Using the author's considerable experience of applying Mathcad to engineering problems, Essential Mathcad introduces the most powerful functions and features of the software and teaches how to apply these to create comprehensive calculations for any quantitative subject. The simple, step-by-step approach makes this book an ideal Mathcad text for professional engineers as well as engineering, science, and math students. Examples from a variety of fields demonstrate the power and utility of Mathcad's tools, while also demonstrating how other software, such as Excel spreadsheets, can be incorporated effectively.
*Many more applied examples and exercises from a wide variety of engineering, science, and math fields
* New: more thorough discussions of differential equations, 3D plotting, and curve fitting.
* A step-by-step approach enables easy learning for professionals and students alike

Materials Science for Engineering Students offers students of introductory materials science and engineering, and their instructors, a fresh perspective on the rapidly evolving world of advanced engineering materials. This new, concise text takes a more contemporary approach to materials science than the more traditional books in this subject, with a special emphasis on using an inductive method to first introduce materials and their particular properties and then to explain the underlying physical and chemical phenomena responsible for those properties. The text pays particular attention to the newer classes of materials, such as ceramics, polymers and composites, and treats them as part of two essential classes, structural materials and functional materials, rather than the traditional method of emphasizing structural materials alone.
*Presents balanced coverage of both "structural" and "functional" materials.
*Types of materials are introduced first, followed by explanation of physical and chemical phenomena that drive their specific properties.
*Strong focus on engineering applications of materials
*The first materials science text to include a whole chapter devoted to batteries.
*Provides clear, mathematically simple explanations of basic chemistry and physics underlying materials properties.

The aim of this Handbook is to acquaint the reader with the current status of the theory of evolutionary partial differential equations, and with some of its applications. Evolutionary partial differential equations made their first appearance in the 18th century, in the endeavor to understand the motion of fluids and other continuous media. The active research effort over the span of two centuries, combined with the wide variety of physical phenomena that had to be explained, has resulted in an enormous body of literature. Any attempt to produce a comprehensive survey would be futile. The aim here is to collect review articles, written by leading experts, which will highlight the present and expected future directions of development of the field. The emphasis will be on nonlinear equations, which pose the most challenging problems today.
. Volume I of this Handbook does focus on the abstract theory of evolutionary equations.
. Volume 2 considers more concrete problems relating to specific applications.
. Together they provide a panorama of this amazingly complex and rapidly developing branch of mathematics.

A unique and thorough investigation of the shift towards Europe-wide energy regulation, markets and business strategies, and the extent to which energy systems have become more liberalised over this period.
"Reshaping of European Gas and Electricity Industries" analyses the key issues facing the European energy industry, from a regulatory, market, and business perspective. Current challenges within the field are also reviewed, including competitive and environmental issues.
* Liberalization: Delivers timely insights into the changes facing the European energy industry in the face of deregulation.
* Competition: A direct look at business and marketing strategies in response to the influx of competition from across the globe.
* Environment: Provides powerful [insights] into the way environmentally-based legislation has now become a key driver of the energy industry in Europe

The book is intended for people (graduates, researchers, but also undergraduates with a good mathematical background) involved in the study of (static) optimization problems (in finite-dimensional spaces). It contains a lot of material, from basic tools of convex analysis to optimality conditions for smooth optimization problems, for non smooth optimization problems and for vector optimization problems.
The development of the subjects are self-contained and the bibliographical references are usually treated in different books (only a few books on optimization theory deal also with vector problems), so the book can be a starting point for further readings in a more specialized literature.
Assuming only a good (even if not advanced) knowledge of mathematical analysis and linear algebra, this book presents various aspects of the mathematical theory in optimization problems. The treatment is performed in finite-dimensional spaces and with no regard to algorithmic questions. After two chapters concerning, respectively, introductory subjects and basic tools and concepts of convex analysis, the book treats extensively mathematical programming problems in the smmoth case, in the nonsmooth case and finally vector optimization problems.
- Self-contained
- Clear style and results are either proved or stated precisely with adequate references
- The authors have several years experience in this field
- Several subjects (some of them non usual in books of this kind) in one single book, including nonsmooth optimization and vector optimization problems
- Useful long references list at the end of each chapter

