The material collected in this volume discusses the present as well as expected future directions of development of the field with particular emphasis on applications. The seven survey articles present different topics in Evolutionary PDE s, written by leading experts.
- Review of new results in the area
- Continuation of previous volumes in the handbook series covering Evolutionary PDEs
- Written by leading experts

Aimed at starting researchers in the field, Realizability gives a rigorous, yet reasonable introduction to the basic concepts of a field which has passed several successive phases of abstraction. Material from previously unpublished sources such as Ph.D. theses, unpublished papers, etc. has been molded into one comprehensive presentation of the subject area.
- The first book to date on this subject area
- Provides an clear introduction to Realizability with a comprehensive bibliography
- Easy to read and mathematically rigorous
- Written by an expert in the field

Fluid mechanics is the study of how fluids behave and interact under various forces and in various applied situations, whether in liquid or gas state or both. The author compiles pertinent information that are introduced in the more advanced classes at the senior level and at the graduate level. "Advanced Fluid Mechanics" courses typically cover a variety of topics involving fluids in various multiple states (phases), with both elastic and non-elastic qualities, and flowing in complex ways. This new text will integrate both the simple stages of fluid mechanics ("Fundamentals") with those involving more complex parameters, including Inviscid Flow in multi-dimensions, Viscous Flow and Turbulence, and a succinct introduction to Computational Fluid Dynamics. It will offer exceptional pedagogy, for both classroom use and self-instruction, including many worked-out examples, end-of-chapter problems, and actual computer programs that can be used to reinforce theory with real-world applications.
Professional engineers as well as Physicists and Chemists working in the analysis of fluid behavior in complex systems will find the contents of this book useful.All manufacturing companies involved in any sort of systems that encompass fluids and fluid flow analysis (e.g., heat exchangers, air conditioning and refrigeration, chemical processes, etc.) or energy generation (steam boilers, turbines and internal combustion engines, jet propulsion systems, etc.), or fluid systems and fluid power (e.g., hydraulics, piping systems, and so on)will reap the benefits of this text.
- Offers detailed derivation of fundamental equations for better comprehension of more advanced mathematical analysis
-Provides groundwork for more advanced topics on boundary layer analysis, unsteady flow, turbulent modeling, and computational fluid dynamics
- Includes worked-out examples and end-of-chapter problems as well as a companion web site with sample computational programs and Solutions Manual

This contemporary first course focuses on concepts and ideas of Measure Theory, highlighting the theoretical side of the subject. Its primary intention is to introduce Measure Theory to a new generation of students, whether in mathematics or in one of the sciences, by offering them on the one hand a text with complete, rigorous and detailed proofs--sketchy proofs have been a perpetual complaint, as demonstrated in the many Amazon reader reviews critical of authors who "omit 'trivial' steps" and "make not-so-obvious 'it is obvious' remarks." On the other hand, Kubrusly offers a unique collection of fully hinted problems. On the other hand, Kubrusly offers a unique collection of fully hinted problems. The author invites the readers to take an active part in the theory construction, thereby offering them a real chance to acquire a firmer grasp on the theory they helped to build. These problems, at the end of each chapter, comprise complements and extensions of the theory, further examples and counterexamples, or auxiliary results. They are an integral part of the main text, which sets them apart from the traditional classroom or homework exercises.
JARGON BUSTER:
measure theory
Measure theory investigates the conditions under which integration can take place.
It considers various ways in which the "size" of a set can be estimated.
This topic is studied in pure mathematics programs but the theory is also foundational for students of statistics and probability, engineering, and financial engineering.
Key Features
* Designed with a minimum of prerequisites (intro analysis, and for Ch 5, linear algebra)
* Includes 140 classical measure-theory problems
* Carefully crafted to present essential elements of the theory in compact form

