Principles of Mathematical Analysis

Author: Walter Rudin

Publisher: McGraw-Hill Publishing Company

ISBN: 9780070856134

Category: Mathematics

Page: 342

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The third edition of this well known text continues to provide a solid foundation in mathematical analysis for undergraduate and first-year graduate students. The text begins with a discussion of the real number system as a complete ordered field. (Dedekind's construction is now treated in an appendix to Chapter I.) The topological background needed for the development of convergence, continuity, differentiation and integration is provided in Chapter 2. There is a new section on the gamma function, and many new and interesting exercises are included. This text is part of the Walter Rudin Student Series in Advanced Mathematics.

Techniques of Functional Analysis for Differential and Integral Equations

Author: Paul Sacks

Publisher: Academic Press

ISBN: 0128114576

Category: Mathematics

Page: 320

View: 560

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Techniques of Functional Analysis for Differential and Integral Equations describes a variety of powerful and modern tools from mathematical analysis, for graduate study and further research in ordinary differential equations, integral equations, and especially partial differential equations. Knowledge of these techniques is particularly useful as preparation for graduate courses and as PhD research preparation in differential equations and numerical analysis, and more specialized topics such as fluid dynamics and control theory. Striking a balance between mathematical depth and accessibility, proofs are limited, and their sources precisely identifie d, proofs involving more technical aspects of measure and integration theory are avoided, but clear statements and precise alternative references are given . The work provides many examples and exercises drawn from the literature. Provides an introduction to the mathematical techniques widely used in applied mathematics and needed for advanced research Establishes the advanced background needed for sophisticated literature review and research in both differential and integral equations Suitable for use as a textbook for a two semester graduate level course for M.S. and Ph.D. students in Mathematics and Applied Mathematics

Mathematical Tools for the Study of the Incompressible Navier-Stokes Equations and Related Models

Author: Franck Boyer,Pierre Fabrie

Publisher: Springer Science & Business Media

ISBN: 1461459753

Category: Mathematics

Page: 526

View: 4684

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The objective of this self-contained book is two-fold. First, the reader is introduced to the modelling and mathematical analysis used in fluid mechanics, especially concerning the Navier-Stokes equations which is the basic model for the flow of incompressible viscous fluids. Authors introduce mathematical tools so that the reader is able to use them for studying many other kinds of partial differential equations, in particular nonlinear evolution problems. The background needed are basic results in calculus, integration, and functional analysis. Some sections certainly contain more advanced topics than others. Nevertheless, the authors’ aim is that graduate or PhD students, as well as researchers who are not specialized in nonlinear analysis or in mathematical fluid mechanics, can find a detailed introduction to this subject. .

The Ricci Flow

Techniques and Applications. Geometric-analytic aspects

Author: Bennett Chow,Sun-Chin Chu,David Glickenstein,Christine Guenther,James Isenberg,Tom Ivey,Dan Knopf,Peng Lu,Feng Luo,Lei Ni

Publisher: American Mathematical Soc.

ISBN: 0821846612

Category:

Page: N.A

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The Ricci flow uses methods from analysis to study the geometry and topology of manifolds. With the third part of their volume on techniques and applications of the theory, the authors give a presentation of Hamilton's Ricci flow for graduate students and mathematicians interested in working in the subject, with an emphasis on the geometric and analytic aspects. The topics include Perelman's entropy functional, point picking methods, aspects of Perelman's theory of $\kappa$-solutions including the $\kappa$-gap theorem, compactness theorem and derivative estimates, Perelman's pseudolocality theorem, and aspects of the heat equation with respect to static and evolving metrics related to Ricci flow. In the appendices, we review metric and Riemannian geometry including the space of points at infinity and Sharafutdinov retraction for complete noncompact manifolds with nonnegative sectional curvature. As in the previous volumes, the authors have endeavored, as much as possible, to make the chapters independent of each other. The book makes advanced material accessible to graduate students and nonexperts. It includes a rigorous introduction to some of Perelman's work and explains some technical aspects of Ricci flow useful for singularity analysis. The authors give the appropriate references so that the reader may further pursue the statements and proofs of the various results.

A Guide to Mathematical Methods for Physicists

With Problems and Solutions

Author: Michela Petrini,Gianfranco Pradisi,Alberto Zaffaroni

Publisher: World Scientific Publishing Company

ISBN: 1786343460

Category: Science

Page: 340

View: 1027

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Mathematics plays a fundamental role in the formulation of physical theories. This textbook provides a self-contained and rigorous presentation of the main mathematical tools needed in many fields of Physics, both classical and quantum. It covers topics treated in mathematics courses for final-year undergraduate and graduate physics programmes, including complex function: distributions, Fourier analysis, linear operators, Hilbert spaces and eigenvalue problems. The different topics are organised into two main parts — complex analysis and vector spaces — in order to stress how seemingly different mathematical tools, for instance the Fourier transform, eigenvalue problems or special functions, are all deeply interconnected. Also contained within each chapter are fully worked examples, problems and detailed solutions. A companion volume covering more advanced topics that enlarge and deepen those treated here is also available. Contents:Complex Analysis:Holomorphic FunctionsIntegrationTaylor and Laurent SeriesResiduesFunctional Spaces:Vector SpacesSpaces of FunctionsDistributionsFourier AnalysisLinear Operators in Hilbert Spaces I: The Finite-Dimensional CaseLinear Operators in Hilbert Spaces II: The Infinite-Dimensional CaseAppendices:Complex Numbers, Series and IntegralsSolutions of the Exercises Readership: Students of undergraduate mathematics and postgraduate students of physics or engineering.

Principles of Differential Equations

Author: Nelson G. Markley

Publisher: John Wiley & Sons

ISBN: 1118031539

Category: Mathematics

Page: 352

View: 1637

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An accessible, practical introduction to the principles ofdifferential equations The field of differential equations is a keystone of scientificknowledge today, with broad applications in mathematics,engineering, physics, and other scientific fields. Encompassingboth basic concepts and advanced results, Principles ofDifferential Equations is the definitive, hands-on introductionprofessionals and students need in order to gain a strong knowledgebase applicable to the many different subfields of differentialequations and dynamical systems. Nelson Markley includes essential background from analysis andlinear algebra, in a unified approach to ordinary differentialequations that underscores how key theoretical ingredientsinterconnect. Opening with basic existence and uniqueness results,Principles of Differential Equations systematically illuminates thetheory, progressing through linear systems to stable manifolds andbifurcation theory. Other vital topics covered include: Basic dynamical systems concepts Constant coefficients Stability The Poincaré return map Smooth vector fields As a comprehensive resource with complete proofs and more than200 exercises, Principles of Differential Equations is the idealself-study reference for professionals, and an effectiveintroduction and tutorial for students.

Berkeley Problems in Mathematics

Author: Paulo Ney de Souza,Jorge-Nuno Silva

Publisher: Springer Science & Business Media

ISBN: 9780387204291

Category: Mathematics

Page: 593

View: 8274

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This book collects approximately nine hundred problems that have appeared on the preliminary exams in Berkeley over the last twenty years. It is an invaluable source of problems and solutions. Readers who work through this book will develop problem solving skills in such areas as real analysis, multivariable calculus, differential equations, metric spaces, complex analysis, algebra, and linear algebra.