Functional Analysis In Modern Applied Mathematics

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Author:
Publisher: Academic Press
ISBN: 9780080956411
Size: 80.56 MB
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Functional Analysis In Modern Applied Mathematics by


Original Title: Functional Analysis In Modern Applied Mathematics

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering

Probability And Partial Differential Equations In Modern Applied Mathematics

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Author: Edward C. Waymire
Publisher: Springer Science & Business Media
ISBN: 038729371X
Size: 14.68 MB
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Probability And Partial Differential Equations In Modern Applied Mathematics by Edward C. Waymire


Original Title: Probability And Partial Differential Equations In Modern Applied Mathematics

"Probability and Partial Differential Equations in Modern Applied Mathematics" is devoted to the role of probabilistic methods in modern applied mathematics from the perspectives of both a tool for analysis and as a tool in modeling. There is a recognition in the applied mathematics research community that stochastic methods are playing an increasingly prominent role in the formulation and analysis of diverse problems of contemporary interest in the sciences and engineering. A probabilistic representation of solutions to partial differential equations that arise as deterministic models allows one to exploit the power of stochastic calculus and probabilistic limit theory in the analysis of deterministic problems, as well as to offer new perspectives on the phenomena for modeling purposes. There is also a growing appreciation of the role for the inclusion of stochastic effects in the modeling of complex systems. This has led to interesting new mathematical problems at the interface of probability, dynamical systems, numerical analysis, and partial differential equations. This volume will be useful to researchers and graduate students interested in probabilistic methods, dynamical systems approaches and numerical analysis for mathematical modeling in the sciences and engineering.

Functional Analysis In Modern Applied Mathematics

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Author: Ruth F. Curtain
Publisher: Elsevier Science & Technology
ISBN:
Size: 62.47 MB
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Functional Analysis In Modern Applied Mathematics by Ruth F. Curtain


Original Title: Functional Analysis In Modern Applied Mathematics

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering

Methods In Approximation

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Author: N.D. Bellman
Publisher: Springer Science & Business Media
ISBN: 9400946007
Size: 18.65 MB
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Methods In Approximation by N.D. Bellman


Original Title: Methods In Approximation

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Modern Applied Mathematics

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Author: J. C. Misra
Publisher: Alpha Science Int'l Ltd.
ISBN: 9788173194924
Size: 61.83 MB
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Modern Applied Mathematics by J. C. Misra


Original Title: Modern Applied Mathematics

Introduces educational units dealing with important topics of Modern Applied Mathematics. In this book, chapters include information on different topics such as: Methods of Approximation for Mapping in Probability Spaces, Mathematical Modelling of Seismic Sources, Climate Variability, Geometry of Differential Equations, and more.

Theory Of Impulsive Differential Equations

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Author: V Lakshmikantham
Publisher: World Scientific
ISBN: 9814507261
Size: 13.87 MB
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Theory Of Impulsive Differential Equations by V Lakshmikantham


Original Title: Theory Of Impulsive Differential Equations

Many evolution processes are characterized by the fact that at certain moments of time they experience a change of state abruptly. These processes are subject to short-term perturbations whose duration is negligible in comparison with the duration of the process. Consequently, it is natural to assume that these perturbations act instantaneously, that is, in the form of impulses. It is known, for example, that many biological phenomena involving thresholds, bursting rhythm models in medicine and biology, optimal control models in economics, pharmacokinetics and frequency modulated systems, do exhibit impulsive effects. Thus impulsive differential equations, that is, differential equations involving impulse effects, appear as a natural description of observed evolution phenomena of several real world problems. Contents:Description of Systems with ImpulsesExistence and ContinuationPulse PhenomenaImpulsive Differential InequalitiesImpulsive Integral InequalitiesGlobal ExistenceDependence on Initial ValuesDifferentiability Relative to Initial ValuesMethod of Upper and Lower SolutionsMonotone Iterative TechniqueStability by Linear ApproximationVector Lyapunov FunctionsStability Concepts in Terms of Two MeasuresQuasistability CriteriaSingularly Perturbed SystemsSystems with Variable StructureIntegro-Differential SystemsPeriodic Boundary Value Problems for Second Order Systems Readership: Mathematicians. Keywords:Impulsive Effects;Rhythmical Beating;Pulse Phenomena;Systems with Variable Structure;Impulses with Fixed Moments;Impulses with Variable Moments;Dynamic Systems with Impulses;Hybrid Systems

An Invitation To Applied Mathematics

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Author: Carmen Chicone
Publisher: Academic Press
ISBN: 0128041544
Size: 28.38 MB
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An Invitation To Applied Mathematics by Carmen Chicone


Original Title: An Invitation To Applied Mathematics

An Invitation to Applied Mathematics: Differential Equations, Modeling, and Computation introduces the reader to the methodology of modern applied mathematics in modeling, analysis, and scientific computing with emphasis on the use of ordinary and partial differential equations. Each topic is introduced with an attractive physical problem, where a mathematical model is constructed using physical and constitutive laws arising from the conservation of mass, conservation of momentum, or Maxwell's electrodynamics. Relevant mathematical analysis (which might employ vector calculus, Fourier series, nonlinear ODEs, bifurcation theory, perturbation theory, potential theory, control theory, or probability theory) or scientific computing (which might include Newton's method, the method of lines, finite differences, finite elements, finite volumes, boundary elements, projection methods, smoothed particle hydrodynamics, or Lagrangian methods) is developed in context and used to make physically significant predictions. The target audience is advanced undergraduates (who have at least a working knowledge of vector calculus and linear ordinary differential equations) or beginning graduate students. Readers will gain a solid and exciting introduction to modeling, mathematical analysis, and computation that provides the key ideas and skills needed to enter the wider world of modern applied mathematics. Presents an integrated wealth of modeling, analysis, and numerical methods in one volume Provides practical and comprehensible introductions to complex subjects, for example, conservation laws, CFD, SPH, BEM, and FEM Includes a rich set of applications, with more appealing problems and projects suggested

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