Inverse Problems is a monograph which contains a self-contained presentation of the theory of several major inverse problems and the closely related results from the theory of ill-posed problems. The book is aimed at a large audience which include graduate students and researchers in mathematical, physical, and engineering sciences and in the area of numerical analysis.
Inverse Problems is a monograph which contains a self-contained presentation of the theory of several major inverse problems and t...
Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Methods for constructing exact solutions of differential equations play an important role in applied mathematics and mechanics. This book aims to provide scientists, engineers and students with an easy-to-follow, but comprehensive, description of the methods for constructing exact solutions of differential equations.
Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Methods for constructing exact...
Stochastic differential equations (SDEs) are a powerful tool in science, mathematics, economics and finance. This book will help the reader to master the basic theory and learn some applications of SDEs. In particular, the reader will be provided with the backward SDE technique for use in research when considering financial problems in the market, and with the reflecting SDE technique to enable study of optimal stochastic population control problems. These two techniques are powerful and efficient, and can also be applied to research in many other problems in nature, science and elsewhere.
Stochastic differential equations (SDEs) are a powerful tool in science, mathematics, economics and finance. This book will help the reader to master ...
The design and development of electrical devices involves choosing from many possible variants that which is the best or optimum according to one or several criteria. These optimization criteria are usually already clear to the designer at the statement of the design problem. The methods of optimization considered in this book, allow us to sort out variants of the realization of a design on the basis of these criteria and to create the best device in the sense of the set criteria. Optimization of devices is one of the major problems in electrical engi neering that is related to an extensive...
The design and development of electrical devices involves choosing from many possible variants that which is the best or optimum according to one or s...
Boundary Element Methods (BEM) play an important role in modern numerical computations in the applied and engineering sciences. These methods turn out to be powerful tools for numerical studies of various physical phenomena which can be described mathematically by partial differential equations.
The most prominent example is the potential equation (Laplace equation), which is used to model physical phenomena in electromagnetism, gravitation theory, and in perfect fluids. A further application leading to the Laplace equation is the model of steady state heat flow. One of the most...
Boundary Element Methods (BEM) play an important role in modern numerical computations in the applied and engineering sciences. These methods turn ...
As it was already seen in the first volume of the present book, its guideline is precisely the mathematical model of mechanics. The classical models which we refer to are in fact models based on the Newtonian model of mechanics, on its five principles, i. e.: the inertia, the forces action, the action and reaction, the parallelogram and the initial conditions principle, respectively. Other models, e. g., the model of attraction forces between the particles of a discrete mechanical system, are part of the considered Newtonian model. Kepler s laws brilliantly verify this model in case of...
As it was already seen in the first volume of the present book, its guideline is precisely the mathematical model of mechanics. The classical models w...
All phenomena in nature are characterized by motion; this is an essential property of matter, having infinitely many aspects. Motion can be mechanical, physical, chemical or biological, leading to various sciences of nature, mechanics being one of them. Mechanics deals with the objective laws of mechanical motion of bodies, the simplest form of motion.
In the study of a science of nature mathematics plays an important role. Mechanics is the first science of nature which was expressed in terms of mathematics by considering various mathematical models, associated to phenomena of the...
All phenomena in nature are characterized by motion; this is an essential property of matter, having infinitely many aspects. Motion can be mechani...
The importance of mathematics in the study of problems arising from the real world, and the increasing success with which it has been used to model situations ranging from the purely deterministic to the stochastic, is well established. The purpose of the set of volumes to which the present one belongs is to make available authoritative, up to date, and self-contained accounts of some of the most important and useful of these analytical approaches and techniques. Each volume provides a detailed introduction to a specific subject area of current importance that is summarized below, and then...
The importance of mathematics in the study of problems arising from the real world, and the increasing success with which it has been used to model si...
Inverse Problems is a monograph which contains a self-contained presentation of the theory of several major inverse problems and the closely related results from the theory of ill-posed problems. The book is aimed at a large audience which include graduate students and researchers in mathematical, physical, and engineering sciences and in the area of numerical analysis.
Inverse Problems is a monograph which contains a self-contained presentation of the theory of several major inverse problems and t...
The theory of singular perturbations has evolved as a response to the need to find approximate solutions (in an analytical form) to complex problems. Typically, such problems are expressed in terms of differential equations which contain at least one small parameter, and they can arise in many fields: fluid mechanics, particle physics, and combustion processes, to name but three.
The theory of singular perturbations has evolved as a response to the need to find approximate solutions (in an analytical form) to complex problem...
