M. Abate F. Tovena M. Abate F. Tovena TX, USA; , Florida ... · M. Abate, Università di Pisa, Italy; F. Tovena, Università di Roma Tor Vergata, Italy Geometria Differenziale L’opera

springer.com/NEWSonline92 Springer News 7/2011Mathematics

M. Abate, Università di Pisa, Italia; F. Tovena, Università Tor Vergata, Roma, Italia

Curves and Surfaces

The book provides an introduction to Differential Geometry of Curves and Surfaces. The theory of curves starts with a discussion of possible defini-tions of the concept of curve, proving in particular the classification of 1-dimensional manifolds. We then present the classical local theory of param-etrized plane and space curves (curves in n-dimen-sional space are discussed in the complementary material): curvature, torsion, Frenet’s formulas and the fundamental theorem of the local theory of curves. Then, after a self-contained presentation of degree theory for continuous self-maps of the circumference, we study the global theory of plane curves, introducing winding and rotation numbers, and proving the Jordan curve theorem for curves of class C2, and Hopf theorem on the rotation number of closed simple curves. The local theory of surfaces begins with a comparison of the concept of parametrized (i.e., immersed) surface with the concept of regular (i.e., embedded) surface. We then develop the basic differential geometry of surfaces in R3: defini-tions, examples, differentiable maps and func-tions, tangent vectors (presented both as vectors tangent to curves in the surface and as derivations on germs of differentiable functions; we shall consistently use both approaches in the whole book) and orientation. Next we study the several notions of curvature on a surface, stressing both the geometrical meaning of the objects introduced and the algebraic/analytical methods needed to study them via the Gauss map, up to the proof of Gauss’ Teorema Egregium.

Fields of interestMathematics, general; Differential Geometry; Geometry

Target groupsResearch

M. Abate, Università di Pisa, Italy; F. Tovena, Università di Roma Tor Vergata, Italy

Geometria Differenziale

L’opera fornisce una introduzione alla geometria delle varietà differenziabili, illustrandone le princi-pali proprietà e descrivendo le principali tecniche e i più importanti strumenti usati per il loro studio. Uno degli obiettivi primari dell’opera è di fungere da testo di riferimento per chi (matematici, fisici, ingegneri) usa la geometria differenziale come strumento; inoltre può essere usato come libro di testo per diversi corsi introduttivi alla geometria differenziale, concentrandosi su alcuni dei vari aspetti della teoria presentati nell’opera. Più in dettaglio, nell’opera saranno trattati i seguenti argomenti: richiami di algebra multilin-eare e tensoriale, spesso non presentati nei corsi standard di algebra lineare; varietà differenziali, incluso il teorema di Whitney; fibrati vettoriali, incluso il teorema di Frobenius e un’introduzione ai fibrati principali; gruppi di Lie, incluso il teorema di corrispondenza fra sottogruppi e sotto-algebre; coomologia di de Rham, inclusa la dualità di Poincaré e il teorema di de Rham; connessioni, inclusa la teoria delle geodetiche; e geometria Riemanniana, con particolare attenzione agli operatori di curvatura e inclusi teoremi di Cartan-Hadamard, Bonnet-Myers, e Synge-Weinstein. Come abitudine degli autori, il testo è scritto in modo da favorire una lettura attiva, cruciale per un buon apprendimento di argomenti matematici; inoltre è corredato da numerosi esempi svolti ed esercizi proposti.

Features7 L'opera è scritta in modo da favorire una lettura attiva 7 Può essere usata sia come libro di testo per diversi insegnamenti di geometria differenziale, sia come testo di riferimento per chi (matematici, fisici, ingegneri) usa la geometria differenziale come strumento 7 Copre una vasta area di risultati, raramente raccolti in un unico testo

Fields of interestGeometria differenzale; Geometria

Target groupsLower undergraduate

R. P. Agarwal, Texas A&M University, Kingsville, TX, USA; K. Perera, Florida Institute of Technology, Melbourne, Fl, USA; S. Pinelas, Universidade dos Açores, Ponta Delgada, Portugal

An Introduction to Complex Analysis

This textbook introduces the subject of complex analysis to advanced undergraduate and graduate students in a clear and concise manner. Key features of this textbook: effectively organizes the subject into easily manageable sections in the form of 50 class-tested lectures, uses detailed examples to drive the presentation, includes numerous exer-cise sets that encourage pursuing extensions of the material, each with an “Answers or Hints” section, covers an array of advanced topics which allow for flexibility in developing the subject beyond the basics, provides a concise history of complex numbers. An Introduction to Complex Analysis will be valuable to students in mathematics, engi-neering and other applied sciences. Prerequisites include a course in calculus.