The Curry-Howard isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as found in type theory. For instance,
minimal propositional logic corresponds to simply typed lambda-calculus, first-order logic corresponds to dependent types, second-order logic corresponds to polymorphic types, sequent calculus is related to explicit substitution, etc.
The isomorphism has many aspects, even at the syntactic level:
formulas correspond to types, proofs correspond to terms, provability corresponds to inhabitation, proof normalization corresponds to term reduction, etc.
But there is more to the isomorphism than this. For instance, it is an old idea---due to Brouwer, Kolmogorov, and Heyting---that a constructive proof of an implication is a procedure that transforms
proofs of the antecedent into proofs of the succedent; the Curry-Howard isomorphism gives syntactic representations of such procedures. The Curry-Howard isomorphism also provides theoretical foundations for many modern proof-assistant systems (e.g. Coq).
This book give an introduction to parts of proof theory and related aspects of type theory relevant for the Curry-Howard isomorphism. It can serve as an introduction to any or both of typed lambda-calculus and intuitionistic logic.

Key features
- The Curry-Howard Isomorphism treated as common theme
- Reader-friendly introduction to two complementary subjects: Lambda-calculus and constructive logics
- Thorough study of the connection between calculi and logics
- Elaborate study of classical logics and control operators
- Account of dialogue games for classical and intuitionistic logic
- Theoretical foundations of computer-assisted reasoning

. The Curry-Howard Isomorphism treated as the common theme.
. Reader-friendly introduction to two complementary subjects: lambda-calculus and constructive logics
. Thorough study of the connection between calculi and logics.
. Elaborate study of classical logics and control operators.
. Account of dialogue games for classical and intuitionistic logic.
. Theoretical foundations of computer-assisted reasoning"

Engineering Ethics is the application of philosophical and moral systems to the proper judgment and behavior by engineers in conducting their work, including the products and systems they design and the consulting services they provide. In light of the work environment that inspired the new Sarbanes/Oxley federal legislation on whistle-blowing protections, a clear understanding of Engineering Ethics is needed like never before.
Beginning with a concise overview of various approaches to engineering ethics, the real heart of the book will be some 13 detailed case studies, delving into the history behind each one, the official outcome and the real story behind what happened. Using a consistent format and organization for each one giving background, historical summary, news media effects, outcome and interpretation--these case histories will be used to clearly illustrate the ethics issues at play and what should or should not have been done by the engineers, scientists and managers involved in each instance.
* Covers importance and practical benefits of systematic ethical behavior in any engineering work environment.
* Only book to explain implications of the Sarbanes/Oxley "Whistle-Blowing" federal legislation
* 13 actual case histories, plus 10 additional "anonymous" case histories-in consistent format-will clearly demonstrate the relevance of ethics in the outcomes of each one
* Offers actual investigative reports, with evidentiary material, legal proceedings, outcome and follow-up analysis
* Appendix offers copies of the National Society of Professional Engineers Code of Ethics for Engineers and the Institute of Electrical and Electronic Engineers Code of Ethics"

In the series of volumes which together will constitute the "Handbook of Differential Geometry" we try to give a rather complete survey of the field of differential geometry. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent).
All chapters are written by experts in the area and contain a large bibliography. In this second volume a wide range of areas in the very broad field of differential geometry is discussed, as there are Riemannian geometry, Lorentzian geometry, Finsler geometry, symplectic geometry, contact geometry, complex geometry, Lagrange geometry and the geometry of foliations. Although this does not cover the whole of differential geometry, the reader will be provided with an overview of some its most important areas.
. Written by experts and covering recent research
. Extensive bibliography
. Dealing with a diverse range of areas
. Starting from the basics

After a brief description of the evolution of thinking on Finslerian geometry starting from Riemann, Finsler, Berwald and Elie Cartan, the book gives a clear and precise treatment of this geometry. The first three chapters develop the basic notions and methods, introduced by the author, to reach the global problems in Finslerian Geometry. The next five chapters are independent of each other, and deal with among others the geometry of generalized Einstein manifolds, the classification of Finslerian manifolds of constant sectional curvatures. They also give a treatment of isometric, affine, projective and conformal vector fields on the unitary tangent fibre bundle.

