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書名：Quantum Electrodynamics 2/e Course of Theoretical Physics Vol:4 作者：BERESTETSKII 出版社：HB ISBN：9780750633710

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書名：Theory of Elasticity 3/e Course of Theoretical Physics Vol:7 作者：LANDAU 出版社：HB ISBN：9780750626330

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Stochastic Finance provides an introduction to mathematical finance that is unparalleled in its accessibility. Through classroom testing, the authors have identified common pain points for students, and their approach takes great care to help the reader to overcome these difficulties and to foster understanding where comparable texts often do not. Written for advanced undergraduate students, and making use of numerous detailed examples to illustrate key concepts, this text provides all the mathematical foundations necessary to model transactions in the world of finance. A first course in probability is the only necessary background. The book begins with the discrete binomial model and the finite market model, followed by the continuous Black–Scholes model. It studies the pricing of European options by combining financial concepts such as arbitrage and self-financing trading strategies with probabilistic tools such as sigma algebras, martingales and stochastic integration. All these concepts are introduced in a relaxed and user-friendly fashion.

PRINCETON LECTURES IN ANALYSIS II COMPLEX ANALYSIS (1版)

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【原文書】 書名：Complex Analysis (Princeton Lectures in Analysis, No. 2) 作者：STEIN 出版社：PRINCETON 出版日期：2003/04/07 ISBN：9780691113852

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Fourier Analysis—An Introduction 系列名：Princeton Lectures in Analysis, Volume 1 ISBN13：9780691113845 替代書名：Fourier Analysis 出版社：Princeton Univ Pr 作者：Elias M. Stein; Rami Shakarchi 裝訂：精裝 規格：24.1cm*16.5cm*1.9cm (高/寬/厚) 出版日：2003/03/17 內容簡介 This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences--that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions. The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as the isoperimetric inequality and equidistribution. The second part deals with the Fourier transform and its applications to classical partial differential equations and the Radon transform; a clear introduction to the subject serves to avoid technical difficulties. The book closes with Fourier theory for finite abelian groups, which is applied to prime numbers in arithmetic progression. In organizing their exposition, the authors have carefully balanced an emphasis on key conceptual insights against the need to provide the technical underpinnings of rigorous analysis. Students of mathematics, physics, engineering and other sciences will find the theory and applications covered in this volume to be of real interest. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Fourier Analysis is the first, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.

Princeton Lectures in Analysis III Real Analysis Measure Theory,Integration ,& Hilbert Spaces (1版)

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書名：Real Analysis: Measure Theory, Integration, And Hilbert Spaces 作者：STEIN 出版社：PRINCETON 出版日期：2005/03/14 ISBN：9780691113869

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【原文書】 書名：ABSTRACT ALGEBRA 3/E 作者：DUMMIT 出版社：JOHN WILEY 出版日期：2003/07/01 ISBN：9780471433347

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<姆斯>Functional Analysis: Introduction to Further Topics in Analysis 2011 (PRINCETON) 978-0-691-11387-6 STEIN 9780691113876

Differential Geometry of Curves and Surfaces: Revised and Updated (2版)

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【原文書】 書名：Differential Geometry of Curves and Surfaces: Revised and Updated 2/E 作者：do Carmo 出版社：Dover 出版日期：2016/12/14 ISBN：9780486806990

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This book studies the fundamental concept of hydrodynamics as part of theoretical physics and demonstrates the connection of macroscopic approach with the description of properties of fluid motion and microscopic kinetic theory. It also presents recent investigations in instabilities and turbulence theory. Sample Chapter(s) Introduction Chapter 2: Gravity Waves and Solitons Contents: Introduction Bases of Hydrodynamics: Equations of Motion Gravity Waves and Solitons Thermodynamics of Fluids Shock Waves Stability and Instabilities in Fluidodynamics: Instabilities in Fluidodynamics and Its Consequences Classical Turbulence in Fluid Dynamics Coherent Hydrodynamic Structures: Vortex Dynamics on the Plane Poisson Systems in Hydrodynamics Introduction of Metric Structure in Hydrodynamic Systems Appendices: Chaplygin's Gas Richtmyer–Meshkov Instability Instabilities and Turbulence in Astrophysics References Index Readership: Researches and post-graduate students for extended study of hydrodynamics.

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