### Higher Order Derivatives

The concept of higher order derivatives is useful in many branches of mathematics and its applications. As they are useful in many places, nth order derivatives are often defined directly. Higher Order Derivatives discusses these derivatives, their uses, and the relations among them. It covers…

Hardback – 2012-01-25

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Stable Solutions of Elliptic Partial Differential Equations

Stable solutions are ubiquitous in differential equations. They represent meaningful solutions from a physical point of view and appear in many applications, including mathematical physics (combustion, phase transition theory) and geometry (minimal surfaces). Stable Solutions of Elliptic Partial…

Hardback – 2011-03-15

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Quasilinear Hyperbolic Systems, Compressible Flows, and Waves

Filled with practical examples, Quasilinear Hyperbolic Systems, Compressible Flows, and Waves presents a self-contained discussion of quasilinear hyperbolic equations and systems with applications. It emphasizes nonlinear theory and introduces some of the most active research in the field. After…

Hardback – 2010-04-29

CRC Press*Monographs and Surveys in Pure and Applied Mathematics*### Asymptotics and Borel Summability

Incorporating substantial developments from the last thirty years into one resource, Asymptotics and Borel Summability provides a self-contained introduction to asymptotic analysis with special emphasis on topics not covered in traditional asymptotics books. The author explains basic ideas,…

Hardback – 2008-12-04

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Difference Methods for Singular Perturbation Problems

Difference Methods for Singular Perturbation Problems focuses on the development of robust difference schemes for wide classes of boundary value problems. It justifies the ε-uniform convergence of these schemes and surveys the latest approaches important for further progress in numerical…

Hardback – 2008-09-22

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Spectral Theory for Random and Nonautonomous Parabolic Equations and Applications

Providing a basic tool for studying nonlinear problems, Spectral Theory for Random and Nonautonomous Parabolic Equations and Applications focuses on the principal spectral theory for general time-dependent and random parabolic equations and systems. The text contains many new results and considers…

Hardback – 2008-03-24

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Isometries in Banach Spaces

#### Vector-valued Function Spaces and Operator Spaces, Volume Two

A continuation of the authors’ previous book, Isometries on Banach Spaces: Vector-valued Function Spaces and Operator Spaces, Volume Two covers much of the work that has been done on characterizing isometries on various Banach spaces. Picking up where the first volume left off, the book begins…

Hardback – 2007-11-15

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Smooth Homogeneous Structures in Operator Theory

Geometric ideas and techniques play an important role in operator theory and the theory of operator algebras. Smooth Homogeneous Structures in Operator Theory builds the background needed to understand this circle of ideas and reports on recent developments in this fruitful field of research.…

Hardback – 2005-11-01

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Fractional Cauchy Transforms

Presenting new results along with research spanning five decades, Fractional Cauchy Transforms provides a full treatment of the topic, from its roots in classical complex analysis to its current state. Self-contained, it includes introductory material and classical results, such as those associated…

Hardback – 2005-11-01

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Stability of Infinite Dimensional Stochastic Differential Equations with Applications

Stochastic differential equations in infinite dimensional spaces are motivated by the theory and analysis of stochastic processes and by applications such as stochastic control, population biology, and turbulence, where the analysis and control of such systems involves investigating their stability…

Hardback – 2005-08-23

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### An Introduction to Semiflows

This book introduces the class of dynamical systems called semiflows, which includes systems defined or modeled by certain types of differential evolution equations (DEEs). It focuses on the basic results of the theory of dynamical systems that can be extended naturally and applied to study the…

Hardback – 2004-10-14

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Shock Waves & Explosions

Understanding the causes and effects of explosions is important to experts in a broad range of disciplines, including the military, industrial and environmental research, aeronautic engineering, and applied mathematics. Offering an introductory review of historic research, Shock Waves and…

Hardback – 2004-06-11

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### An Elementary Approach to Homological Algebra

Homological algebra was developed as an area of study almost 50 years ago, and many books on the subject exist. However, few, if any, of these books are written at a level appropriate for students approaching the subject for the first time.An Elementary Approach to Homological Algebra fills that…

