Linear Algebra: An Introduction With Mathematica uses a matrix-based presentation and covers the standard topics any mathematician will need to understand linear algebra while using Mathematica. Development of analytical and computational skills is emphasized, and worked examples provide step-by-step methods for solving basic problems using Mathematica. The subject's rich pertinence to problem solving across disciplines is illustrated with applications in engineering, the natural sciences, computer animation, and statistics.

Quantification and modalities have always been topics of great interest for logicians. These two themes emerged from philosophy and
language in ancient times; they were studied by traditional informal
methods until the 20th century. In the last century the tools became
highly mathematical, and both modal logic and quantification found numerous applications in Computer Science. At the same time many other kinds of nonclassical logics were investigated and applied to Computer Science.
Although there exist several good books in propositional modal logics, this book is the first detailed monograph in nonclassical first-order quantification. It includes results obtained during the past thirty years. The field is very large, so we confine ourselves with only two kinds of logics: modal and superintuitionistic. The main emphasis of Volume 1 is model-theoretic, and it concentrates on descriptions of different sound semantics and completeness problem --- even for these seemingly simple questions we have our hands full. The major part of the presented material has never been published before. Some results are very recent, and for other results we either give new proofs or first proofs in full detail.

Handbook of Differential Equations: Evolutionary Equations is the last text of a five-volume reference in mathematics and methodology. This volume follows the format set by the preceding volumes, presenting numerous contributions that reflect the nature of the area of evolutionary partial differential equations. The book is comprised of five chapters that feature the following: A thorough discussion of the shallow-equations theory, which is used as a model for water waves in rivers, lakes and oceans. It covers the issues of modeling, analysis and applications * Evaluation of the singular limits of reaction-diffusion systems, where the reaction is fast compared to the other processes; and applications that range from the theory of the evolution of certain biological processes to the phenomena of Turing and cross-diffusion instability Detailed discussion of numerous problems arising from nonlinear optics, at the high-frequency and high-intensity regime * Geometric and diffractive optics, including wave interactions Presentation of the issues of existence, blow-up and asymptotic stability of solutions, from the equations of solutions to the equations of linear and non-linear thermoelasticity Answers to questions about unique space, such as continuation and backward uniqueness for linear second-order parabolic equations. Research mathematicians, mathematics lecturers and instructors, and academic students will find this book invaluable

Progress in mathematics is based on a thorough understanding of the mathematical objects under consideration, and yet many textbooks and monographs proceed to discuss general statements and assume that the reader can and will provide the mathematical infrastructure of examples and counterexamples. This book makes a deliberate effort to correct this situation: it is a collection of examples. The following table of contents describes its breadth and reveals the underlying motivation--differential geometry--in its many facets: Riemannian, symplectic, K*adahler, hyperK*adahler, as well as complex and quaternionic.

This handbook is the fourth volume in a series of volumes devoted to self-contained and up-to-date surveys in the theory of ordinary differential equations, with an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wider audience.
* Covers a variety of problems in ordinary differential equations
* Pure mathematical and real-world applications
* Written for mathematicians and scientists of many related fields

This handbook is the sixth and last volume in the series devoted to stationary partial differential equations. The topics covered by this volume include in particular domain perturbations for boundary value problems, singular solutions of semilinear elliptic problems, positive solutions to elliptic equations on unbounded domains, symmetry of solutions, stationary compressible Navier-Stokes equation, Lotka-Volterra systems with cross-diffusion, and fixed point theory for elliptic boundary value problems.
* Collection of self-contained, state-of-the-art surveys
* Written by well-known experts in the field
* Informs and updates on all the latest developments

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

A collection of self contained state-of-the art surveys. The authors have made an effort to achieve readability for mathematicians and scientists from other fields, for this series of handbooks to be a new reference for research, learning and teaching.
* Written by well-known experts in the field
* Self contained volume in series covering one of the most rapid developing topics in mathematics
* Informed and thoroughly updated for students, academics and researchers