The extensive additions, and the inclusion of a new chapter, has made this classic work by Jeffrey, now joined by co-author Dr. H.H. Dai, an even more essential reference for researchers and students in applied mathematics, engineering, and physics. It provides quick access to important formulas, relationships between functions, and mathematical techniques that range from matrix theory and integrals of commonly occurring functions to vector calculus, ordinary and partial differential equations, special functions, Fourier series, orthogonal polynomials, and Laplace and Fourier transforms. During the preparation of this edition full advantage was taken of the recently updated seventh edition of Gradshteyn and Ryzhik's Table of Integrals, Series, and Products and other important reference works. Suggestions from users of the third edition of the Handbook have resulted in the expansion of many sections, and because of the relevance to boundary value problems for the Laplace equation in the plane, a new chapter on conformal mapping, has been added, complete with an atlas of useful mappings. A unique feature of the fourth edition is the provision of a CD-ROM that provides ready access to the most frequently used parts of the book, together with helpful notes for users of the Handbook.
- Comprehensive coverage in reference form of the branches of mathematics used in science and engineering
- Organized to make results involving integrals and functions easy to locate
- Results illustrated by worked examples
- Unique CD-ROMthat provides access to the most frequently used parts of the book
- CD-ROM contains helpful notes for users

"A Concrete Approach to Abstract Algebra"begins with a concrete and thorough examination of familiar objects like integers, rational numbers, real numbers, complex numbers, complex conjugation and polynomials, in this unique approach, the author builds upon these familar objects and then uses them to introduce and motivate advanced concepts in algebra in a manner that is easier to understand for most students.The text will be of particular interest to teachers and future teachers as it links abstract algebra to many topics wich arise in courses in algebra, geometry, trigonometry, precalculus and calculus. The final four chapters presentthe more theoretical material needed for graduate study.

Ancillary list: * Online ISM- http: //textbooks.elsevier.com/web/manuals.aspx?isbn=9780123749413 * Online SSM- http: //www.elsevierdirect.com/product.jsp?isbn=9780123749413 * Ebook- http: //www.elsevierdirect.com/product.jsp?isbn=9780123749413
Presents a more natural 'rings first' approachto effectively leading the student into the the abstract material of the course by the use of motivating concepts from previous math courses to guide the discussion of abstract algebraBridges the gap for students by showing how most of the concepts within an abstract algebra course are actually tools used to solve difficult, but well-known problems Builds on relatively familiar material (Integers, polynomials) and moves onto more abstract topics, while providing a historical approach of introducing groups first as automorphisms Exercises provide a balanced blend of difficulty levels, while the quantity allows the instructor a latitude of choices

"

This book treats modal logic as a theory, with several subtheories, such as completeness theory, correspondence theory, duality theory and transfer theory and is intended as a course in modal logic for students who have had prior contact with modal logic and who wish to study it more deeply. It presupposes training in mathematical or logic. Very little specific knowledge is presupposed, most results which are needed are proved in this book.

This book has evolved from the lecture course on Functional Analysis I had given several times at the ETH. The text has a strict logical order, in the style of "Definition - Theorem - Proof - Example - Exercises". The proofs are rather thorough and there many examples. The first part of the book(the first three chapters, resp. the first two volumes) is devoted to the theory of Banach spaces in the most general sense of the term. The purpose of the first chapter (resp. first volume) is to introduce those results on Banach spaces which are used later or which are closely connected with the book. It therefore only contains a small part of the theory, and several results are stated (and proved) in a diluted form. The second chapter (which together with Chapter 3 makes the second volume) deals with Banach algebras (and involutive Banach algebras), which constitute the main topic of the first part of the book. The third chapter deals with compact operators on Banach spaces and linear (ordinary and partial) differential equations - applications of the, theory of Banach algebras.