Hardback – 2003-05-28

CRC Press*Monographs and Surveys in Pure and Applied Mathematics*### Isometries on Banach Spaces

#### function spaces

Fundamental to the study of any mathematical structure is an understanding of its symmetries. In the class of Banach spaces, this leads naturally to a study of isometries-the linear transformations that preserve distances. In his foundational treatise, Banach showed that every linear isometry on…

Hardback – 2002-12-23

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Hyperbolic Conservation Laws and the Compensated Compactness Method

The method of compensated compactness as a technique for studying hyperbolic conservation laws is of fundamental importance in many branches of applied mathematics. Until now, however, most accounts of this method have been confined to research papers. Offering the first comprehensive treatment,…

Hardback – 2002-09-27

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Canonical Problems in Scattering and Potential Theory Part II

#### Acoustic and Electromagnetic Diffraction by Canonical Structures

Although the analysis of scattering for closed bodies of simple geometric shape is well developed, structures with edges, cavities, or inclusions have seemed, until now, intractable to analytical methods. This two-volume set describes a breakthrough in analytical techniques for accurately…

Hardback – 2002-04-29

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Canonical Problems in Scattering and Potential Theory - Two volume set

Although the analysis of scattering for closed bodies of simple geometric shape is well developed, structures with edges, cavities, or inclusions have seemed, until now, intractable to analytical methods. This two-volume set describes a breakthrough in analytical techniques for accurately…

Hardback – 2002-04-26

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Unbounded Functionals in the Calculus of Variations

#### Representation, Relaxation, and Homogenization

Over the last few decades, research in elastic-plastic torsion theory, electrostatic screening, and rubber-like nonlinear elastomers has pointed the way to some interesting new classes of minimum problems for energy functionals of the calculus of variations. This advanced-level monograph addresses…

Hardback – 2001-12-12

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### The Thermophysics of Porous Media

Models for the mechanical behavior of porous media introduced more than 50 years ago are still relied upon today, but more recent work shows that, in some cases, they may violate the laws of thermodynamics. In The Thermophysics of Porous Media, the author shows that physical consistency requires a…

Hardback – 2001-11-28

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Interfacial Phenomena and Convection

Interfacial phenomena driven by heat or mass transfer are widespread in science and various branches of engineering. Research in this area has become quite active in recent years, attributable in part, at least, to the entry of physicists and their sophisticated experimental techniques into the…

Hardback – 2001-11-13

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Inverse Boundary Spectral Problems

Inverse boundary problems are a rapidly developing area of applied mathematics with applications throughout physics and the engineering sciences. However, the mathematical theory of inverse problems remains incomplete and needs further development to aid in the solution of many important practical…

Hardback – 2001-07-30

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Canonical Problems in Scattering and Potential Theory Part 1

#### Canonical Structures in Potential Theory

Although the analysis of scattering for closed bodies of simple geometric shape is well developed, structures with edges, cavities, or inclusions have seemed, until now, intractable to analytical methods. This two-volume set describes a breakthrough in analytical techniques for accurately…

Hardback – 2001-05-30

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Nonlinear Hyperbolic Waves in Multidimensions

The propagation of curved, nonlinear wavefronts and shock fronts are very complex phenomena. Since the 1993 publication of his work Propagation of a Curved Shock and Nonlinear Ray Theory, author Phoolan Prasad and his research group have made significant advances in the underlying theory of these…

Hardback – 2001-05-18

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Large Deviations and Idempotent Probability

In the view of many probabilists, author Anatolii Puhalskii's research results stand among the most significant achievements in the modern theory of large deviations. In fact, his work marked a turning point in the depth of our understanding of the connections between the large deviation principle…

Hardback – 2001-05-07

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Abstract Cauchy Problems

#### Three Approaches

Although the theory of well-posed Cauchy problems is reasonably understood, ill-posed problems-involved in a numerous mathematical models in physics, engineering, and finance- can be approached in a variety of ways. Historically, there have been three major strategies for dealing with such problems…