Key features

- Theory of connections of vectors and directions on the unitary tangent fibre bundle.
- Complete list of Bianchi identities for a regular conection of directions.
- Geometry of generalized Einstein manifolds.
- Classification of Finslerian manifolds.
- Affine, isometric, conformal and projective vector fields on the unitary tangent fibre bundle.
- Theory of connections of vectors and directions on the unitary tangent fibre bundle.
- Complete list of Bianchi identities for a regular conection of directions.
- Geometry of generalized Einstein manifolds.
- Classification of Finslerian manifolds.
- Affine, isometric, conformal and projective vector fields on the unitary tangent fibre bundle.

Provides mathematical tools and techniques used to solve problems in physics. This work covers the mathematics necessary for advanced study in physics and engineering. It includes differential forms and the elegant forms of Maxwell's equations, and a chapter on probability and statistics. It also illustrates and proves mathematical relations.

The book contains seven survey papers about ordinary differential equations.
The common feature of all papers consists in the fact that nonlinear equations are focused on. This reflects the situation in modern mathematical modelling - nonlinear mathematical models are more realistic and describe the real world problems more accurately. The implications are that new methods and approaches have to be looked for, developed and adopted in order to understand and solve nonlinear ordinary differential equations.
The purpose of this volume is to inform the mathematical community and also other scientists interested in and using the mathematical apparatus of ordinary differential equations, about some of these methods and possible applications.

The book could be a good companion for any graduate student in partial differential equations or in applied mathematics. Each chapter brings indeed new ideas and new techniques which can be used in these fields. The differents chapters can be read independently and are of great pedagogical value. The advanced researcher will find along the book the most recent achievements in various fields.
.Independent chapters
.Most recent advances in each fields
.Hight didactic quality
.Self contained
.Excellence of the contributors
.Wide range of topics

An in-depth look at real analysis and its applications, including an introduction to wavelet
analysis, a popular topic in "applied real analysis." This text makes a very natural connection between the classic pure analysis and the applied topics, including measure theory, Lebesgue Integral,
harmonic analysis and wavelet theory with many associated applications.
*The text is relatively elementary at the start, but the level of difficulty steadily increases
*The book contains many clear, detailed examples, case studies and exercises
*Many real world applications relating to measure theory and pure analysis
*Introduction to wavelet analysis

This is the unique book on cross-fertilisations between stream ciphers and number theory. It systematically and comprehensively covers known connections between the two areas that are available only in research papers. Some parts of this book consist of new research results that are not available elsewhere. In addition to exercises, over thirty research problems are presented in this book. In this revised edition almost every chapter was updated, and some chapters were completely rewritten. It is useful as a textbook for a graduate course on the subject, as well as a reference book for researchers in related fields.
.Unique book on interactions of stream ciphers and number theory.
.Research monograph with many results not available elsewhere.
.A revised edition with the most recent advances in this subject.
.Over thirty research problems for stimulating interactions between the two areas.
.Written by leading researchers in stream ciphers and number theory.

The text is for a two semester course in advanced calculus. It develops the basic ideas of calculus rigorously but with an eye to showing how mathematics connects with other areas of science and engineering. In particular, effective numerical computation is developed as an important aspect of mathematical analysis.
* Maintains a rigorous presentation of the main ideas of advanced calculus, interspersed with applications that show how to analyze real problems
* Includes a wide range of examples and exercises drawn from mechanics, biology, chemical engineering and economics
* Describes links to numerical analysis and provides opportunities for computation; some MATLAB
codes are available on the author's webpage
* Enhanced by an informal and lively writing style

Science and engineering students depend heavily on concepts of mathematical modeling. In an age where almost everything is done on a computer, author Clive Dym believes that students need to understand and "own" the underlying mathematics that computers are doing on their behalf. His goal for Principles of Mathematical Modeling, Second Edition, is to engage the student reader in developing a foundational understanding of the subject that will serve them well into their careers.
The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools including dimensional analysis, scaling techniques, and approximation and validation techniques. The second half demonstrates the latest applications for these tools to a broad variety of subjects, including exponential growth and decay in fields ranging from biology to economics, traffic flow, free and forced vibration of mechanical and other systems, and optimization problems in biology, structures, and social decision making.
Prospective students should have already completed courses in elementary algebra, trigonometry, and first-year calculus and have some familiarity with differential equations and basic physics.