Information Security is usually achieved through a mix of technical, organizational and legal measures. These may include the application of cryptography, the hierarchical modeling of organizations in order to assure confidentiality, or the distribution of accountability and responsibility by law, among interested parties.
The history of Information Security reaches back to ancient times and starts with the emergence of bureaucracy in administration and warfare. Some aspects, such as the interception of encrypted messages during World War II, have attracted huge attention, whereas other aspects have remained largely uncovered.
There has never been any effort to write a comprehensive history. This is most unfortunate, because Information Security should be perceived as a set of communicating vessels, where technical innovations can make existing legal or organisational frame-works obsolete and a breakdown of political authority may cause an exclusive reliance on technical means.
This book is intended as a first field-survey. It consists of twenty-eight contributions, written by experts in such diverse fields as computer science, law, or history and political science, dealing with episodes, organisations and technical developments that may considered to be exemplary or have played a key role in the development of this field.
These include: the emergence of cryptology as a discipline during the Renaissance, the Black Chambers in 18th century Europe, the breaking of German military codes during World War II, the histories of the NSA and its Soviet counterparts and contemporary cryptology. Other subjects are: computer security standards, viruses and worms on the Internet, computer transparency and free software, computer crime, export regulations for encryption software and the privacy debate.
- Interdisciplinary coverage of the history Information Security
- Written by top experts in law, history, computer and information science
- First comprehensive work in Information Security

This Handbook covers latent variable models, which are a flexible class of models for modeling multivariate data to explore relationships among observed and latent variables.
- Covers a wide class of important models
- Models and statistical methods described provide tools for analyzing a wide spectrum of complicated data
- Includes illustrative examples with real data sets from business, education, medicine, public health and sociology.
- Demonstrates the use of a wide variety of statistical, computational, and mathematical techniques.

Geometric Function Theory is that part of Complex Analysis which covers the theory of conformal and quasiconformal mappings.
Beginning with the classical Riemann mapping theorem, there is a lot of existence theorems for canonical conformal mappings. On the other side there is an extensive theory of qualitative properties of conformal and quasiconformal mappings, concerning mainly a prior estimates, so called distortion theorems (including the Bieberbach conjecture with the proof of the Branges). Here a starting point was the classical Scharz lemma, and then Koebe's distortion theorem.
There are several connections to mathematical physics, because of the relations to potential theory (in the plane). The Handbook of Geometric Function Theory contains also an article about constructive methods and further a Bibliography including applications eg: to electroxtatic problems, heat conduction, potential flows (in the plane).
- A collection of independent survey articles in the field of GeometricFunction Theory
- Existence theorems and qualitative properties of conformal and quasiconformal mappings
- A bibliography, including many hints to applications in electrostatics, heat conduction, potential flows (in the plane).

The material collected in this volume reflects the active present of this area of mathematics, ranging from the abstract theory of gradient flows to stochastic representations of non-linear parabolic PDE's.
Articles will highlight the present as well as expected future directions of development of the field with particular emphasis on applications.
The article by Ambrosio and Savare discusses
the most recent development in the theory of gradient flow of probability measures. After an introduction reviewing the properties of the Wasserstein space and corresponding subdifferential calculus, applications are given to evolutionary
partial differential equations. The contribution of Herrero provides a description of some mathematical approaches developed to account for quantitative as well as qualitative aspects of chemotaxis. Particular attention is paid to the limits of cell's
capability to measure external cues on the one hand, and to provide an overall description of aggregation models for the slim mold " Dictyostelium discoideum" on the other.
The chapter written by Masmoudi deals with a rather different topic - examples of singular limits in hydrodynamics. This is nowadays a well-studied issue given the amount of new results based on the development of the existence theory for rather general systems of equations in hydrodynamics. The paper by DeLellis addreses the most recent results for the transport equations with regard to possible applications in the theory of hyperbolic systems of conservation laws. Emphasis is put on the development of the theory in the case when the governing field is only a BV function.
The chapter by Rein represents a comprehensive survey of results on the Poisson-Vlasov system in astrophysics. The question of global stability of steady states is addressed in detail. The contribution of Soner is devoted to different representations of non-linear parabolic equations in terms of Markov processes. After a brief introduction on the linear theory, a class of
non-linear equations is investigated, with applications to stochastic control and differential games.
The chapter written by Zuazua presents some of the recent progresses done on the problem of controllabilty of partial differential equations. The applications include the linear wave and heat equations, parabolic equations with coefficients of low regularity, and some fluid-structure interaction models.
- Volume 1 focuses on the abstract theory of evolution
- Volume 2 considers more concrete probelms relating to specific applications
- Volume 3 reflects the active present of this area of mathematics, ranging from the abstract theory of gradient flows to stochastic representations of non-linear PDEs"