System administration is about the design, running and maintenance of human-computer systems. Examples of human-computer systems include business enterprises, service institutions and any extensive machinery that is operated by, or interacts with human beings. System administration is often thought of as the technological side of a system: the architecture, construction and optimization of the collaborating parts, but it also occasionally touches on softer factors such as user assistance (help desks), ethical considerations in deploying a system, and the larger implications of its design for others who come into contact with it.
This book summarizes the state of research and practice in this emerging field of network and system administration, in an anthology of chapters written by the top academics in the field. The authors include members of the IST-EMANICS Network of Excellence in Network Management.
This book will be a valuable reference work for researchers and senior system managers wanting to understand the essentials of system administration, whether in practical application of a data center or in the design of new systems and data centers.
- Covers data center planning and design
- Discusses configuration management
- Illustrates business modeling and system administration
- Provides the latest theoretical developments

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

This handbook is volume III in a series devoted to stationary partial differential quations. Similarly as volumes I and II, it is a collection of self contained state-of-the-art surveys written by well known experts in the field. The topics covered by this handbook include singular and higher order equations, problems near critically, problems with anisotropic nonlinearities, dam problem, T-convergence and Schauder-type estimates. These surveys will be useful for both beginners and experts and speed up the progress of corresponding (rapidly developing and fascinating) areas of mathematics.

Key features:

- Written by well-known experts in the field
- Self-contained volume in series covering one of the most rapid developing topics in mathematics
- Written by well-known experts in the field
- Self-contained volume in series covering one of the most rapid developing topics in mathematics

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"

The ability of a structural assembly to carry loads and forces determines how stable it will be over time. Viewing structural assemblages as comprising columns, beams, arches, rings, and plates, this book will introduce the student to both a classical and advanced understanding of the mechanical behavior of such structural systems under load and how modeling the resulting strains can predict the overall future performance the stability of that structure. While covering traditional beam theory, the book is more focused on elastica theory in keeping with modern approaches. This text will be an expanded and updated version a similar, previously published book, but with pedagogical improvements and updated analytical methods.
This engineering textbook will provide a focused treatment on the study of how structures behave and perform when under stress loading, including plastic deformation and buckling. All advanced engineering students studying engineering mechanics, structural analysis and design, fatigue and failure, and other related subjects need to have this knowledge, and this book will provide it in a thorough and coherent fashion. Written by two of the world s leading engineering professors in this subject area, the pedagogy has been classroom-tested over many years and should find a receptive readership among both students and instructors.

* An understandable introduction to the theory of structural stability, useful for a wide variety of engineering disciplines, including mechanical, civil and aerospace engineering
* Covers both static and dynamic loads, for both conservative and nonconservative systems
* Emphasizes elastic behavior under loads, including vertical buckling, torsional buckling and nonlinear affects of structural system buckling and stability
* Case examples to illustrate real-world applications of Stability Theory"

This monograph provides the most recent and up-to-date developments on fractional differential and fractional integro-differential equations involving many different potentially useful operators of fractional calculus.
The subject of fractional calculus and its applications (that is, calculus of integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past three decades or so, due mainly to its demonstrated applications in numerous seemingly diverse and widespread fields of science and engineering.
Some of the areas of present-day applications of fractional models include Fluid Flow, Solute Transport or Dynamical Processes in Self-Similar and Porous Structures, Diffusive Transport akin to Diffusion, Material Viscoelastic Theory, Electromagnetic Theory, Dynamics of Earthquakes, Control Theory of Dynamical Systems, Optics and Signal Processing, Bio-Sciences, Economics, Geology, Astrophysics, Probability and Statistics, Chemical Physics, and so on.
In the above-mentioned areas, there are phenomena with estrange kinetics which have a microscopic complex behaviour, and their macroscopic dynamics can not be characterized by classical derivative models.
The fractional modelling is an emergent tool which use fractional differential equations including derivatives of fractional order, that is, we can speak about a derivative of order 1/3, or square root of 2, and so on. Some of such fractional models can have solutions which are non-differentiable but continuous functions, such as Weierstrass type functions. Such kinds of properties are, obviously, impossible for the ordinary models.
What are the useful properties of these fractional operators which help in the modelling of so many anomalous processes? From the point of view of the authors and from known experimental results, most of the processes associated with complex systems have non-local dynamics involving long-memory in time, and the fractional integral and fractional derivative operators do have some of those characteristics.
This book is written primarily for the graduate students and researchers in many different disciplines in the mathematical, physical, engineering and so many others sciences, who are interested not only in learning about the various mathematical tools and techniques used in the theory and widespread applications of fractional differential equations, but also in further investigations which emerge naturally from (or which are motivated substantially by) the physical situations modelled mathematically in the book.
This monograph consists of a total of eight chapters and a very extensive bibliography. The main objective of it is to complement the contents of the other books dedicated to the study and the applications of fractional differential equations. The aim of the book is to present, in a systematic manner, results including the existence and uniqueness of solutions for the Cauchy type problems involving nonlinear ordinary fractional differential equations, explicit solutions of linear differential equations and of the corresponding initial-value problems through different methods, closed-form solutions of ordinary and partial differential equations, and a theory of the so-called sequential linear fractional differential equations including a generalization of the classical Frobenius method, and also to include an interesting set of applications of the developed theory.
Key features:
- It is mainly application oriented.
- It contains a complete theory of Fractional Differential Equations.
- It can be used as a postgraduate-level textbook in many different disciplines within science and engineering.
- It contains an up-to-date bibliography.
- It provides problems and directions for further investigations.
- Fractional Modelling is an emergent tool with demonstrated applications in numerous seemingly diverse and widespread fields of science and engineering.
- It contains many examples.
- and so on

