This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields.
Key Features
* First full treatment of the subject and its applications
* Written by the pioneer of this field
* Broad applications in mathematics
* Of interest across most fields
* Ideal as an introduction and survey
* Examples treated include:
@subbul* the space of Penrose tilings
* the space of leaves of a foliation
* the space of irreducible unitary representations of a discrete group
* the phase space in quantum mechanics
* the Brillouin zone in the quantum Hall effect
* A model of space time

Now inits 7th edition, "Mathematical Methods for Physicists" continues to provide all the mathematical methods that aspiring scientists and engineers are likely to encounter as students and beginning researchers. This bestselling text provides mathematical relations and their proofs essential to the study of physics and related fields. While retaining thekey features of the 6th edition, the new edition provides a more careful balance of explanation, theory, and examples. Taking a problem-solving-skills approach to incorporating theorems with applications, the book's improved focus will help students succeed throughout their academic careers and well into their professions. Some notable enhancements include more refined and focused content in important topics, improved organization, updated notations, extensive explanations and intuitive exercise sets, a wider range of problem solutions, improvement in the placement, and a wider range of difficulty of exercises.
Revised and updated version of the leading text in mathematical physicsFocuses on problem-solving skills and active learning, offering numerous chapter problemsClearly identified definitions, theorems, and proofs promote clarity and understanding

New to this edition: Improved modular chaptersNew up-to-date examplesMore intuitive explanations"

The new edition of "Mathematical Modeling," the survey text of choice for mathematical modeling courses, adds ample instructor support and online delivery for solutions manuals and software ancillaries.

From genetic engineering to hurricane prediction, mathematical models guide much of the decision making in our society. If the assumptions and methods underlying the modeling are flawed, the outcome can be disastrously poor. With mathematical modeling growing rapidly in so many scientific and technical disciplines, "Mathematical Modeling, Fourth Edition" provides a rigorous treatment of the subject. The book explores a range of approaches including optimization models, dynamic models and probability models.
Offers increased support for instructors, including MATLAB material as well as other on-line resourcesFeatures new sections on time series analysis and diffusion modelsProvides additional problems with international focus such as whale and dolphin populations, plus updated optimization problems

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

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"

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.

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

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.

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

The second edition of this text has sold over 6,000 copies since publication in 1986 and this revision will make it even more useful. This is the only book available that is approachable by "beginners" in this subject. It has become an essential introduction to the subject for mathematics students, engineers, physicists, and economists who need to learn how to apply these vital methods. It is also the only book that thoroughly reviews certain areas of advanced calculus that are necessary to understand the subject.

Line and surface integrals
Divergence and curl of vector fields

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.

An Introduction to Non-Harmonic Fourier Series, Revised Edition is an update of a widely known and highly respected classic textbook.
Throughout the book, material has also been added on recent developments, including stability theory, the frame radius, and applications to signal analysis and the control of partial differential equations.

A collection of problems and solutions in real analysis based on the major textbook, "Principles of Real Analysis" (also by Aliprantis and Burkinshaw), "Problems in Real Analysis" is the ideal companion for senior science and engineering undergraduates and first-year graduate courses in real analysis. It is intended for use as an independent source, and is an invaluable tool for students who wish to develop a deep understanding and proficiency in the use of integration methods.
"Problems in Real Analysis" teaches the basic methods of proof and problem-solving by presenting the complete solutions to over 600 problems that appear in "Principles of Real Analysis, Third Edition." The problems are distributed in forty sections, and cover the entire spectrum of difficulty.

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.

General concepts and methods that occur throughout mathematics and now also in theoretical computer science are the subject of this book. It is a thorough introduction to Categories, emphasizing the geometric nature of the subject and explaining its connections to mathematical logic. The book should appeal to the inquisitive reader who has seen some basic topology and algebra and would like to learn and explore further.
The first part contains a detailed treatment of the fundamentals of Geometric Logic, which combines four central ideas: natural transformations, sheaves, adjoint functors, and topoi.
A special feature of the work is a general calculus of relations presented in the second part. This calculus offers another, often more amenable framework for concepts and methods discussed in part one. Some aspects of this approach find their origin in the relational calculi of Peirce and Schroeder from the last century, and in the 1940's in the work of Tarski and others on relational algebras. The representation theorems discussed are an original feature of this approach.
"

Chapter 1 presents theorems on differentiable functions often used in differential topology, such as the implicit function theorem, Sard's theorem and Whitney's approximation theorem.
The next chapter is an introduction to real and complex manifolds. It contains an exposition of the theorem of Frobenius, the lemmata of Poincare and Grothendieck with applications of Grothendieck's lemma to complex analysis, the imbedding theorem of Whitney and Thom's transversality theorem.
Chapter 3 includes characterizations of linear differentiable operators, due to Peetre and Hormander. The inequalities of Garding and of Friedrichs on elliptic operators are proved and are used to prove the regularity of weak solutions of elliptic equations. The chapter ends with the approximation theorem of Malgrange-Lax and its application to the proof of the Runge theorem on open Riemann surfaces due to Behnke and Stein.

