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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. Maximum Modulus Principle

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 132-137
  2. Sequences and Series of Numbers

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 138-144
  3. Sequences and Series of Functions

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 145-150
  4. Power Series

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 151-158
  5. Taylor’s Series

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 159-168
  6. Laurent’s Series

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 169-176
  7. Zeros of Analytic Functions

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 177-182
  8. Analytic Continuation

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 183-189
  9. Symmetry and Reflection

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 190-194
  10. Singularities and Poles I

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 195-199
  11. Singularities and Poles II

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 200-206
  12. Cauchy’s Residue Theorem

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 207-214
  13. Evaluation of Real Integrals by Contour Integration I

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 215-219
  14. Evaluation of Real Integrals by Contour Integration II

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 220-228
  15. Indented Contour Integrals

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 229-234
  16. Contour Integrals Involving Multi-valued Functions

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 235-241
  17. Summation of Series

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 242-246
  18. Argument Principle and Rouché and Hurwitz Theorems

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 247-252
  19. Behavior of Analytic Mappings

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 253-257
  20. Conformal Mappings

    • Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
    Pages 258-266

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