Course in Complex Analysis (eBook)

Saeed Zakeri (Autor)

eBook Download: PDF

2021
448 Seiten
Princeton University Press (Verlag)
978-0-691-21850-2 (ISBN)

Infos

A comprehensive graduate-level textbook that takes a fresh approach to complex analysisA Course in Complex Analysis explores a central branch of mathematical analysis, with broad applications in mathematics and other fields such as physics and engineering. Ideally designed for a year-long graduate course on complex analysis and based on nearly twenty years of classroom lectures, this modern and comprehensive textbook is equally suited for independent study or as a reference for more experienced scholars.Saeed Zakeri guides the reader through a journey that highlights the topological and geometric themes of complex analysis and provides a solid foundation for more advanced studies, particularly in Riemann surfaces, conformal geometry, and dynamics. He presents all the main topics of classical theory in great depth and blends them seamlessly with many elegant developments that are not commonly found in textbooks at this level. They include the dynamics of Mobius transformations, Schlicht functions and distortion theorems, boundary behavior of conformal and harmonic maps, analytic arcs and the general reflection principle, Hausdorff dimension and holomorphic removability, a multifaceted approach to the theorems of Picard and Montel, Zalcman's rescaling theorem, conformal metrics and Ahlfors's generalization of the Schwarz lemma, holomorphic branched coverings, geometry of the modular group, and the uniformization theorem for spherical domains.Written with exceptional clarity and insightful style, A Course in Complex Analysis is accessible to beginning graduate students and advanced undergraduates with some background knowledge of analysis and topology. Zakeri includes more than 350 problems, with problem sets at the end of each chapter, along with numerous carefully selected examples. This well-organized and richly illustrated book is peppered throughout with marginal notes of historical and expository value.Presenting a wealth of material in a single volume, A Course in Complex Analysis will be a valuable resource for students and working mathematicians.

Produkt-Details

• Erscheint lt. Verlag: 2.11.2021
• Zusatzinfo: 77 color + 63 b/w illus. 2 tables
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Schlagworte: affine transformation • algebraic equation • algebraic variety • Allegory (category theory) • Analogy • Arc (geometry) • asymptotic analysis • Bernhard Riemann • Branched covering • Cardinality • Cauchy's Integral Formula • Cauchy's theorem (group theory) • Chemical composition • coefficient • Complex Analysis • Complex conjugate • complex multiplication • complex number • conformal map • Conjugate transpose • Consciousness • Consideration • Continuous function (set theory) • corollary • Covering space • Critical Value • Curve • Decision Theory • Differential operator • Disjoint union • Disk (mathematics) • Effective action • Elementary proof • elliptic function • Elliptic Integral • engraving • Explicit formulae (L-function) • Exponential map (Riemannian geometry) • Fixed-point theorem • fundamental group • Group 3 element • Group homomorphism • Hausdorff dimension • holomorphic function • Homotopy • Ideology • Imaginary unit • International finance • Jordan Curve Theorem • Lecture • Line segment • Management • Meromorphic Function • Mode of Production • Modular group • Montel's theorem • multivariate analysis • Norm (mathematics) • Notation • Open mapping theorem (complex analysis) • overproduction • Pareto Efficiency • Payment • Piecewise • Planning • polynomial • power series • Prevalence • Production Function • Proper map • Provision (contracting) • Quantity • radius of convergence • Radon–Nikodym theorem • reflection group • Requirement • Requirements contract • Riemann surface • Scale (map) • Schwarz lemma • science, technology and society • Scientist • Service Level • Several Complex Variables • sine • social conflict • Society • Special Functions • Stone–Weierstrass theorem • submanifold • Subset • Suggestion • Tangent Space • tessellation • Theorem • Topology • Total Cost • uniformization theorem • Variable (mathematics) • Work order
• ISBN-10: 0-691-21850-1 / 0691218501
• ISBN-13: 978-0-691-21850-2 / 9780691218502