In this book the authors try to bridge the gap between the treatments of matrix theory and linear algebra. It is aimed at graduate and advanced undergraduate students seeking a foundation in mathematics, computer science, or engineering. It will also be useful as a reference book for those working on matrices and linear algebra for use in their scientific work.

Studies in Logic and the Foundations of Mathematics, Volume 102: Set Theory: An Introduction to Independence Proofs offers an introduction to relative consistency proofs in axiomatic set theory, including combinatorics, sets, trees, and forcing. The book first tackles the foundations of set theory and infinitary combinatorics. Discussions focus on the Suslin problem, Martin's axiom, almost disjoint and quasi-disjoint sets, trees, extensionality and comprehension, relations, functions, and well-ordering, ordinals, cardinals, and real numbers. The manuscript then ponders on well-founded sets and easy consistency proofs, including relativization, absoluteness, reflection theorems, properties of well-founded sets, and induction and recursion on well-founded relations. The publication examines constructible sets, forcing, and iterated forcing. Topics include Easton forcing, general iterated forcing, Cohen model, forcing with partial functions of larger cardinality, forcing with finite partial functions, and general extensions. The manuscript is a dependable source of information for mathematicians and researchers interested in set theory.

Designed for advanced engineering, physical science, and applied mathematics students, this innovative textbook is an introduction to both the theory and practical application of linear algebra and functional analysis. The book is self-contained, beginning with elementary principles, basic concepts, and definitions. The important theorems of the subject are covered and effective application tools are developed, working up to a thorough treatment of eigenanalysis and the spectral resolution theorem. Building on a fundamental understanding of finite vector spaces, infinite dimensional Hilbert spaces are introduced from analogy. Wherever possible, theorems and definitions from matrix theory are called upon to drive the analogy home. The result is a clear and intuitive segue to functional analysis, culminating in a practical introduction to the functional theory of integral and differential operators. Numerous examples, problems, and illustrations highlight applications from all over engineering and the physical sciences. Also included are several numerical applications, complete with "Mathematica" solutions and code, giving the student a "hands-on" introduction to numerical analysis. Linear Algebra and Linear Operators in Engineering is ideally suited as the main text of an introductory graduate course, and is a fine instrument for self-study or as a general reference for those applying mathematics.
. Contains numerous "Mathematica" examples complete with full code and solutions
. Provides complete numerical algorithms for solving linear and nonlinear problems
. Spans elementary notions to the functional theory of linear integral and differential equations
. Includes over 130 examples, illustrations, and exercises and over 220 problems ranging from basic concepts to challenging applications
. Presents real-life applications from chemical, mechanical, and electrical engineering and the physical sciences"

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

This book is an exposition of "semi-Riemannian geometry" (also called "pseudo-Riemannian geometry")--the study of a smooth manifold furnished with a metric tensor of arbitrary signature. The principal special cases are Riemannian geometry, where the metric is positive definite, and Lorentz geometry. For many years these two geometries have developed almost independently: Riemannian geometry reformulated in coordinate-free fashion and directed toward global problems, Lorentz geometry in classical tensor notation devoted to general relativity. More recently, this divergence has been reversed as physicists, turning increasingly toward invariant methods, have produced results of compelling mathematical interest.

Essential Computational Modeling for the Human Body presents key contributions selected from the volume in the Handbook of Numerical Analysis: Computational Modeling for the Human Body Vol. 12 (2005).

Computational (Mathematical) Modeling is used by scientists and researchers with various applications in chemical, biological, behavioral, environmental sciences, etc. This guide presents essential research techniques for analysis and essential concrete examples of computational models, while supplying a wide range of commonly used methods and applications, followed by various numerical simulations.

Provides various viewpoints of methods and applications are available for researchers to chose and experiment with; Numerical analysis and open problems useful for experimentation; Computational Models useful for surgery simulations;