This book comes out of need and urgency (expressed especially in areas of Information Retrieval with respect to Image, Audio, Internet and Biology) to have a working tool to compare data.
The book will provide powerful resource for all researchers using Mathematics as well as for mathematicians themselves. In the time when over-specialization and terminology fences isolate researchers, this Dictionary try to be "centripedal" and "oikoumeni," providing some access and altitude of vision but without taking the route of scientific vulgarisation. This attempted balance is the main philosophy of this Dictionary which defined its structure and style.
Key features:
- Unicity: it is the first book treating the basic notion of Distance in whole generality.
- Interdisciplinarity: this Dictionary is larger in scope than majority of thematic dictionaries.
- Encyclopedicity: while an Encyclopedia of Distances seems now too difficult to produce, this book (by its scope, short introductions and organization) provides the main material for it and for future tutorials on some parts of this material.
- Applicability: the distances, as well as distance-related notions and paradigms, are provided in ready-to-use fashion.
- Worthiness: the need and urgency for such dictionary was great in several huge areas, esp. Information Retrieval, Image Analysis, Speech Recognition and Biology.
- Accessibility: the definitions are easy to locate by subject or, in Index, by alphabetic order; the introductions and definitions are reader-friendly and maximally independent one from another; still the text is structured, in the 3D HTML style, by hyperlink-like boldfaced references to similar definitions.
* Covers a large range of subjects in pure and applied mathematics
* Designed to be easily applied--the distances and distance-related notions and paradigms are ready to use
* Helps users quickly locate definitions by subject or in alphabetical order; stand-alone entries include references to other entries and sources for further investigation

This monograph provides a comprehensive treatment of expansion theorems for regular systems of first order differential equations and "n"-th order ordinary differential equations.
In 10 chapters and one appendix, it provides a comprehensive treatment from abstract foundations to applications in physics and engineering. The focus is on non-self-adjoint problems. Bounded operators are associated to these problems, and Chapter 1 provides an in depth investigation of eigenfunctions and associated functions for bounded Fredholm valued operators in Banach spaces. Since every "n"-th order differential equation is equivalent
to a first order system, the main techniques are developed for systems. Asymptotic fundamental
systems are derived for a large class of systems of differential equations. Together with boundary
conditions, which may depend polynomially on the eigenvalue parameter, this leads to the definition of Birkhoff and Stone regular eigenvalue problems. An effort is made to make the conditions relatively easy verifiable; this is illustrated with several applications in chapter 10.
The contour integral method and estimates of the resolvent are used to prove expansion theorems.
For Stone regular problems, not all functions are expandable, and again relatively easy verifiable
conditions are given, in terms of auxiliary boundary conditions, for functions to be expandable.
Chapter 10 deals exclusively with applications; in nine sections, various concrete problems such as
the Orr-Sommerfeld equation, control of multiple beams, and an example from meteorology are investigated.

Key features:
Expansion Theorems for Ordinary Differential Equations
Discusses Applications to Problems from Physics and Engineering
Thorough Investigation of Asymptotic Fundamental Matrices and Systems
Provides a Comprehensive Treatment
Uses the Contour Integral Method
Represents the Problems as Bounded Operators
Investigates Canonical Systems of Eigen- and Associated Vectors for Operator Functions
"

Mechatronics is a core subject for engineers, combining elements of mechanical and electronic engineering into the development of computer-controlled mechanical devices such as DVD players or anti-lock braking systems. This book is the most comprehensive text available for both mechanical and electrical engineering students and will enable them to engage fully with all stages of mechatronic system design. It offers broader and more integrated coverage than other books in the field with practical examples, case studies and exercises throughout and an Instructor's Manual. A further key feature of the book is its integrated coverage of programming the PIC microcontroller, and the use of MATLAB and Simulink programming and modelling, along with code files for downloading from the accompanying website.
*Integrated coverage of PIC microcontroller programming, MATLAB and Simulink modelling
*Fully developed student exercises, detailed practical examples
*Accompanying website with Instructor's Manual, downloadable code and image bank

