Overview

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.

Full Product Details

Author:   Ravi P. Agarwal ,  Kanishka Perera ,  Sandra Pinelas
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   2011 ed.
Dimensions:   Width: 15.50cm , Height: 2.00cm , Length: 23.50cm
Weight:   1.470kg
ISBN:  

9781461401940

ISBN 10:   1461401941
Pages:   331
Publication Date:   01 July 2011
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Awaiting stock  
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Table of Contents

Preface.-Complex Numbers.-Complex Numbers II .- Complex Numbers III.-Set Theory in the Complex Plane.-Complex Functions.-Analytic Functions I.-Analytic Functions II.-Elementary Functions I.- Elementary Functions II.- Mappings by Functions.- Mappings by Functions II.- Curves, Contours, and Simply Connected Domains.- Complex Integration.- Independence of Path.- Cauchy–Goursat Theorem.- Deformation Theorem.- Cauchy’s Integral Formula.- Cauchy’s Integral Formula for Derivatives.- Fundamental Theorem of Algebra.- Maximum Modulus Principle.- Sequences and Series of Numbers.- Sequences and Series of Functions.- Power Series.- Taylor’s Series.- Laurent’s Series.- Zeros of Analytic Functions.- Analytic Continuation.- Symmetry and Reflection.- Singularities and Poles I.- Singularities and Poles II.- Cauchy’s Residue Theorem.- Evaluation of Real Integrals by Contour Integration I.- Evaluation of Real Integrals by Contour Integration II.- Indented Contour Integrals.- Contour Integrals Involving Multi–valued Functions .- Summation of Series. Argument Principle and Rouch´e and Hurwitz Theorems.- Behavior of Analytic Mappings.- Conformal Mappings.- Harmonic Functions.- The Schwarz–Christoffel Transformation.- Infinite Products.- Weierstrass’s Factorization Theorem.- Mittag–Leffler’s Theorem.- Periodic Functions.- The Riemann Zeta Function.- Bieberbach’s Conjecture.- The Riemann Surface.- Julia and Mandelbrot Sets.- History of Complex Numbers.- References for Further Reading.- Index.

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)"

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 Radulescu, Zentralblatt MATH, Vol. 1230, 2012)

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)

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)

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