* Serves as an introductory text on the development and application of mathematical models
* Focuses on techniques of particular interest to engineers, scientists, and others who model continuous systems
* Offers more than 360 problems, providing ample opportunities for practice
* Covers a wide range of interdisciplinary topics--from engineering to economics to the sciences
* Uses straightforward language and explanations that make modeling easy to understand and apply
New to this Edition:
* A more systematic approach to mathematical modeling, outlining ten specific principles
* Expanded and reorganized chapters that flow in an increasing level of complexity
* Several new problems and updated applications
* Expanded figure captions that provide more information
* Improved accessibility and flexibility for teaching

Algorithmic Graph Theory and Perfect Graphs, first published in 1980, has become the classic introduction to the field. This new Annals edition continues to convey the message that intersection graph models are a necessary and important tool for solving real-world problems. It remains a stepping stone from which the reader may embark on one of many fascinating research trails.
The past twenty years have been an amazingly fruitful period of research in algorithmic graph theory and structured families of graphs. Especially important have been the theory and applications of new intersection graph models such as generalizations of permutation graphs and interval graphs. These have lead to new families of perfect graphs and many algorithmic results. These are surveyed in the new Epilogue chapter in this second edition.
-New edition of the "Classic" book on the topic
-Wonderful introduction to a rich research area
-Leading author in the field of algorithmic graph theory
-Beautifully written for the new mathematician or computer scientist
-Comprehensive treatment

This book is written to meet the needs of undergraduates in applied mathematics, physics and engineering studying partial differential equations. It is a more modern, comprehensive treatment intended for students who need more than the purely numerical solutions provided by programs like the MATLAB PDE Toolbox, and those obtained by the method of separation of variables, which is usually the only theoretical approach found in the majority of elementary textbooks.
This will fill a need in the market for a more modern text for future working engineers, and one that students can read and understand much more easily than those currently on the market.
* Includes new and important materials necessary to meet current demands made by diverse applications
* Very detailed solutions to odd numbered problems to help students
* Instructor's Manual Available

This is the first book that can be considered a textbook on thin film science, complete with exercises at the end of each chapter. Ohring has contributed many highly regarded reference books to the AP list, including Reliability and Failure of Electronic Materials and the Engineering Science of Thin Films. The knowledge base is intended for science and engineering students in advanced undergraduate or first-year graduate level courses on thin films and scientists and engineers who are entering or require an overview of the field.
Since 1992, when the book was first published, the field of thin films has expanded tremendously, especially with regard to technological applications. The second edition will bring the book up-to-date with regard to these advances. Most chapters have been greatly updated, and several new chapters have been added.

Offering a concise collection of MatLab programs and exercises to accompany a third semester course in multivariable calculus, "A MatLab Companion for Multivariable Calculus" introduces simple numerical procedures such as numerical differentiation, numerical integration and Newton's method in several variables, thereby allowing students to tackle realistic problems. The many examples show students how to use MatLab effectively and easily in many contexts. Numerous exercises in mathematics and applications areas are presented, graded from routine to more demanding projects requiring some programming. Matlab M-files are provided on the Harcourt/Academic Press web site at http: //www.harcourt-ap.com/matlab.html.
* Computer-oriented material that complements the essential topics in multivariable calculus
* Main ideas presented with examples of computations and graphics displays using MATLAB
* Numerous examples of short code in the text, which can be modified for use with the exercises
* MATLAB files are used to implement graphics displays and contain a collection of mfiles which can serve as demos

"Difference Equations, Second Edition," presents a practical introduction to this important field of solutions for engineering and the physical sciences. Topic coverage includes numerical analysis, numerical methods, differential equations, combinatorics and discrete modeling. A hallmark of this revision is the diverse application to many subfields of mathematics.