The book is meant to serve two purposes. The first and more obvious one is to present state of the art results in algebraic research into residuated structures related to substructural logics. The second, less obvious but equally important, is to provide a reasonably gentle introduction to algebraic logic. At the beginning, the second objective is predominant. Thus, in the first few chapters the reader will find a primer of universal algebra for logicians, a crash course in nonclassical logics for algebraists, an introduction to residuated structures, an outline of Gentzen-style calculi as well as some titbits of proof theory - the celebrated Hauptsatz, or cut elimination theorem, among them. These lead naturally to a discussion of interconnections between logic and algebra, where we try to demonstrate how they form two sides of the same coin. We envisage that the initial chapters could be used as a textbook for a graduate course, perhaps entitled Algebra and Substructural Logics.
As the book progresses the first objective gains predominance over the second. Although the precise point of equilibrium would be difficult to specify, it is safe to say that we enter the technical part with the discussion of various completions of residuated structures. These include Dedekind-McNeille completions and canonical extensions. Completions are used later in investigating several finiteness properties such as the finite model property, generation of varieties by their finite members, and finite embeddability. The algebraic analysis of cut elimination that follows, also takes recourse to completions. Decidability of logics, equational and quasi-equational theories comes next, where we show how proof theoretical methods like cut elimination are preferable for small logics/theories, but semantic tools like Rabin's theorem work better for big ones. Then we turn to Glivenko's theorem, which says that a formula is an intuitionistic tautology if and only if its double negation is a classical one. We generalise it to the substructural setting, identifying for each substructural logic its Glivenko equivalence class with smallest and largest element. This is also where we begin investigating lattices of logics and varieties, rather than particular examples. We continue in this vein by presenting a number of results concerning minimal varieties/maximal logics. A typical theorem there says that for some given well-known variety its subvariety lattice has precisely such-and-such number of minimal members (where values for such-and-such include, but are not limited to, continuum, countably many and two). In the last two chapters we focus on the lattice of varieties corresponding to logics without contraction. In one we prove a negative result: that there are no nontrivial splittings in that variety. In the other, we prove a positive one: that semisimple varieties coincide with discriminator ones.
Within the second, more technical part of the book another transition process may be traced. Namely, we begin with logically inclined technicalities and end with algebraically inclined ones. Here, perhaps, algebraic rendering of Glivenko theorems marks the equilibrium point, at least in the sense that finiteness properties, decidability and Glivenko theorems are of clear interest to logicians, whereas semisimplicity and discriminator varieties are universal algebra par exellence. It is for the reader to judge whether we succeeded in weaving these threads into a seamless fabric.
- Considers both the algebraic and logical perspective within a common framework.
- Written by experts in the area.
- Easily accessible to graduate students and researchers from other fields.
- Results summarized in tables and diagrams to provide an overview of the area.
- Useful as a textbook for a course in algebraic logic, with exercises and suggested research directions.
- Provides a concise introduction to the subject and leads directly to research topics.
- The ideas from algebra and logic are developed hand-in-hand and the connections are shown in every level.

Mathematics for Electrical Engineering and Computing embraces many applications of modern mathematics, such as Boolean Algebra and Sets and Functions, and also teaches both discrete and continuous systems - particularly vital for Digital Signal Processing (DSP). In addition, as most modern engineers are required to study software, material suitable for Software Engineering - set theory, predicate and prepositional calculus, language and graph theory - is fully integrated into the book.
Excessive technical detail and language are avoided, recognising that the real requirement for practising engineers is the need to understand the "applications" of mathematics in everyday engineering contexts. Emphasis is given to an appreciation of the fundamental concepts behind the mathematics, for problem solving and undertaking critical analysis of results, whether using a calculator or a computer.
The text is backed up by numerous exercises and worked examples throughout, firmly rooted in engineering practice, ensuring that all mathematical theory introduced is directly relevant to real-world engineering. The book includes introductions to advanced topics such as Fourier analysis, vector calculus and random processes, also making this a suitable introductory text for second year undergraduates of electrical, electronic and computer engineering, undertaking engineering mathematics courses.
The book is supported with a number of free online resources. On the companion website readers will find:
* over 60 pages of "Background Mathematics" reinforcing introductory material for revision purposes in advance of your first year course
* plotXpose software (for equation solving, and drawing graphs of simple functions, their derivatives, integrals and Fourier transforms)
* problems and projects (linking directly to the software)
In addition, for lecturers only, http: //textbooks.elsevier.com features a complete worked solutions manual for the exercises in the book.
Dr Attenborough is a former Senior Lecturer in the School of Electrical, Electronic and Information Engineering at South Bank University. She is currently Technical Director of The Webbery - Internet development company, Co. Donegal, Ireland.
* Fundamental principles of mathematics introduced and applied in engineering practice, reinforced through over 300 examples directly relevant to real-world engineering
* Over 60 pages of basic revision material available to download in advance of embarking on a first year course
* Free website support, featuring complete solutions manual, background mathematics, plotXpose software, and further problems and projects enabling students to build on the concepts introduced, and put the theory into practice

