Canonical Products and Convergence of Entire Functions

    • Hemant Kumar Pathak
    Pages 807-840
  10. The Range of an Analytic Function

    • Hemant Kumar Pathak
    Pages 841-858
  11. Univalent Functions and Applications

    • Hemant Kumar Pathak
    Pages 859-888
  12. Function Theory of Several Complex Variables

    • Hemant Kumar Pathak
    Pages 889-907
  13. Back Matter

    Pages 909-928

About this book

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.

Keywords

  • 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.

Bibliographic Information

  • Book Title: Complex Analysis and Applications

  • Authors: Hemant Kumar Pathak

  • DOI: https://doi.org/10.1007/978-981-13-9734-9

  • Publisher: Springer Singapore

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • 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

  • Topics: Analysis, Applications of Mathematics, Number Theory

Buy it now

Buying options

eBook USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access