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Integral And Functional Analysis

Author : Jie Xiao
ISBN : 1600217842
Genre : Mathematics
File Size : 82.79 MB
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This book is based on two closely-related courses. The first of these courses is Integration and Metric Spaces, and the second being Functional Analysis. Though the contents of Functional Analysis have been used for both an undergraduate course and an introductory graduate course, this text is designed primarily for undergraduate students. The prerequisites of this book are deliberately modest, and it is assumed that the students have some familiarity with Introductory Calculus and Linear Algebra plus the basic (direct, indirect) proof methods.
Category: Mathematics

Functional Analysis

Author : Peter D. Lax
ISBN : 9781118626740
Genre : Mathematics
File Size : 54.86 MB
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Includes sections on the spectral resolution and spectralrepresentation of self adjoint operators, invariant subspaces,strongly continuous one-parameter semigroups, the index ofoperators, the trace formula of Lidskii, the Fredholm determinant,and more. * Assumes prior knowledge of Naive set theory, linear algebra,point set topology, basic complex variable, and realvariables. * Includes an appendix on the Riesz representation theorem.
Category: Mathematics

Applied Functional Analysis

Author : Jean-Pierre Aubin
ISBN : 9781118030974
Genre : Mathematics
File Size : 80.74 MB
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A novel, practical introduction to functional analysis In the twenty years since the first edition of Applied FunctionalAnalysis was published, there has been an explosion in the numberof books on functional analysis. Yet none of these offers theunique perspective of this new edition. Jean-Pierre Aubin updateshis popular reference on functional analysis with new insights andrecent discoveries-adding three new chapters on set-valued analysisand convex analysis, viability kernels and capture basins, andfirst-order partial differential equations. He presents, for thefirst time at an introductory level, the extension of differentialcalculus in the framework of both the theory of distributions andset-valued analysis, and discusses their application for studyingboundary-value problems for elliptic and parabolic partialdifferential equations and for systems of first-order partialdifferential equations. To keep the presentation concise and accessible, Jean-Pierre Aubinintroduces functional analysis through the simple Hilbertianstructure. He seamlessly blends pure mathematics with applied areasthat illustrate the theory, incorporating a broad range of examplesfrom numerical analysis, systems theory, calculus of variations,control and optimization theory, convex and nonsmooth analysis, andmore. Finally, a summary of the essential theorems as well asexercises reinforcing key concepts are provided. Applied FunctionalAnalysis, Second Edition is an excellent and timely resource forboth pure and applied mathematicians.
Category: Mathematics

Functional Analysis

Author : Terry J. Morrison
ISBN : 9781118031247
Genre : Mathematics
File Size : 77.54 MB
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A powerful introduction to one of the most active areas oftheoretical and applied mathematics This distinctive introduction to one of the most far-reaching andbeautiful areas of mathematics focuses on Banach spaces as themilieu in which most of the fundamental concepts are presented.While occasionally using the more general topological vector spaceand locally convex space setting, it emphasizes the development ofthe reader's mathematical maturity and the ability to bothunderstand and "do" mathematics. In so doing, Functional Analysisprovides a strong springboard for further exploration on the widerange of topics the book presents, including: * Weak topologies and applications * Operators on Banach spaces * Bases in Banach spaces * Sequences, series, and geometry in Banach spaces Stressing the general techniques underlying the proofs, FunctionalAnalysis also features many exercises for immediate clarificationof points under discussion. This thoughtful, well-organizedsynthesis of the work of those mathematicians who created thediscipline of functional analysis as we know it today also providesa rich source of research topics and reference material.
Category: Mathematics

Functional Differential Equations

Author : Constantin Corduneanu
ISBN : 9781119189480
Genre : Mathematics
File Size : 38.64 MB
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Features new results and up-to-date advances in modeling and solving differential equations Introducing the various classes of functional differential equations, Functional Differential Equations: Advances and Applications presents the needed tools and topics to study the various classes of functional differential equations and is primarily concerned with the existence, uniqueness, and estimates of solutions to specific problems. The book focuses on the general theory of functional differential equations, provides the requisite mathematical background, and details the qualitative behavior of solutions to functional differential equations. The book addresses problems of stability, particularly for ordinary differential equations in which the theory can provide models for other classes of functional differential equations, and the stability of solutions is useful for the application of results within various fields of science, engineering, and economics. Functional Differential Equations: Advances and Applications also features: • Discussions on the classes of equations that cannot be solved to the highest order derivative, and in turn, addresses existence results and behavior types • Oscillatory motion and solutions that occur in many real-world phenomena as well as in man-made machines • Numerous examples and applications with a specific focus on ordinary differential equations and functional differential equations with finite delay • An appendix that introduces generalized Fourier series and Fourier analysis after periodicity and almost periodicity • An extensive Bibliography with over 550 references that connects the presented concepts to further topical exploration Functional Differential Equations: Advances and Applications is an ideal reference for academics and practitioners in applied mathematics, engineering, economics, and physics. The book is also an appropriate textbook for graduate- and PhD-level courses in applied mathematics, differential and difference equations, differential analysis, and dynamics processes. CONSTANTIN CORDUNEANU, PhD, is Emeritus Professor in the Department of Mathematics at The University of Texas at Arlington, USA. The author of six books and over 200 journal articles, he is currently Associate Editor for seven journals; a member of the American Mathematical Society, Society for Industrial and Applied Mathematics, and the Romanian Academy; and past president of the American Romanian Academy of Arts and Sciences. YIZENG LI, PhD, is Professor in the Department of Mathematics at Tarrant County College, USA. He is a member of the Society for Industrial and Applied Mathematics. MEHRAN MAHDAVI, PhD, is Professor in the Department of Mathematics at Bowie State University, USA. The author of numerous journal articles, he is a member of the American Mathematical Society, Society for Industrial and Applied Mathematics, and the Mathematical Association of America.
Category: Mathematics

