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Introduction to complex analysis

In this text, the reader will learn that all the basic functions that arise in calculus--such as powers and fractional powers, exponentials and logs, trigonometric functions and their inverses, as well as many new functions that the reader will meet--are naturally defined for complex arguments. Furt...

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Detalles Bibliográficos
Autor principal: Taylor, Michael E
Lenguaje:eng
Publicado: American Mathematical Society 2019
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Acceso en línea:http://cds.cern.ch/record/2707525
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author Taylor, Michael E
author_facet Taylor, Michael E
author_sort Taylor, Michael E
collection CERN
description In this text, the reader will learn that all the basic functions that arise in calculus--such as powers and fractional powers, exponentials and logs, trigonometric functions and their inverses, as well as many new functions that the reader will meet--are naturally defined for complex arguments. Furthermore, this expanded setting leads to a much richer understanding of such functions than one could glean by merely considering them in the real domain. For example, understanding the exponential function in the complex domain via its differential equation provides a clean path to Euler's formula and hence to a self-contained treatment of the trigonometric functions. Complex analysis, developed in partnership with Fourier analysis, differential equations, and geometrical techniques, leads to the development of a cornucopia of functions of use in number theory, wave motion, conformal mapping, and other mathematical phenomena, which the reader can learn about from material presented here. This book could serve for either a one-semester course or a two-semester course in complex analysis for beginning graduate students or for well-prepared undergraduates whose background includes multivariable calculus, linear algebra, and advanced calculus.
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spelling cern-27075252021-04-21T18:11:06Zhttp://cds.cern.ch/record/2707525engTaylor, Michael EIntroduction to complex analysisMathematical Physics and MathematicsIn this text, the reader will learn that all the basic functions that arise in calculus--such as powers and fractional powers, exponentials and logs, trigonometric functions and their inverses, as well as many new functions that the reader will meet--are naturally defined for complex arguments. Furthermore, this expanded setting leads to a much richer understanding of such functions than one could glean by merely considering them in the real domain. For example, understanding the exponential function in the complex domain via its differential equation provides a clean path to Euler's formula and hence to a self-contained treatment of the trigonometric functions. Complex analysis, developed in partnership with Fourier analysis, differential equations, and geometrical techniques, leads to the development of a cornucopia of functions of use in number theory, wave motion, conformal mapping, and other mathematical phenomena, which the reader can learn about from material presented here. This book could serve for either a one-semester course or a two-semester course in complex analysis for beginning graduate students or for well-prepared undergraduates whose background includes multivariable calculus, linear algebra, and advanced calculus.American Mathematical Societyoai:cds.cern.ch:27075252019
spellingShingle Mathematical Physics and Mathematics
Taylor, Michael E
Introduction to complex analysis
title Introduction to complex analysis
title_full Introduction to complex analysis
title_fullStr Introduction to complex analysis
title_full_unstemmed Introduction to complex analysis
title_short Introduction to complex analysis
title_sort introduction to complex analysis
topic Mathematical Physics and Mathematics
url http://cds.cern.ch/record/2707525
work_keys_str_mv AT taylormichaele introductiontocomplexanalysis