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An Introduction to Complex Analysis

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Cover of 'An Introduction to Complex Analysis'

Table of Contents

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    Book Overview
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    Chapter 1 Complex Numbers I
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    Chapter 2 Complex Numbers II
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    Chapter 3 Complex Numbers III
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    Chapter 4 Set Theory in the Complex Plane
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    Chapter 5 Complex Functions
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    Chapter 6 Analytic Functions I
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    Chapter 7 Analytic Functions II
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    Chapter 8 Elementary Functions I
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    Chapter 9 Elementary Functions II
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    Chapter 10 Mappings by Functions I
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    Chapter 11 Mappings by Functions II
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    Chapter 12 Curves, Contours, and Simply Connected Domains
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    Chapter 13 Complex Integration
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    Chapter 14 Independence of Path
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    Chapter 15 Cauchy-Goursat Theorem
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    Chapter 16 Deformation Theorem
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    Chapter 17 Cauchy’s Integral Formula
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    Chapter 18 Cauchy’s Integral Formula for Derivatives
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    Chapter 19 The Fundamental Theorem of Algebra
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    Chapter 20 Maximum Modulus Principle
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    Chapter 21 Sequences and Series of Numbers
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    Chapter 22 Sequences and Series of Functions
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    Chapter 23 Power Series
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    Chapter 24 Taylor’s Series
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    Chapter 25 Laurent’s Series
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    Chapter 26 Zeros of Analytic Functions
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    Chapter 27 Analytic Continuation
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    Chapter 28 Symmetry and Reflection
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    Chapter 29 Singularities and Poles I
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    Chapter 30 Singularities and Poles II
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    Chapter 31 Cauchy’s Residue Theorem
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    Chapter 32 Evaluation of Real Integrals by Contour Integration I
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    Chapter 33 Evaluation of Real Integrals by Contour Integration II
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    Chapter 34 Indented Contour Integrals
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    Chapter 35 Contour Integrals Involving Multi-valued Functions
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    Chapter 36 Summation of Series
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    Chapter 37 Argument Principle and Rouché and Hurwitz Theorems
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    Chapter 38 Behavior of Analytic Mappings
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    Chapter 39 Conformal Mappings
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    Chapter 40 Harmonic Functions
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    Chapter 41 The Schwarz-Christoffel Transformation
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    Chapter 42 Infinite Products
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    Chapter 43 Weierstrass’s Factorization Theorem
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    Chapter 44 Mittag-Leffler Theorem
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    Chapter 45 Periodic Functions
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    Chapter 46 The Riemann Zeta Function
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    Chapter 47 Bieberbach’s Conjecture
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    Chapter 48 The Riemann Surfaces
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    Chapter 49 Julia and Mandelbrot Sets
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    Chapter 50 History of Complex Numbers
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Title
An Introduction to Complex Analysis
Published by
Springer Science & Business Media, July 2011
DOI 10.1007/978-1-4614-0195-7
ISBNs
978-1-4614-0195-7, 978-1-4614-0194-0
Authors

Agarwal, Ravi P., Perera, Kanishka, Pinelas, Sandra

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Mendeley readers

Mendeley readers

The data shown below were compiled from readership statistics for 57 Mendeley readers of this research output. Click here to see the associated Mendeley record.

Geographical breakdown

Country Count As %
Czechia 1 2%
France 1 2%
South Africa 1 2%
Unknown 54 95%

Demographic breakdown

Readers by professional status Count As %
Student > Ph. D. Student 11 19%
Researcher 8 14%
Student > Master 6 11%
Student > Bachelor 5 9%
Student > Postgraduate 3 5%
Other 9 16%
Unknown 15 26%
Readers by discipline Count As %
Mathematics 14 25%
Physics and Astronomy 8 14%
Computer Science 7 12%
Engineering 5 9%
Nursing and Health Professions 2 4%
Other 5 9%
Unknown 16 28%