* Phase plane analysis for systems of two linear equations
* Use of equations of variation to approximate solutions
* Fundamental matrices and Floquet theory for periodic systems
* LaSalle invariance theorem
* Additional applications: secant line method, Bison problem, juvenile-adult population model, probability theory
* Appendix on the use of "Mathematica" for analyzing difference equaitons
* Exponential generating functions
* Many new examples and exercises

This revised edition presents the relevant aspects of transformational geometry, matrix algebra, and calculus to those who may be lacking the necessary mathematical foundations of applied multivariate analysis. It brings up-to-date many definitions of mathematical concepts and their operations. It also clearly defines the relevance of the exercises to concerns within the business community and the social and behavioral sciences. Readers gain a technical background for tackling applications-oriented multivariate texts and receive a geometric perspective for understanding multivariate methods."Mathematical Tools for Applied Multivariate Analysis, Revised Edition illustrates major concepts in matrix algebra, linear structures, and eigenstructures geometrically, numerically, and algebraically. The authors emphasize the applications of these techniques by discussing potential solutions to problems outlined early in the book. They also present small numerical examples of the various concepts.
Key Features
* Provides a technical base for tackling most applications-oriented multivariate texts
* Presents a geometric perspective for aiding ones intuitive grasp of multivariate methods
* Emphasizes technical terms current in the social and behavioral sciences, statistics, and mathematics
* Can be used either as a stand-alone text or a supplement to a multivariate statistics textbook
* Employs many pictures and diagrams to convey an intuitive perception of matrix algebra concepts
* Toy problems provide a step-by-step approach to each model and matrix algebra concept
* Provides solutions for all exercises

This volume is a thorough introduction to contemporary research in elasticity, and may be used as a working textbook at the graduate level for courses in pure or applied mathematics or in continuum mechanics. It provides a thorough description (with emphasis on the nonlinear aspects) of the two competing mathematical models of three-dimensional elasticity, together with a mathematical analysis of these models. The book is as self-contained as possible.

This book is a landmark title in the continuous move from integer to non-integer in mathematics: from integer numbers to real numbers, from factorials to the gamma function, from integer-order models to models of an arbitrary order. For historical reasons, the word 'fractional' is used instead of the word 'arbitrary'.
This book is written for readers who are new to the fields of fractional derivatives and fractional-order mathematical models, and feel that they need them for developing more adequate mathematical models.
In this book, not only applied scientists, but also pure mathematicians will find fresh motivation for developing new methods and approaches in their fields of research.
A reader will find in this book everything necessary for the initial study and immediate application of fractional derivatives fractional differential equations, including several necessary special functions, basic theory of fractional differentiation, uniqueness and existence theorems, analytical numerical methods of solution of fractional differential equations, and many inspiring examples of applications.

Key Features
* A unique survey of many applications of fractional calculus
* Presents basic theory
* Includes a unified presentation of selected classical results, which are important for applications
* Provides many examples
* Contains a separate chapter of fractional order control systems, which opens new perspectives in control theory
* The first systematic consideration of Caputo's fractional derivative in comparison with other selected approaches
* Includes tables of fractional derivatives, which can be used for evaluation of all considered types of fractional derivatives

An Introduction to Wavelets is the first volume in a new series, WAVELET ANALYSIS AND ITS APPLICATIONS. This is an introductory treatise on wavelet analysis, with an emphasis on spline wavelets and time-frequency analysis. Among the basic topics covered in this book are time-frequency localization, integral wavelet transforms, dyadic wavelets, frames, spline-wavelets, orthonormal wavelet bases, and wavelet packets. In addition, the author presents a unified treatment of nonorthogonal, semiorthogonal, and orthogonal wavelets. This monograph is self-contained, the only prerequisite being a basic knowledge of function theory and real analysis. It is suitable as a textbook for a beginning course on wavelet analysis and is directed toward both mathematicians and engineers who wish to learn about the subject. Specialists may use this volume as a valuable supplementary reading to the vast literature that has already emerged in this field.
Key Features
* This is an introductory treatise on wavelet analysis, with an emphasis on spline-wavelets and time-frequency analysis
* This monograph is self-contained, the only prerequisite being a basic knowledge of function theory and real analysis
* Suitable as a textbook for a beginning course on wavelet analysis

This book constitutes a first- or second-year graduate course in operator theory. It is a field that has great importance for other areas of mathematics and physics, such as algebraic topology, differential geometry, and quantum mechanics. It assumes a basic knowledge in functional analysis but no prior acquaintance with operator theory is required.