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A First Course in Complex Analysis [electronic resource] / by Allan R. Willms.

By: Willms, Allan R [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Synthesis Lectures on Mathematics & Statistics: Publisher: Cham : Springer International Publishing : Imprint: Springer, 2022Edition: 1st ed. 2022.Description: IV, 237 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783031791765.Subject(s): Mathematics | Statistics  | Engineering mathematics | Mathematics | Statistics | Engineering MathematicsAdditional physical formats: Printed edition:: No title; Printed edition:: No title; Printed edition:: No titleDDC classification: 510 Online resources: Click here to access online
Contents:
Preface -- Acknowledgments -- Basics of Complex Numbers -- Functions of a Complex Variable -- Differentiation -- Contour Integration -- Cauchy Theory -- Series -- Residues -- Conformal Mapping -- Author's Biography -- Index.
In: Springer Nature eBookSummary: This book introduces complex analysis and is appropriate for a first course in the subject at typically the third-year University level. It introduces the exponential function very early but does so rigorously. It covers the usual topics of functions, differentiation, analyticity, contour integration, the theorems of Cauchy and their many consequences, Taylor and Laurent series, residue theory, the computation of certain improper real integrals, and a brief introduction to conformal mapping. Throughout the text an emphasis is placed on geometric properties of complex numbers and visualization of complex mappings.
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Preface -- Acknowledgments -- Basics of Complex Numbers -- Functions of a Complex Variable -- Differentiation -- Contour Integration -- Cauchy Theory -- Series -- Residues -- Conformal Mapping -- Author's Biography -- Index.

This book introduces complex analysis and is appropriate for a first course in the subject at typically the third-year University level. It introduces the exponential function very early but does so rigorously. It covers the usual topics of functions, differentiation, analyticity, contour integration, the theorems of Cauchy and their many consequences, Taylor and Laurent series, residue theory, the computation of certain improper real integrals, and a brief introduction to conformal mapping. Throughout the text an emphasis is placed on geometric properties of complex numbers and visualization of complex mappings.

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