Features7 Provides a rigorous introduction to complex analysis 7 Arranges the material effectively in 50 class-tested lectures 7 Uses ample illustrations and examples to explain the subject 7 Provides problems for practice

From the contentsPreface.-Complex Numbers.-Complex Numbers II .- Complex Numbers III.-Set Theory in the Complex Plane.-Complex Functions.-Analytic Functions I.-Analytic Functions II.-Elementary Functions I.- Elementary Functions II.- Mappings by Functions.- Mappings by Functions II.- Curves, Contours, and Simply Connected Domains.- Complex Integration.- Independence of Path.- Cauchy–Goursat Theorem.- Deformation Theorem.- Cauchy’s Integral Formula.- Cauchy’s Integral Formula for Derivatives.- Fundamental Theorem of Algebra.- Maximum Modulus Principle.- Sequences and Series of Numbers.- Sequences and Series of Functions.- Power Series.- Taylor’s Series.- Laurent’s Series.

Fields of interestFunctions of a Complex Variable; Analysis

Target groupsUpper undergraduate

Type of publicationUndergraduate textbook

Due October 2011

2012. XIII, 393 p. 66 illus., 1 in color. (UNITEXT / La Matematica per il 3+2) Softcover

7 approx. € 59,95 | £53.997 approx. * € (D) 64,15 | € (A) 65,95 | sFr 86,00ISBN 978-88-470-1940-9

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Type of publicationLibro di testo introduttivo

Pubblicazione prevista per il mese di luglio 2011

2011. X, 390 pagg. 10 figg. (UNITEXT / La Matematica per il 3+2) Brossura


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Type of publicationGraduate/Advanced undergraduate textbook

Due August 2011

2011. XIV, 346 p. 92 illus. Hardcover

7 € 59,95 | £53.997 * € (D) 64,15 | € (A) 65,95 | sFr 86,00ISBN 978-1-4614-0194-0

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www.springer.com/978-88-470-1940-9



springer.com/NEWSonline 93Springer News 7/2011 Mathematics

V. Anandam, University of Madras, Chennai, India

Harmonic Functions and Potentials on Finite or Infinite Networks

Random walks, Markov chains and electrical networks serve as an introduction to the study of real-valued functions on finite or infinite graphs, with appropriate interpretations using probability theory and current-voltage laws. The relation between this type of function theory and the (Newton) potential theory on the Euclidean spaces is well-established. The latter theory has been variously generalized, one example being the axiomatic potential theory on locally compact spaces developed by Brelot, with later ramifica-tions from Bauer, Constantinescu and Cornea. A network is a graph with edge-weights that need not be symmetric. This book presents an autonomous theory of harmonic functions and potentials defined on a finite or infinite network, on the lines of axiomatic potential theory. Random walks and electrical networks are important sources for the advancement of the theory.

Features7 Number of examples to illustrate the main theory 7 Historical perspectives included to show the development of potential theory in various forms 7 Self-contained text for an easy reading

Contents1 Laplace Operators on Networks and Trees.- 2 Potential Theory on Finite Networks.- 3 Harmonic Function Theory on Infinite Networks.- 4 Schrödinger Operators and Subordinate Structures on Infinite Networks.- 5 Polyharmonic Functions on Trees.

Fields of interestPotential Theory; Functions of a Complex Vari-able; Partial Differential Equations


G. A. Anastassiou, The University of Memphis, TN, USA

Advances on Fractional Inequalities

Advances on Fractional Inequalities use primarily the Caputo fractional derivative, as the most important in applications, and presents the first fractional differentiation inequalities of Opial type which involves the balanced fractional deriva-tives. The book continues with right and mixed fractional differentiation Ostrowski inequalities in the univariate and multivariate cases. Next the right and left, as well as mixed, Landau fractional differentiation inequalities in the univariate and multivariate cases are illustrated. Throughout the book many applications are given. Fractional differentiation inequalities are by themselves an important and great mathematical topic for research. Furthermore they have many applica-tions, the most important ones are in establishing uniqueness of solution in fractional differential equations and systems and in fractional partial differential equations. Also they provide upper bounds to the solutions of the above equations.