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

The book addresses many important new developments in the field. All the topics covered are of great interest to the readers because such inequalities have become a major tool in the analysis of various branches of mathematics.
* It contains a variety of inequalities which find numerous applications in various branches of mathematics.
* It contains many inequalities which have only recently appeared in the literature and cannot yet be found in other books.
* It will be a valuable reference for someone requiring a result about inequalities for use in some applications in various other branches of mathematics.
* Each chapter ends with some miscellaneous inequalities for futher study.
* The work will be of interest to researchers working both in pure and applied mathematics, and it could also be used as the text for an advanced graduate course.

It has widely been recognized that submodular functions play essential roles in efficiently solvable combinatorial optimization problems. Since the publication of the 1st edition of this book fifteen years ago, submodular functions have been showing further increasing importance in optimization, combinatorics, discrete mathematics, algorithmic computer science, and algorithmic economics, and there have been made remarkable developments of theory and algorithms in submodular functions. The 2nd edition of the book supplements the 1st edition with a lot of remarks and with new two chapters: "Submodular Function Minimization" and "Discrete Convex Analysis." The present 2nd edition is still a unique book on submodular functions, which is essential to students and researchers interested in combinatorial optimization, discrete mathematics, and discrete algorithms in the fields of mathematics, operations research, computer science, and economics.

Key features:

- Self-contained exposition of the theory of submodular functions.
- Selected up-to-date materials substantial to future developments.
- Polyhedral description of Discrete Convex Analysis.
- Full description of submodular function minimization algorithms.
- Effective insertion of figures.
- Useful in applied mathematics, operations research, computer science, and economics.
- Self-contained exposition of the theory of submodular functions.
- Selected up-to-date materials substantial to future developments.
- Polyhedral description of Discrete Convex Analysis.
- Full description of submodular function minimization algorithms.
- Effective insertion of figures.
- Useful in applied mathematics, operations research, computer science, and economics.

This book contains around 80 articles on major writings in mathematics published between 1640 and 1940. All aspects of mathematics are covered: pure and applied, probability and statistics, foundations and philosophy. Sometimes two writings from the same period and the same subject are taken together. The biography of the author(s) is recorded, and the circumstances of the preparation of the writing are given. When the writing is of some lengths an analytical table of its contents is supplied. The contents of the writing is reviewed, and its impact described, at least for the immediate decades. Each article ends with a bibliography of primary and secondary items.
.First book of its kind
.Covers the period 1640-1940 of massive development in mathematics
.Describes many of the main writings of mathematics
.Articles written by specialists in their field

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

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

This monograph is the first and an initial introduction to the theory of bitopological spaces and its applications. In particular, different families of subsets of bitopological spaces are introduced and various relations between two topologies are analyzed on one and the same set; the theory of dimension of bitopological spaces and the theory of Baire bitopological spaces are constructed, and various classes of mappings of bitopological spaces are studied. The previously known results as well the results obtained in this monograph are applied in analysis, potential theory, general topology, and theory of ordered topological spaces. Moreover, a high level of modern knowledge of bitopological spaces theory has made it possible to introduce and study algebra of new type, the corresponding representation of which brings one to the special class of bitopological spaces.
It is beyond any doubt that in the nearest future the areas of essential applications will be the theories of linear topological spaces and topological groups, algebraic and differential topologies, the homotopy theory, not to mention other fundamental areas of modern mathematics such as geometry, mathematical logic, the probability theory and many other areas, including those of applied nature.
Key Features:
- First monograph is "Generalized Lattices"
* The first introduction to the theory of bitopological spaces and its applications.

