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The integral equation approach to solving problems specifically includes the boundary conditions--a valuable advantage. It also leads naturally to the solution of the problem (under suitable conditions) in the form of an infinite series. Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, accompanied by simple examples of a variety of integral equations and the methods of their solution. The treatment becomes gradually more abstract, with discussions of Hilbert space and linear operators, the resolvent, Fredholm theory, and the Hilbert-Schmidt theory of linear operators in Hilbert space. 1977 ed.
Hilbert space. --- Integral equations. --- Linear operators.
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Most mathematicians, engineers, and many other scientists are well-acquainted with theory and application of ordinary differential equations. This book presents Volterra integral and functional differential equations in that same framework, allowing the readers to parlay their knowledge of ordinary differential equations into theory.
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Functional analysis is a powerful tool when applied to mathematical problems arising from physical situations. The present book provides, by careful selection of material, a collection of concepts and techniques essential for the modern practitioner. Emphasis is placed on the solution of equations (including nonlinear and partial differential equations). The assumed background is limited to elementary real variable theory and finite-dimensional vector spaces. Key Features- Provides an ideal transition between introductory math courses and advanced graduate study in applied math
Functional analysis. --- Operator theory. --- Functional analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations
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Differential equations --- 517.9 --- 517.9 Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Differential equations - Popular works.
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This book familiarizes both popular and fundamental notions and techniques from the theory of non-normed topological algebras with involution, demonstrating with examples and basic results the necessity of this perspective. The main body of the book is focussed on the Hilbert-space (bounded) representation theory of topological *-algebras and their topological tensor products, since in our physical world, apart from the majority of the existing unbounded operators, we often meet operators that are forced to be bounded, like in the case of symmetric *-algebras. So, one gets an account of how th
Topological algebras. --- Functional analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Algebras, Topological --- Functional analysis --- Linear topological spaces --- Rings (Algebra)
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The Romanian conferences in operator theory, as they are now commonly called, havestartedintheyear1976asanannualworkshoponoperatortheoryheldatthe University of Timi¸ soara, originally only with Romanian attendance. The meeting soon evolved into an international conference, with an increasingly larger parti- pation. It has been organized jointly, initially by the Department of Mathematics of INCREST and by the Faculty of Sciences of the University of Timi¸ soara, then (since 1990) by the Institute of Mathematics of the Romanian Academy and the Faculty of Mathematics of the West University of Timi¸ soara. The venue was u- ally Timi¸ soara (and, occasionally, Herculane, Bucharest or Predeal). Since 1986 the conference has been regularly held biannually at the beginning of the summer. The 19th Conference on Operator Theory (OT 19) took place between June 27th and July 2nd 2002, at the West University of Timi¸ soara. It is a pleasure to acknowledge the considerable ?nancial support received through the p- gramme EURROMMAT of the European Community, under contract ICA1-CT- 2000-70022. Partial support has also been provided by the Romanian Ministry of Education, Research and Youth, grants CERES 152/2001 and 153/2001. The full programme of the conference is included in the sequel. It is worth mentioning also a special event that has taken place during the conference: p- fessor Israel Gohberg has been awarded the title of Doctor Honoris Causa of the West University of Timi¸ soara.