Features7 Use primarily the Caputo fractional deriva-tive, as the most important in applications, and we present first fractional differentiation inequali-ties of Opial type where we involve the so called balanced fractional derivatives 7 Fractional differentiation inequalities have many applica-tions, the most important ones are in establishing uniqueness of solution in fractional differential equations and systems and in fractional partial differential equations

Fields of interestOrdinary Differential Equations; Calculus of Varia-tions and Optimal Control; Optimization; Real Functions


G. A. Anastassiou, The University of Memphis, TN, USA

Approximation by Multivariate Singular Integrals

Approximation by Multivariate Singular Integrals is the first monograph to illustrate the approxi-mation of multivariate singular integrals to the identity-unit operator. The basic approximation properties of the general multivariate singular integral operators is presented quantitatively, particularly special cases such as the multivariate Picard, Gauss-Weierstrass, Poisson-Cauchy and trigonometric singular integral operators are examined thoroughly. This book studies the rate of convergence of these operators to the unit operator as well as the related simultaneous approximation. The last chapter, which includes many examples, presents a related Korovkin type approximation theorem for functions of two variables. Relevant background information and motivation is included in this exposition, and as a result this book can be used as supplementary text for several advanced courses. The results presented apply to many areas of pure and applied mathematics, such a mathematical analysis, probability, statistics and partial differential equations. This book is appro-priate for researchers and selected seminars at the graduate level.

Features7 First monograph to deal exclusively with the study of the approximation of multivariate singular integrals to the identity-unit operator 7 Quanti-tatively studies the basic approximation properties of the general multivariate singular integral opera-tors, special cases of which are the multivariate Picard, Gauss-Weierstrass, Poisson-Cauchy and trigonometric singular integral operators, etc.

Fields of interestIntegral Transforms, Operational Calculus; Partial Differential Equations; Probability Theory and Stochastic Processes

Target groupsResearchType of publication

Monograph

Due July 2011

2011. X, 190 p. (Lecture Notes of the Unione Matematica Italiana, Volume 12) Softcover

7 € 34,95 | £31.997 * € (D) 37,40 | € (A) 38,45 | sFr 50,50ISBN 978-3-642-21398-4

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Type of publicationSpringerBriefs

Due August 2011

2011. X, 127 p. (SpringerBriefs in Mathematics) Softcover

7 € 49,95 | £44.997 * € (D) 53,45 | € (A) 54,95 | sFr 72,00ISBN 978-1-4614-0702-7

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Type of publicationSpringerBriefs

Due October 2011

2011. IX, 86 p. (SpringerBriefs in Mathematics) Softcover

7 € 49,95 | £44.997 * € (D) 53,45 | € (A) 54,95 | sFr 72,00ISBN 978-1-4614-0588-7

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J. Barmak, University of Buenos Aires, Argentina

Algebraic Topology of Finite Topological Spaces and Applications

This volume deals with the theory of finite topo-logical spaces and its relationship with the homo-topy and simple homotopy theory of polyhedra. The interaction between their intrinsic combinato-rial and topological structures makes finite spaces a useful tool for studying problems in Topology, Algebra and Geometry from a new perspective. In particular, the methods developed in this manu-script are used to study Quillen’s conjecture on the poset of p-subgroups of a finite group and the Andrews-Curtis conjecture on the 3-deformability of contractible two-dimensional complexes. This self-contained work constitutes the first detailed exposition on the algebraic topology of finite spaces. It is intended for topologists and combina-torialists, but it is also recommended for advanced undergraduate students and graduate students with a modest knowledge of Algebraic Topology.

Features7 It is the first complete exposition of the topic 7 Has applications to the study of two long-standing conjectures It is self-contained

Contents1 Preliminaries.- 2 Basic topological properties of finite spaces.- 3 Minimal finite models.- 4 Simple homotopy types and finite spaces.- 5 Strong homo-topy types.- 6 Methods of reduction.- 7 h-regular complexes and quotients.- 8 Group actions and a conjecture of Quillen.- 9 Reduced lattices.- 10 Fixed points and the Lefschetz number.- 11 The Andrews-Curtis conjecture.