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

The present work is a continuation of the authors' acclaimed multi-volume A
Practical Logic of Cognitive Systems. After having investigated the notion of
relevance in their previous volume, Gabbay and Woods now turn to abduction. In
this highly original approach, abduction is construed as ignorance-preserving
inference, in which conjecture plays a pivotal role. Abduction is a response to a
cognitive target that cannot be hit on the basis of what the agent currently knows.
The abducer selects a hypothesis which were it true would enable the reasoner to attain his target. He concludes from this fact that the hypothesis may be conjectured. In allowing conjecture to stand in for the knowledge he fails to have, the abducer reveals himself to be a satisficer, since an abductive solution is not a solution from knowledge. Key to the authors' analysis is the requirement that a conjectured proposition is not just what a reasoner might allow himself to assume, but a proposition he must defeasibly release as a premiss for further inferences in the domain of enquiry in which the original abduction problem has arisen.

The coverage of the book is extensive, from the philosophy of science to
computer science and AI, from diagnostics to the law, from historical explanation to linguistic interpretation. One of the volume's strongest contributions is its exploration of the abductive character of criminal trials, with special attention given to the standard of proof beyond a reasonable doubt.

Underlying their analysis of abductive reasoning is the authors' conception of
practical agency. In this approach, practical agency is dominantly a matter of the
comparativemodesty of an agent's cognitive agendas, together with comparatively scant resources available for their advancement. Seen in these ways, abduction has a significantly practical character, precisely because it is a form of inference that satisfices rather than maximizes its response to the agent's cognitive target.

The Reach of Abduction will be necessary reading for researchers, graduate
students and senior undergraduates in logic, computer science, AI, belief dynamics, argumentation theory, cognitive psychology and neuroscience, linguistics, forensic science, legal reasoning and related areas.

Key features:

- Reach of Abduction is fully integrated with a background logic of cognitive systems.

- The most extensive coverage compared to competitive works.

- Demonstrates not only that abduction is a form of ignorance preserving
inference but that it is a mode of inference that is wholly rational.

- Demonstrates the satisficing rather than maximizing character of
abduction.

- The development of formal models of abduction is considerably more extensive than one finds in existing literature. It is an especially impressive amalgam of sophisticated
conceptual analysis and extensive logical modelling.
- Reach of Abduction is fully integrated with a background logic of cognitive systems.
- The most extensive coverage compared to competitive works
- Demonstrates not only that abduction is a form of ignorance preserving
inference but that it is a mode of inference that is wholly rational.
- Demonstrates the satisficing rather than maximizing character of
abduction.
- The development of formal models of abduction isconsiderably more extensive than one finds in existing literature. It is an especially impressive amalgam of sophisticated
conceptual analysis and extensive logical modelling.

One of the most frequently occurring types of optimization problems involves decision variables which have to take integer values. From a practical point of view, such problems occur in countless areas of management, engineering, administration, etc., and include such problems as location of plants or warehouses, scheduling of aircraft, cutting raw materials to prescribed dimensions, design of computer chips, increasing reliability or capacity of networks, etc. This is the class of problems known in the professional literature as "discrete optimization" problems. While these problems are of enormous applicability, they present many challenges from a computational point of view. This volume is an update on the impressive progress achieved by mathematicians, operations researchers, and computer scientists in solving discrete optimization problems of very large sizes. The surveys in this volume present a comprehensive overview of the state of the art in discrete optimization and are written by the most prominent researchers from all over the world.

This volume describes the tremendous progress in discrete optimization achieved in the last 20 years since the publication of Discrete Optimization '77, Annals of Discrete Mathematics, volumes 4 and 5, 1979 (Elsevier). It contains surveys of the state of the art written by the most prominent researchers in the field from all over the world, and covers topics like neighborhood search techniques, lift and project for mixed 0-1 programming, pseudo-Boolean optimization, scheduling and assignment problems, production planning, location, bin packing, cutting planes, vehicle routing, and applications to graph theory, mechanics, chip design, etc.

Key features:
state of the art surveys
comprehensiveness
prominent authors
theoretical, computational and applied aspects.

This book is a reprint of "Discrete Applied Mathematics" Volume 23, Numbers 1-3
"