Operator theory --- Operator algebras --- Functional analysis. --- Global analysis (Mathematics). --- Operator theory. --- Topological Groups. --- Integral equations. --- Distribution (Probability theory. --- Functional Analysis. --- Analysis. --- Operator Theory. --- Topological Groups, Lie Groups. --- Integral Equations. --- Probability Theory and Stochastic Processes. --- Equations, Integral --- Functional equations --- Functional analysis --- Groups, Topological --- Continuous groups --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Functional calculus --- Calculus of variations --- Integral equations --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Mathematical analysis. --- Analysis (Mathematics). --- Topological groups. --- Lie groups. --- Probabilities. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- 517.1 Mathematical analysis --- Mathematical analysis
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Questo testo contiene una raccolta di esercizi riferiti agli argomenti tipici di un corso di metodi analitici e numerici proposto in un corso di laurea in Ingegneria o in Matematica. A partire da esercizi di analisi funzionale e di teoria dell'approssimazione, il testo sviluppa problemi legati alla risoluzione con metodi numerici di equazioni alle derivate parziali di tipo ellittico, parabolico ed iperbolico, scalari o vettoriali, in una o più dimensioni spaziali. Si affrontano quindi problemi di pura diffusione o di pura convezione, accanto a problemi di diffusione-trasporto e problemi di fluidodinamica comprimibile ed incomprimibile. Particolare enfasi viene data al metodo degli elementi finiti per la discretizzazione in spazio dei problemi considerati, anche se sono presenti esercizi sul metodo delle differenze finite e dei volumi finiti. La presenza di problemi dipendenti dal tempo giustifica l'esistenza di un capitolo di esercizi sui problemi di Cauchy e sulle principali tecniche numeriche per la loro discretizzazione. Ogni paragrafo è preceduto da un breve richiamo delle principali nozioni di teoria necessarie affinché l'allievo possa risolvere gli esercizi proposti. La risoluzione della maggior parte degli esercizi si avvale della libreria MLife, sviluppata dagli autori, in linguaggio MATLAB. Questo consente l'immediata verifica da parte degli studenti delle principali proprietà teoriche introdotte.
Differential equations, Partial. --- Numerical analysis. --- Functional analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Mathematical analysis --- Partial differential equations --- Differential equations, partial. --- Mathematics. --- Partial Differential Equations. --- Functional Analysis. --- Mathematics, general. --- Numerical Analysis. --- Math --- Science --- Partial differential equations.
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Differential equations, Partial --- Computer-assisted instruction --- 519.63 --- 517.9 --- 681.3*G18 --- Numerical methods for solution of partial differential equations --- Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Basic Sciences. Mathematics --- Computer-assisted instruction. --- Differential and Integral Equations --- MATLAB. --- Differential and Integral Equations. --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- 517.9 Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- 519.63 Numerical methods for solution of partial differential equations --- Partial differential equations --- MATLAB (Computer program) --- Matrix laboratory --- 681.3 *G18 --- MATLAB (Computer file) --- Differential equations, Partial - Computer-assisted instruction --- Acqui 2006
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This text is designed both for students of probability and stochastic processes, and for students of functional analysis. For the reader not familiar with functional analysis a detailed introduction to necessary notions and facts is provided. However, this is not a straight textbook in functional analysis; rather, it presents some chosen parts of functional analysis that can help understand ideas from probability and stochastic processes. The subjects range from basic Hilbert and Banach spaces, through weak topologies and Banach algebras, to the theory of semigroups of bounded linear operators. Numerous standard and non-standard examples and exercises make the book suitable as a course textbook or for self-study.
Functional analysis --- Probabilities --- Stochastic processes --- Analyse fonctionnelle --- Probabilités --- Processus stochastiques --- Functional analysis. --- Probabilities. --- Stochastic processes. --- Random processes --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations
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The Sixth Edition of this influential best-selling book delivers the most up-to-date and comprehensive text and reference yet on the basis of the finite element method (FEM) for all engineers and mathematicians. Since the appearance of the first edition 38 years ago, The Finite Element Method provides arguably the most authoritative introductory text to the method, covering the latest developments and approaches in this dynamic subject, and is amply supplemented by exercises, worked solutions and computer algorithms.The classic FEM text, written by the subject's leading authors
Finite element method. --- Engineering mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- FEA (Numerical analysis) --- FEM (Numerical analysis) --- Finite element analysis --- Numerical analysis --- Isogeometric analysis --- Mathematics --- 519.63 --- 517.96 --- 517.96 Finite differences. Functional and integral equations --- Finite differences. Functional and integral equations --- 519.63 Numerical methods for solution of partial differential equations --- Numerical methods for solution of partial differential equations --- Mechanical properties of solids --- finite element method --- computer-aided engineering --- eindige elementen --- CAE (computer aided engineering)
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