Fields of interestAlgebraic Topology; Combinatorics; Convex and Discrete Geometry


J. M. Borwein, M. P. Skerritt, University of Newcastle, NSW, Australia

An Introduction to Modern Mathematical ComputingWith Maple™

Thirty years ago mathematical, as opposed to applied numerical, computation was difficult to perform and so relatively little used. Three threads changed that: the emergence of the personal computer; the discovery of fiber-optics and the consequent development of the modern internet; and the building of the Three “M’s” Maple, Math-ematica and Matlab. We intend to persuade that Maple and other like tools are worth knowing assuming only that one wishes to be a math-ematician, a mathematics educator, a computer scientist, an engineer or scientist, or anyone else who wishes/needs to use mathematics better. We also hope to explain how to become an `experi-mental mathematician’ while learning to be better at proving things. To accomplish this our material is divided into three main chapters followed by a postscript. These cover elementary number theory, calculus of one and several variables, introductory linear algebra, and visualization and interactive geometric computation.

Features7 Places primary importance on the mathematics, rather than being a 'how to' manual for making computations Integrates numerous worked examples and introduces all key programming constructions 7 Includes exercises, sample tests, and a careful selection of 'explorations' suitable for either independent studies or for term projects

Fields of interestComputational Mathematics and Numerical Analysis; Mathematical Software; Simulation and Modeling


D. v. Dalen, Dirk van Dalen, Utrecht University, Utrecht, The Netherlands

The Selected Correspondence of L.E.J. Brouwer

L.E.J. Brouwer (1881-1966) is best known for his revolutionary ideas on topology and foundations of mathematics (intuitionism). The present collec-tion contains a mixture of letters; university and faculty correspondence has been included, some of which shed light on the student years, and in particular on the exchange of letters with his PhD adviser, Korteweg. Acting as the natural sequel to the publication of Brouwer’s biography, this book provides instrumental reading for those wishing to gain a deeper understanding of Brouwer and his role in the twentieth century. Striking a good balance of biographical and scientific informa-tion, the latter deals with innovations in topology (Cantor-Schoenflies style and the new topology) and foundations. The topological period in his research is well represented in correspondence with Hilbert, Schoenflies, Poincaré, Blumenthal, Lebesgue, Baire, Koebe, and foundational topics are discussed in letters exchanged with Weyl, Fraenkel, Heyting, van Dantzig and others. There is also a large part of correspondence on matters related to the interbellum scientific politics. This book will appeal to both graduate students and researchers with an interest in topology, the history of mathematics, the foundations of mathematics, philosophy and general science.

Features7 Facilitates a deeper understanding of L.E.J.Brouwer and his role in the 20th century 7 Presents a wide collection of original letters spanning the personal, business and scientific life of Brouwer 7 Sheds light on Brouwer’s innova-tions in topology and foundations (intuitionism)

Fields of interestHistory of Mathematical Sciences; Topology; Mathematical Logic and Foundations


Type of publicationMonograph

Due August 2011

2011. X, 174 p. 33 illus. (Lecture Notes in Mathematics, Volume 2032) Softcover


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Due August 2011

2011. XVI, 216 p. 82 illus., 78 in color. (Springer Undergraduate Texts in Mathematics and Technology) Hardcover


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Due August 2011

2011. VIII, 528 p. With online files/update. (Sources and Studies in the History of Mathematics and Physical Sciences) Hardcover

7 € 129,95 | £117.007 * € (D) 139,05 | € (A) 142,94 | sFr 186,50ISBN 978-0-85729-527-9

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J. Duistermaat, Universiteit Utrecht, The Netherlands

The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator

Reprinted as it originally appeared in the 1990s, this work is as an affordable text that will be of interest to a range of researchers in geometric analysis and mathematical physics. The book covers a variety of concepts fundamental to the study and applications of the spin-c Dirac operator, making use of the heat kernels theory of Berline, Getzlet, and Vergne. True to the precision and clarity for which J.J. Duistermaat was so well known, the exposition is elegant and concise.

Features7 Affordable softcover edition of the only book ever published on the subject 7 Written by one of the leading geometric analysts of the late 20th century 7 Presents interesting applications of theory 7 Gives an accessible approach to the field

Contents1 Introduction.- 2 The Dolbeault-Dirac Operator.- 3 Clifford Modules.- 4 The Spin Group and the Spin-c Group.- 5 The Spin-c Dirac Operator.- 6 Its Square.- 7 The Heat Kernel Method.- 8 The Heat Kernel Expansion.- 9 The Heat Kernel on a Principal Bundle.- 10 The Automorphism.- 11 The Hirzebruch-Riemann-Roch Integrand.- 12 The Local Lefschetz Fixed Point Formula.- 13 Charac-teristic Case.- 14 The Orbifold Version.- 15 Appli-cation to Symplectic Geometry.- 16 Appendix: Equivariant Forms.