Hardback – 2001-03-27

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Mathematical Aspects of Numerical Solution of Hyperbolic Systems

This important new book sets forth a comprehensive description of various mathematical aspects of problems originating in numerical solution of hyperbolic systems of partial differential equations. The authors present the material in the context of the important mechanical applications of such…

Hardback – 2000-12-21

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Supersymmetry In Quantum and Classical Mechanics

Following Witten's remarkable discovery of the quantum mechanical scheme in which all the salient features of supersymmetry are embedded, SCQM (supersymmetric classical and quantum mechanics) has become a separate area of research . In recent years, progress in this field has been dramatic and the…

Hardback – 2000-09-21

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Self-Similarity and Beyond

#### Exact Solutions of Nonlinear Problems

Nonlinearity plays a major role in the understanding of most physical, chemical, biological, and engineering sciences. Nonlinear problems fascinate scientists and engineers, but often elude exact treatment. However elusive they may be, the solutions do exist-if only one perseveres in seeking them…

Hardback – 2000-08-24

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Fundamentals of Infinite Dimensional Representation Theory

Infinite dimensional representation theory blossomed in the latter half of the twentieth century, developing in part with quantum mechanics and becoming one of the mainstays of modern mathematics. Fundamentals of Infinite Dimensional Representation Theory provides an accessible account of the…

Hardback – 2000-06-28

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Evolution Equations in Thermoelasticity

Although the study of classical thermoelasticity has provided information on linear systems, only recently have results on the asymptotic behavior completed our basic understanding of the generic behavior of solutions. Through systematic work that began in the 80s, we now also understand the basic…

Hardback – 2000-06-21

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Nonlinear Differential Equations in Ordered Spaces

Extremality results proved in this Monograph for an abstract operator equation provide the theoretical framework for developing new methods that allow the treatment of a variety of discontinuous initial and boundary value problems for both ordinary and partial differential equations, in explicit…

Hardback – 2000-06-14

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Variational and Potential Methods in the Theory of Bending of Plates with Transverse Shear Deformation

Elastic plates form a class of very important mechanical structures that appear in a wide range of practical applications, from building bodies to microchip production. As the sophistication of industrial designs has increased, so has the demand for greater accuracy in analysis. This in turn has…

Hardback – 2000-06-13

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Iterative Dynamic Programming

Dynamic programming is a powerful method for solving optimization problems, but has a number of drawbacks that limit its use to solving problems of very low dimension. To overcome these limitations, author Rein Luus suggested using it in an iterative fashion. Although this method required vast…

Hardback – 2000-01-27

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Painleve Analysis and Its Applications

With interest in the study of nonlinear systems at an all-time high, researchers are eager to explore the mysteries behind the nonlinear equations that govern various physical processes. Painléve analysis may be the only tool available that allows the analysis of both integrable and non-integrable…

Hardback – 1999-12-27

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Singular Partial Differential Equations

Singular Partial Differential Equations provides an analytical, constructive, and elementary approach to non-elementary problems. In the first monograph to consider such equations, the author investigates the solvability of partial differential equations and systems in a class of bounded functions…

Hardback – 1999-11-29

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Constructive Methods for Linear and Nonlinear Boundary Value Problems for Analytic Functions

Constructive methods developed in the framework of analytic functions effectively extend the use of mathematical constructions, both within different branches of mathematics and to other disciplines. This monograph presents some constructive methods-based primarily on original techniques-for…

Hardback – 1999-11-29

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Differential-Operator Equations

#### Ordinary and Partial Differential Equations

The theory of differential-operator equations is one of two modern theories for the study of both ordinary and partial differential equations, with numerous applications in mechanics and theoretical physics. Although a number of published works address differential-operator equations of the first…

Hardback – 1999-11-24

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Matrix Variate Distributions

Useful in physics, economics, psychology, and other fields, random matrices play an important role in the study of multivariate statistical methods. Until now, however, most of the material on random matrices could only be found scattered in various statistical journals. Matrix Variate…

