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Delay and Functional Differential Equations and Their Applications
Delay and Functional Differential Equations and Their Applications provides information pertinent to the fundamental aspects of functional differential equations and its applications. This book covers a variety of topics, including qualitative and geometric theory, control theory, Volterra equations, numerical methods, the theory of epidemics, problems in physiology, and other areas of applications. Organized into two parts encompassing 25 chapters, this book begins with an overview of problems involving functional differential equations with terminal conditions in function spaces. This text then examines the numerical methods for functional differential equations. Other chapters consider the theory of radiative transfer, which give rise to several interesting functional partial differential equations. This book discusses as well the theory of embedding fields, which studies systems of nonlinear functional differential equations that can be derived from psychological postulates and interpreted as neural networks. The final chapter deals with the usefulness of the flip-flop circuit. This book is a valuable resource for mathematicians.
Solving Ordinary Differential Equations I
"So far as I remember, I have never seen an Author's Pre face which had any purpose but one - to furnish reasons for the publication of the Book. " (Mark Twain) "Gauss' dictum, "when a building is completed no one should be able to see any trace of the scaffolding," is often used by mathematicians as an excuse for neglecting the motivation behind their own work and the history of their field. For tunately, the opposite sentiment is gaining strength, and numerous asides in this Essay show to which side go my sympathies. " (B. B. Mandelbrot, 1982) 'This gives us a good occasion to work out most of the book until the next year. " (the Authors in a letter, dated c. kt. 29, 1980, to Springer Verl...
Partial Differential Equations
For more than 250 years partial di?erential equations have been clearly the most important tool available to mankind in order to understand a large variety of phenomena, natural at ?rst and then those originating from - man activity and technological development. Mechanics, physics and their engineering applications were the ?rst to bene?t from the impact of partial di?erential equations on modeling and design, but a little less than a century ago the Schr ̈ odinger equation was the key opening the door to the application of partial di?erential equations to quantum chemistry, for small atomic and molecular systems at ?rst, but then for systems of fast growing complexity. The place of partia...
Scientific Computing
This is the third of three volumes providing a comprehensive presentation of the fundamentals of scientific computing. This volume discusses topics that depend more on calculus than linear algebra, in order to prepare the reader for solving differential equations. This book and its companions show how to determine the quality of computational results, and how to measure the relative efficiency of competing methods. Readers learn how to determine the maximum attainable accuracy of algorithms, and how to select the best method for computing problems. This book also discusses programming in several languages, including C++, Fortran and MATLAB. There are 90 examples, 200 exercises, 36 algorithms, 40 interactive JavaScript programs, 91 references to software programs and 1 case study. Topics are introduced with goals, literature references and links to public software. There are descriptions of the current algorithms in GSLIB and MATLAB. This book could be used for a second course in numerical methods, for either upper level undergraduates or first year graduate students. Parts of the text could be used for specialized courses, such as nonlinear optimization or iterative linear algebra.
Computational Geomechanics
Recent years have witnessed the development of computational geomechanics as an important branch of engineering. The use of modern computational techniques makes it possible to deal with many complex engineering problems, taking into account many of the typical properties of geotechnical materials (soil and rock), such as the coupled behaviour of pore water and solid material, nonlinear elasto-plastic behaviour, and transport processes. This book provides an introduction to these methods, presenting the basic principles of the geotechnical phenomena involved as well as the numerical models for their analysis, and including full listings of computer programs (in PASCAL). The types of geotechnical problems considered cover a wide range of applications, varying from classical problems such as slope stability, analysis of foundation piles and sheet pile walls to finite element analysis of groundwater flow, elasto-plastic deformations, consolidation and transport problems.
Computing Methods in Applied Sciences and Engineering
IRIA LABORIA, Institut de Recherche d'Informatique et d'Automatique
Delay Equations, Approximation and Application
The international symposium held in October 1984 at the Uni versity of Mannheim was the first with the special aim to expose the connection of the Theory of Delay Eauations and Approximation Theory with the emphasis on constructive methods and applications. Although the separate character of both domains is reflected by their historical development, the latest research shows that the numerical treatment of Delay Equations leads to various appro ximation and optimization problems. An introductory survey of this circle of problems written by the editors is included at the beginning of the book. Delay Equations have their origin in domains of applications, such as physics, engineering, biology,...
Analytical and Numerical Methods for Volterra Equations
Presents an aspect of activity in integral equations methods for the solution of Volterra equations for those who need to solve real-world problems. Since there are few known analytical methods leading to closed-form solutions, the emphasis is on numerical techniques. The major points of the analytical methods used to study the properties of the solution are presented in the first part of the book. These techniques are important for gaining insight into the qualitative behavior of the solutions and for designing effective numerical methods. The second part of the book is devoted entirely to numerical methods. The author has chosen the simplest possible setting for the discussion, the space of real functions of real variables. The text is supplemented by examples and exercises.
Contributions In Numercial Mathematics
World Scientific Series in Applicable Analysis (WSSIAA) aims at reporting new developments of a high mathematical standard and of current interest. Each volume in the series shall be devoted to mathematical analysis that has been applied, or potentially applicable to the solutions of scientific, engineering and social problems.This second volume of WSSIAA contains 34 research articles on numerical mathematics by leading mathematicians from all over the world. This volume is dedicated to the memory of Lothar Collatz (1910 - 1990) for his significant contributions to numerical mathematics.Contributors: G Adomian, E L Allgower, C T H Baker, B Beckermann, R W Brankin, C Brezinski, L Brugnano, J ...
Annual Review of Cybertherapy and Telemedicine 2014
The evolution of healthcare delivery systems has included an increased reliance on technology. There has been a significant shift in the nature of care prevention, diagnosis and treatment, which has decreased the importance of traditional methods of care delivery. Cybertherapy has started to make progress in treating a variety of disorders, but more work is needed in a number of areas, including the development of easy-to-use and more affordable hardware and software and objective measurement tools, the need to address potential side-effects, and the implementation of more controlled studies to evaluate cybertherapy in comparison to traditional therapies._x000D_ This book, the 2014 Annual Re...