Fields of interestGlobal Analysis and Analysis on Manifolds; Partial Differential Equations; Differential Geometry


S. Ferrara, Cern, Geneva, Switzerland; R. Fioresi, University of Bologna, Italy; V. Varadarajan, UCLA Los Angeles CA, USA (Eds.)

Supersymmetry in Mathematics and PhysicsUCLA Los Angeles, USA 2010

Supersymmetry was created by the physicists in the 1970’s to give a unified treatment of fermions and bosons, the basic constituents of matter. Since then its mathematical structure has been recog-nized as that of a new development in geometry, and mathematicians have busied themselves with exploring this aspect. This volume collects recent advances in this field, both from a physical and a mathematical point of view, with an accent on a rigorous treatment of the various questions raised.

ContentsIntroduction.- Black Holes and First Order Flows in Supergravity.- Representations of Super Lie Groups: Some Remarks.- On Chiral Quantum Superspaces.- On the Construction of Chevalley Supergroup.- Indecomposable Finite-dimensional Representations of a Class o f Lie algebras and Lie Superalgebras.- On the Geometry of Super Riemann Surfaces.- Charge Orbits and Moduli Spaces of Black Hole Attractors.- Maximal Super-symmetry.- Lie Supergroups, Unitary Representa-tions, and Invariant Cones.- Geometry of Dual Pairs of Complex Supercurves.- On the Superdi-mension of an Irreducible Representation.

Fields of interestGeometry; Quantum Field Theories, String Theory; Mathematical Methods in Physics


M. N. Fried, Ben-Gurion University of the Negev, Program for Science and Technology Education, Marcus Family Campus, Building 72, Beer-Sheva 84105, Israel

Edmond Halley’s Reconstruction of the Lost Book of Apollonius’s ConicsTranslation and Commentary

Apollonius’s Conics was one of the greatest works of advanced mathematics in antiquity. The work comprised eight books, of which four have come down to us in their original Greek and three in Arabic. By the time the Arabic translations were produced, the eighth book had already been lost. In 1710, Edmond Halley, then Savilian Professor of Geometry at Oxford, produced an edition of the Greek text of the Conics of Books I-IV, a transla-tion into Latin from the Arabic versions of Books V-VII, and a reconstruction of Book VIII. The present work provides the first complete English translation of Halley’s reconstruction of Book VIII with supplementary notes on the text. It also contains 1) an introduction discussing aspects of Apollonius’s Conics 2) an investigation of Edmond Halley’s understanding of the nature of his venture into ancient mathematics, and 3) an appendices giving a brief account of Apol-lonius’s approach to conic sections and his math-ematical techniques.This book will be of interest to students and researchers interested in the history of ancient Greek mathematics and mathematics in the early modern period.

Features7 Presents the first complete English transla-tion of Edmond Halley's historic reconstruction of book VIII of Apollonius's Conics 7 Serves as an invaluable companion volume to existing literature on the subject 7 Will be an asset to any researcher studying the mathematics of ancient Greece

Fields of interestHistory of Mathematical Sciences; Geometry



Due August 2011

2011. VIII, 247 p. (Modern Birkhäuser Classics) Softcover


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Type of publicationContributed volume

Due August 2011

2011. 250 p. (Lecture Notes in Mathematics, Volume 2027) Softcover

7 € 44,95 | £40.997 * € (D) 48,10 | € (A) 49,45 | sFr 64,50ISBN 978-3-642-21743-2

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Due September 2011

2011. X, 144 p. 65 illus. in color. (Sources and Studies in the History of Mathematics and Physical Sciences, Volume) Hardcover

7 € 89,95 | £81.007 * € (D) 96,25 | € (A) 98,95 | sFr 129,00ISBN 978-1-4614-0145-2

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P. A. Fuhrmann, Ben-Gurion University of the Negev, Beer Sheva, Israel

A Polynomial Approach to Linear Algebra

A Polynomial Approach to Linear Algebra” is a text which is heavily biased towards functional methods. In using the shift operator as a central object, it makes linear algebra a perfect introduc-tion to other areas of mathematics, operator theory in particular. This technique is very powerful as becomes clear from the analysis of canonical forms (Frobenius, Jordan). It should be emphasized that these functional methods are not only of great theoretical interest, but lead to computational algorithms. Quadratic forms are treated from the same perspective, with emphasis on the important examples of Bezoutian and Hankel forms. These topics are of great importance in applied areas such as signal processing, numerical linear algebra, and control theory. Stability theory and system theoretic concepts, up to realization theory, are treated as an integral part of linear algebra. New sections added on rational interpolation, interpola-tion using H^{\nfty} functions and tensor prod-ucts and models (scalar case). Review from first edition:”Fuhrmann has written an interesting book bring a fresh approach to the structure theory of linear transformations and containing mate-rial that is not readily available elsewhere.”(New Zealand Mathematical Society Newsletter, October 1999)

