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Author: Enrique Castillo
Publisher: CRC Press
ISBN: 9780824787172
Category : Mathematics
Languages : en
Pages : 354
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Book Description
Provides engineers and applied scientists with some selected results of functional equations and their applications, with the intention of changing the way they think about mathematical modelling. Many of the proofs are simplified or omitted, so as not to bore or confuse engineers. Functional equati
Author: Enrique Castillo
Publisher: CRC Press
ISBN: 9780824787172
Category : Mathematics
Languages : en
Pages : 354
Get Book Here
Book Description
Provides engineers and applied scientists with some selected results of functional equations and their applications, with the intention of changing the way they think about mathematical modelling. Many of the proofs are simplified or omitted, so as not to bore or confuse engineers. Functional equati
Author: Enrique Castillo
Publisher: Elsevier
ISBN: 0080477917
Category : Mathematics
Languages : en
Pages : 410
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Book Description
The book provides the reader with the different types of functional equations that s/he can find in practice, showing, step by step, how they can be solved.A general methodology for solving functional equations is provided in Chapter 2. The different types of functional equations are described and solved in Chapters 3 to 8. Many examples, coming from different fields, as geometry, science, engineering, economics, probability, statistics, etc, help the reader to change his/her mind in order to state problems as functional equations as an alternative to differential equations, and to state new problems in terms of functional equations or systems.An interesting feature of the book is that it deals with functional networks, a powerful generalization of neural networks that allows solving many practical problems. The second part of the book, Chapters 9 to 13, is devoted to the applications of this important paradigm.The book contains many examples and end of chapter exercises, that facilitates the understanding of the concepts and applications.· A general methodology for solving functional equations is provided in Chapter 2.· It deals with functional networks, a powerful generalization of neural networks.· Many examples, coming from different fields, as geometry, science, engineering, economics, probability, statistics, etc, illustrate the concept of functional equation.· Functional equations are presented as a powerful alternative to differential equations. · The book contains end of chapter exercises.
Author: Themistocles RASSIAS
Publisher: Springer Science & Business Media
ISBN: 9401143412
Category : Mathematics
Languages : en
Pages : 335
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Book Description
This volume provides an extensive study of some of the most important topics of current interest in functional equations and inequalities. Subjects dealt with include: a Pythagorean functional equation, a functional definition of trigonometric functions, the functional equation of the square root spiral, a conditional Cauchy functional equation, an iterative functional equation, the Hille-type functional equation, the polynomial-like iterative functional equation, distribution of zeros and inequalities for zeros of algebraic polynomials, a qualitative study of Lobachevsky's complex functional equation, functional inequalities in special classes of functions, replicativity and function spaces, normal distributions, some difference equations, finite sums, decompositions of functions, harmonic functions, set-valued quasiconvex functions, the problems of expressibility in some extensions of free groups, Aleksandrov problem and mappings which preserve distances, Ulam's problem, stability of some functional equation for generalized trigonometric functions, Hyers-Ulam stability of Hosszú's equation, superstability of a functional equation, and some demand functions in a duopoly market with advertising. Audience: This book will be of interest to mathematicians and graduate students whose work involves real functions, functions of a complex variable, functional analysis, integral transforms, and operational calculus.
Author: Palaniappan Kannappan
Publisher: Springer Science & Business Media
ISBN: 0387894926
Category : Mathematics
Languages : en
Pages : 817
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Book Description
Functional Equations and Inequalities with Applications presents a comprehensive, nearly encyclopedic, study of the classical topic of functional equations. This self-contained monograph explores all aspects of functional equations and their applications to related topics, such as differential equations, integral equations, the Laplace transformation, the calculus of finite differences, and many other basic tools in analysis. Each chapter examines a particular family of equations and gives an in-depth study of its applications as well as examples and exercises to support the material.
Author: Gregory Richard Baker
Publisher: World Scientific Publishing Company
ISBN: 9814656992
Category : Mathematics
Languages : en
Pages : 391
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Book Description
This textbook develops a coherent view of differential equations by progressing through a series of typical examples in science and engineering that arise as mathematical models. All steps of the modeling process are covered: formulation of a mathematical model; the development and use of mathematical concepts that lead to constructive solutions; validation of the solutions; and consideration of the consequences. The volume engages students in thinking mathematically, while emphasizing the power and relevance of mathematics in science and engineering. There are just a few guidelines that bring coherence to the construction of solutions as the book progresses through ordinary to partial differential equations using examples from mixing, electric circuits, chemical reactions and transport processes, among others. The development of differential equations as mathematical models and the construction of their solution is placed center stage in this volume.
