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|a 9781461401957
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|a Agarwal, Ravi P.
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| 245 |
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|a An Introduction to Complex Analysis
|h Elektronische Ressource
|c by Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
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| 250 |
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|a 1st ed. 2011
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| 260 |
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|a New York, NY
|b Springer US
|c 2011, 2011
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| 300 |
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|a XIV, 331 p
|b online resource
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| 505 |
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|a 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
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| 653 |
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|a Functions of complex variables
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| 653 |
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|a Mathematical analysis
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| 653 |
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|a Analysis
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| 653 |
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|a Functions of a Complex Variable
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| 700 |
1 |
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|a Perera, Kanishka
|e [author]
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| 700 |
1 |
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|a Pinelas, Sandra
|e [author]
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| 041 |
0 |
7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b Springer
|a Springer eBooks 2005-
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| 028 |
5 |
0 |
|a 10.1007/978-1-4614-0195-7
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| 856 |
4 |
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|u https://doi.org/10.1007/978-1-4614-0195-7?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
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|a 515.9
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| 520 |
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|a 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
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