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  • © 2011

An Introduction to Complex Analysis

  • Provides a rigorous introduction to complex analysis

  • Arranges the material effectively in 50 class-tested lectures

  • Uses ample illustrations and examples to explain the subject

  • Provides problems for practice

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Table of contents (50 chapters)

  1. Front Matter

    Pages i-xiv
  2. Complex Numbers I

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 1-5
  3. Complex Numbers II

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 6-10
  4. Complex Numbers III

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 11-19
  5. Set Theory in the Complex Plane

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 20-27
  6. Complex Functions

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 28-36
  7. Analytic Functions I

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 37-41
  8. Analytic Functions II

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 42-51
  9. Elementary Functions I

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 52-56
  10. Elementary Functions II

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 57-63
  11. Mappings by Functions I

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 64-68
  12. Mappings by Functions II

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 69-76
  13. Curves, Contours, and Simply Connected Domains

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 77-82
  14. Complex Integration

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 83-90
  15. Independence of Path

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 91-95
  16. Cauchy-Goursat Theorem

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 96-101
  17. Deformation Theorem

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 102-110
  18. Cauchy’s Integral Formula

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 111-115
  19. Cauchy’s Integral Formula for Derivatives

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 116-124
  20. The Fundamental Theorem of Algebra

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 125-131

About this book

This textbook introduces the subject of complex analysis to advanced undergraduate and graduate students in a clear and concise manner. Key features of this textbook: effectively organizes the subject into easily manageable sections in the form of 50 class-tested lectures, uses detailed examples to drive the presentation, includes numerous exercise sets that encourage pursuing extensions of the material, each with an “Answers or Hints” section, covers an array of advanced topics which allow for flexibility in developing the subject beyond the basics, provides a concise history of complex numbers. An Introduction to Complex Analysis will be valuable to students in mathematics, engineering and other applied sciences. Prerequisites include a course in calculus.

Reviews

From the reviews:

“This work, directed toward majors in the applied sciences, is presented as a series of 50 lectures on standard topics in introductory complex analysis. Agarwal and Perera (both, Florida Institute of Technology) and Pinelas (Azores Univ., Portugal) have organized each lecture/chapter around certain theorems and their proofs and accompany each with a problem set and solutions. … Summing Up: Recommended. Upper-division undergraduates and graduate students.” (D. Robbins, Choice, Vol. 49 (5), January, 2012)

“This volume provides a compact and thorough introduction to complex analysis. The text takes account of varying needs and backgrounds and provides a self-study text for students in mathematics, science and engineering. … This concise text not only provides efficient proofs but also shows students how to derive them. The excellent exercises are accompanied by selected solutions. … The exposition is clear, concise, and lively. The book is mainly addressed to undergraduate and graduate students interested in complex analysis.” (Teodora-Liliana Rădulescu, Zentralblatt MATH, Vol. 1230, 2012)

“It consists of 50 ‘class-tested lectures’ in which the subject matter has been organized in the form of theorems, proofs and examples. Most of the lectures are … followed by graded exercises that go from the routine to the richly informative. Solutions and hints are provided for nearly all of these, which means that the book is highly suited for self-tuition purposes. … it is also suited to the needs of non-specialists, such as those concerned with the applied sciences.” (P. N. Ruane, The Mathematical Association of America, October, 2011)

Authors and Affiliations

  • Department of Mathematics, Florida Institute of Technology, Melbourne, USA

    Ravi P. Agarwal

  • , Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, USA

    Kanishka Perera

  • , Department of Mathematics, Azores University, Ponta Delgada, Portugal

    Sandra Pinelas

Bibliographic Information

  • Book Title: An Introduction to Complex Analysis

  • Authors: Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas

  • DOI: https://doi.org/10.1007/978-1-4614-0195-7

  • Publisher: Springer New York, NY

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

  • Copyright Information: Springer Science+Business Media, LLC 2011

  • Hardcover ISBN: 978-1-4614-0194-0Published: 01 July 2011

  • Softcover ISBN: 978-1-4899-9716-6Published: 01 October 2014

  • eBook ISBN: 978-1-4614-0195-7Published: 01 July 2011

  • Edition Number: 1

  • Number of Pages: XIV, 331

  • Topics: Functions of a Complex Variable, Analysis

Buy it now

Buying options

eBook USD 49.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 64.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 99.99
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