Sobolev Spaces presents an introduction to the theory of Sobolev Spaces and other related spaces of function, also to the imbedding characteristics of these spaces. This theory is widely used in pure and Applied Mathematics and in the Physical Sciences.
This second edition of Adam's 'classic' reference text contains many additions and much modernizing and refining of material. The basic premise of the book remains unchanged: Sobolev Spaces is intended to provide a solid foundation in these spaces for graduate students and researchers alike.
* Self-contained and accessible for readers in other disciplines.
* Written at elementary level making it accessible to graduate students.

This book is designed for the reader who wants to get a general view of the terminology of General Topology with minimal time and effort. The reader, whom we assume to have only a rudimentary knowledge of set theory, algebra and analysis, will be able to find what they want if they will properly use the index. However, this book contains very few proofs and the reader who wants to study more systematically will find sufficiently many references in the book.

Key features:

- More terms from General Topology than any other book ever published
- Short and informative articles
- Authors include the majority of top researchers in the field
- Extensive indexing of terms

There has been a common perception that computational complexity is a theory of "bad news" because its most typical results assert that various real-world and innocent-looking tasks are infeasible. In fact, "bad news" is a relative term, and, indeed, in some situations (e.g., in cryptography), we want an adversary to not be able to perform a certain task. However, a "bad news" result does not automatically become useful in such a scenario. For this to happen, its hardness features have to be quantitatively evaluated and shown to manifest extensively.
The book undertakes a quantitative analysis of some of the major results in complexity that regard either classes of problems or individual concrete problems. The size of some important classes are studied using resource-bounded topological and measure-theoretical tools. In the case of individual problems, the book studies relevant quantitative attributes such as approximation properties or the number of hard inputs at each length.
One chapter is dedicated to abstract complexity theory, an older field which, however, deserves attention because it lays out the foundations of complexity. The other chapters, on the other hand, focus on recent and important developments in complexity. The book presents in a fairly detailed manner concepts that have been at the centre of the main research lines in complexity in the last decade or so, such as: average-complexity, quantum computation, hardness amplification, resource-bounded measure, the relation between one-way functions and pseudo-random generators, the relation between hard predicates and pseudo-random generators, extractors, derandomization of bounded-error probabilistic algorithms, probabilistically checkable proofs, non-approximability of optimization problems, and others.
The book should appeal to graduate computer science students, and to researchers who have an interest in computer science theory and need a good understanding of computational complexity, e.g., researchers in algorithms, AI, logic, and other disciplines.
-Emphasis is on relevant quantitative attributes of important results in complexity.
-Coverage is self-contained and accessible to a wide audience.
-Large range of important topics including: derandomization techniques, non-approximability of optimization problems, average-case complexity, quantum computation, one-way functions and pseudo-random generators, resource-bounded measure and topology.

The Handbook of Mathematical Fluid Dynamics is a compendium of essays that provides a survey of the major topics in the subject. Each article traces developments, surveys the results of the past decade, discusses the current state of knowledge and presents major future directions and open problems. Extensive bibliographic material is provided. The book is intended to be useful both to experts in the field and to mathematicians and other scientists who wish to learn about or begin research in mathematical fluid dynamics. The Handbook illuminates an exciting subject that involves rigorous mathematical theory applied to an important physical problem, namely the motion of fluids.