Hardback – 1999-10-22

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Trends in Applications of Mathematics to Mechanics

The International Society for the Interaction of Mechanics and Mathematics has a long-standing and respected tradition of hosting symposia that provide a forum for disseminating new developments and methods. Trends in Applications of Mathematics to Mechanics represents the proceedings of the…

Hardback – 1999-10-22

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Introduction to Hamiltonian Fluid Dynamics and Stability Theory

Hamiltonian fluid dynamics and stability theory work hand-in-hand in a variety of engineering, physics, and physical science fields. Until now, however, no single reference addressed and provided background in both of these closely linked subjects. Introduction to Hamiltonian Fluid Dynamics and…

Hardback – 1999-09-29

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Direct and Indirect Boundary Integral Equation Methods

The computational power currently available means that practitioners can find extremely accurate approximations to the solutions of more and more sophisticated mathematical models-providing they know the right analytical techniques. In relatively simple terms, this book describes a class of…

Hardback – 1999-09-28

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### The Characteristic Method and Its Generalizations for First-Order Nonlinear Partial Differential Equations

Despite decades of research and progress in the theory of generalized solutions to first-order nonlinear partial differential equations, a gap between the local and the global theories remains: The Cauchy characteristic method yields the local theory of classical solutions. Historically, the global…

Hardback – 1999-06-25

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Partial Differential Equations in Clifford Analysis

Clifford analysis represents one of the most remarkable fields of modern mathematics. With the recent finding that almost all classical linear partial differential equations of mathematical physics can be set in the context of Clifford analysis-and that they can be obtained without applying any…

Hardback – 1999-01-06

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Analysis of Systems of Conservation Laws

Systems of partial differential equations reflecting conservation laws hold significant relevance to a variety of theoretical and practical applications, including compressible fluid flow, electromagnetism, elasticity theory, and other areas of continuum mechanics. This field of nonlinear analysis…

Hardback – 1998-12-30

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### The Two-Dimensional Riemann Problem in Gas Dynamics

The Riemann problem is the most fundamental problem in the entire field of non-linear hyperbolic conservation laws. Since first posed and solved in 1860, great progress has been achieved in the one-dimensional case. However, the two-dimensional case is substantially different. Although research…

Hardback – 1998-08-21

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Functional Differential Equations

#### II. C*-Applications Part 1: Equations with Continuous Coefficients

Together with the authors' Volume I. C*-Theory, the two parts comprising Functional Differential Equations: II. C*-Applications form a masterful work-the first thorough, up-to-date exposition of this field of modern analysis lying between differential equations and C*-algebras. The two parts of…

Hardback – 1998-08-15

CRC Press*Monographs and Surveys in Pure and Applied Mathematics*### Functional Differential Equations

#### II. C*-Applications Part 2: Equations with Disontinuous Coefficients and Boundary Value Problems

Together with the authors' Volume I. C*-Theory, the two parts comprising Functional Differential Equations: II. C*-Applications form a masterful work-the first thorough, up-to-date exposition of this field of modern analysis lying between differential equations and C*-algebras. The two parts of…

Hardback – 1998-08-15

CRC Press*Monographs and Surveys in Pure and Applied Mathematics*### Fundamentals of Applied Functional Analysis

Hardback – 1997-11-12

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Thermodynamics of Chaos and Order

The discovery of chaotic motion in low-dimensional systems raised the question: What kind of thermodynamics describes a system if it is neither ergodic nor Hamiltonian or possesses a finite number of degrees of freedom? This Monographs is the first to discuss this question.…

Hardback – 1997-10-24

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*### Representations on Krein Spaces [Hot] and Derivations of C*-Algebras

This text provides a comprehensive treatment of representations on indefinite metric spaces, and their applications to the theory of *-derivations of C*-algebras.The book consists of two parts. The first studies the geometry of indefinite metric spaces (Krein and (Pi)(kappa)-spaces) and describes…

Hardback – 1997-10-03

Chapman and Hall/CRC*Monographs and Surveys in Pure and Applied Mathematics*