Author: Nikos I. Kavallaris
Publisher: Springer
ISBN: 3319679449
Category : Technology & Engineering
Languages : en
Pages : 310
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Book Description
This book presents new developments in non-local mathematical modeling and mathematical analysis on the behavior of solutions with novel technical tools. Theoretical backgrounds in mechanics, thermo-dynamics, game theory, and theoretical biology are examined in details. It starts off with a review and summary of the basic ideas of mathematical modeling frequently used in the sciences and engineering. The authors then employ a number of models in bio-science and material science to demonstrate applications, and provide recent advanced studies, both on deterministic non-local partial differential equations and on some of their stochastic counterparts used in engineering. Mathematical models applied in engineering, chemistry, and biology are subject to conservation laws. For instance, decrease or increase in thermodynamic quantities and non-local partial differential equations, associated with the conserved physical quantities as parameters. These present novel mathematical objects are engaged with rich mathematical structures, in accordance with the interactions between species or individuals, self-organization, pattern formation, hysteresis. These models are based on various laws of physics, such as mechanics of continuum, electro-magnetic theory, and thermodynamics. This is why many areas of mathematics, calculus of variation, dynamical systems, integrable systems, blow-up analysis, and energy methods are indispensable in understanding and analyzing these phenomena. This book aims for researchers and upper grade students in mathematics, engineering, physics, economics, and biology.
Author: Andrei D. Polyanin
Publisher: CRC Press
ISBN: 1420010514
Category : Mathematics
Languages : en
Pages : 1542
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Book Description
Covering the main fields of mathematics, this handbook focuses on the methods used for obtaining solutions of various classes of mathematical equations that underlie the mathematical modeling of numerous phenomena and processes in science and technology. The authors describe formulas, methods, equations, and solutions that are frequently used in scientific and engineering applications and present classical as well as newer solution methods for various mathematical equations. The book supplies numerous examples, graphs, figures, and diagrams and contains many results in tabular form, including finite sums and series and exact solutions of differential, integral, and functional equations.
Author: Anatoli Torokhti
Publisher: Elsevier
ISBN: 0080475388
Category : Mathematics
Languages : en
Pages : 413
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Book Description
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
Author:
Publisher: Elsevier
ISBN: 0080955363
Category : Mathematics
Languages : en
Pages : 269
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Book Description
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; andmethods 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 particularbranches, 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
Author: Enrique Castillo
Publisher: Springer Science & Business Media
ISBN: 1402091826
Category : Technology & Engineering
Languages : en
Pages : 232
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Book Description
This book is an attempt to provide a uni?ed methodology to derive models for fatigue life. This includes S-N, ?-N and crack propagation models. This is not a conventional book aimed at describing the fatigue fundamentals, but rather a book in which the basic models of the three main fatigue approaches, the stress-based, the strain-based and the fracture mechanics approaches, are contemplated from a novel and integrated point of view. On the other hand, as an alternative to the preferential attention paid to deterministic models based on the physical, phenomenological and empirical description of fatigue, their probabilistic nature is emphasized in this book, in which stochastic fatigue and crack growth models are presented. This book is the result of a long period of close collaborationbetween its two authors who, although of di?erent backgrounds, mathematical and mechanical, both have a strong sense of engineering with respect to the fatigue problem. When the authors of this book ?rst approached the fatigue ?eld in 1982 (twenty six years ago), they found the following scenario: 1. Linear, bilinear or trilinear models were frequently proposed by relevant laboratoriesandacademiccenterstoreproducetheW ̈ ohler?eld. Thiswas the case of well known institutions, which justi?ed these models based on clientrequirementsorpreferences. Thisledtotheinclusionofsuchmodels and methods as, for example, the up-and-down, in standards and o?cial practical directives (ASTM, Euronorm, etc.), which have proved to be unfortunate.