Solutions Manual To Accompany Beginning Partial Differential Equations

Author : Peter V. O'Neil
ISBN : 9781118630099
Genre : Mathematics
File Size : 77.56 MB
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Solutions Manual to Accompany Beginning Partial Differential Equations, 3rd Edition Featuring a challenging, yet accessible, introduction to partial differential equations, Beginning Partial Differential Equations provides a solid introduction to partial differential equations, particularly methods of solution based on characteristics, separation of variables, as well as Fourier series, integrals, and transforms. Thoroughly updated with novel applications, such as Poe's pendulum and Kepler's problem in astronomy, this third edition is updated to include the latest version of Maples, which is integrated throughout the text. New topical coverage includes novel applications, such as Poe's pendulum and Kepler's problem in astronomy.
Category: Mathematics

Fibonacci And Lucas Numbers With Applications

Author : Thomas Koshy
ISBN : 9781118031315
Genre : Mathematics
File Size : 78.11 MB
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The first comprehensive survey of mathematics' most fascinatingnumber sequences Fibonacci and Lucas numbers have intrigued amateur and professionalmathematicians for centuries. This volume represents the firstattempt to compile a definitive history and authoritative analysisof these famous integer sequences, complete with a wealth ofexciting applications, enlightening examples, and fun exercisesthat offer numerous opportunities for exploration andexperimentation. The author has assembled a myriad of fascinating properties of bothFibonacci and Lucas numbers-as developed by a wide range ofsources-and catalogued their applications in a multitude of widelyvaried disciplines such as art, stock market investing,engineering, and neurophysiology. Most of the engaging anddelightful material here is easily accessible to college and evenhigh school students, though advanced material is included tochallenge more sophisticated Fibonacci enthusiasts. A historicalsurvey of the development of Fibonacci and Lucas numbers,biographical sketches of intriguing personalities involved indeveloping the subject, and illustrative examples round out thisthorough and amusing survey. Most chapters conclude with numericand theoretical exercises that do not rely on long and tediousproofs of theorems. Highlights include: * Balanced blend of theory and real-world applications * Excellent reference material for student reports andprojects * User-friendly, informal, and entertaining writing style * Historical interjections and short biographies that add a richerperspective to the topic * Reference sections providing important symbols, problemsolutions, and fundamental properties from the theory of numbersand matrices Fibonacci and Lucas Numbers with Applications providesmathematicians with a wealth of reference material in oneconvenient volume and presents an in-depth and entertainingresource for enthusiasts at every level and from any background.
Category: Mathematics

A First Course In Functional Analysis

Author : S. David Promislow
ISBN : 0470146192
Genre : Mathematics
File Size : 70.92 MB
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A concise introduction to the major concepts of functional analysis Requiring only a preliminary knowledge of elementary linear algebra and real analysis, A First Course in Functional Analysis provides an introduction to the basic principles and practical applications of functional analysis. Key concepts are illustrated in a straightforward manner, which facilitates a complete and fundamental understanding of the topic. This book is based on the author's own class-tested material and uses clear language to explain the major concepts of functional analysis, including Banach spaces, Hilbert spaces, topological vector spaces, as well as bounded linear functionals and operators. As opposed to simply presenting the proofs, the author outlines the logic behind the steps, demonstrates the development of arguments, and discusses how the concepts are connected to one another. Each chapter concludes with exercises ranging in difficulty, giving readers the opportunity to reinforce their comprehension of the discussed methods. An appendix provides a thorough introduction to measure and integration theory, and additional appendices address the background material on topics such as Zorn's lemma, the Stone-Weierstrass theorem, Tychonoff's theorem on product spaces, and the upper and lower limit points of sequences. References to various applications of functional analysis are also included throughout the book. A First Course in Functional Analysis is an ideal text for upper-undergraduate and graduate-level courses in pure and applied mathematics, statistics, and engineering. It also serves as a valuable reference for practitioners across various disciplines, including the physical sciences, economics, and finance, who would like to expand their knowledge of functional analysis.
Category: Mathematics

Numerical Solution Of Ordinary Differential Equations

Author : Kendall Atkinson
ISBN : 9781118164525
Genre : Mathematics
File Size : 34.27 MB
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A concise introduction to numerical methodsand the mathematicalframework neededto understand their performance Numerical Solution of Ordinary Differential Equationspresents a complete and easy-to-follow introduction to classicaltopics in the numerical solution of ordinary differentialequations. The book's approach not only explains the presentedmathematics, but also helps readers understand how these numericalmethods are used to solve real-world problems. Unifying perspectives are provided throughout the text, bringingtogether and categorizing different types of problems in order tohelp readers comprehend the applications of ordinary differentialequations. In addition, the authors' collective academic experienceensures a coherent and accessible discussion of key topics,including: Euler's method Taylor and Runge-Kutta methods General error analysis for multi-step methods Stiff differential equations Differential algebraic equations Two-point boundary value problems Volterra integral equations Each chapter features problem sets that enable readers to testand build their knowledge of the presented methods, and a relatedWeb site features MATLAB® programs that facilitate theexploration of numerical methods in greater depth. Detailedreferences outline additional literature on both analytical andnumerical aspects of ordinary differential equations for furtherexploration of individual topics. Numerical Solution of Ordinary Differential Equations isan excellent textbook for courses on the numerical solution ofdifferential equations at the upper-undergraduate and beginninggraduate levels. It also serves as a valuable reference forresearchers in the fields of mathematics and engineering.
Category: Mathematics