Features7 Many additions including Rational interpola-tion, interpolation using H^{\nfty} functions and tensor products and models (scalar case) 7 Almost 100 new pages added 7 Allows the reader to access ideas and results on the frontier of current research

Fields of interestLinear and Multilinear Algebras, Matrix Theory; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization

Target groupsProfessional/practitioner

G. Galdi, University of Pittsburgh, PA, USA

An Introduction to the Mathematical Theory of the Navier-Stokes EquationsSteady-State Problems

The book provides a comprehensive, detailed and self-contained treatment of the fundamental mathematical properties of boundary-value problems related to the Navier-Stokes equations. These properties include existence, uniqueness and regularity of solutions in bounded as well as unbounded domains. Whenever the domain is unbounded, the asymptotic behavior of solutions is also investigated. This book is the new edition of the original two volume book, under the same title, published in 1994. In this new edition, the two volumes have merged into one and two more chapters on steady general-ized oseen flow in exterior domains and steady Navier–Stokes flow in three-dimensional exterior domains have been added. Most of the proofs given in the previous edition were also updated.

Features7 Chapter and summary sections included 7 Exercises at the ends of the chapters 7 Two new chapters have been added

ContentsSteady-State Solutions of the Navier–Stokes Equations: Statement of the Problem and Open Questions.- Basic Function Spaces and Related Inequalities.- The Function Spaces of Hydro-dynamics.- Steady Stokes Flow in Bounded Domains.- Steady Stokes Flow in Exterior Domains.- Steady Stokes Flow in Domains with Unbounded Boundaries.- Steady Oseen Flow in Exterior Domains.- Steady Generalized Oseen Flow in Exterior Domains.

Fields of interestPartial Differential Equations; Engineering Fluid Dynamics; Applications of Mathematics


I. P. Gavrilyuk, University of Cooperative Education, Staatliche Studienakademie Thüringen, Berufsakademie Eisenach, Germany; V. L. Makarov, V. Vasylyk, National Academy of Sciences of Ukraine, Kiev, Ukraine

Exponentially Convergent Algorithms for the Differential Equations with Operator Coefficients in Banach Spaces

This book presents new accurate and efficient exponentially convergent methods for abstract differential equations with unbounded operator coefficients in Banach space. These methods are highly relevant for practical scientific computing since the equations under consideration can be seen as the meta-models of systems of ordinary differential equations (ODE) as well as of partial differential equations (PDEs) describing various applied problems. The framework of functional analysis allows one to obtain very general but at the same time transparent algorithms and mathematical results which then can be applied to mathematical models of the real world. The problem class includes initial value problems (IVP) for first order differential equations with constant and variable unbounded operator coefficients in a Banach space (the heat equation is a simple example), boundary value problems for the second order elliptic differential equation with an operator coefficient (e.g. the Laplace equation),

Features7 Contains the first comprehensive and unified theory of exponentially convergent numerical methods for the differential equations with operator coefficients including many important PDEs as particular cases 7 Algorithms inherit a two-level parallelism with respect to both the spatial and the time variables 7 All other books deal with polynomially convergent methods such as the finite difference methods, finite element methods etc.

Fields of interestMathematics, general

Target groupsResearchType of publication

Undergraduate textbook

Due August 2011

2nd ed. 2011. X, 440 p. (Universitext) Softcover


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Due July 2011

Originally published as volume 38 in series: Springer Tracts in Natural Philosophy

2nd ed. 2011. X, 1020 p. 1 illus. (Springer Monographs in Mathematics) Hardcover

7 € 114,95 | £103.507 * € (D) 123,00 | € (A) 126,45 | sFr 165,00ISBN 978-0-387-09619-3

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Due July 2011

2011. VII, 181 p. (Frontiers in Mathematics) Softcover


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P. Gillibert, Charles University in Prague, Czech Republic; F. Wehrung, CNRS, Université de Caen, France

From Objects to Diagrams for Ranges of Functors

This work introduces tools, from the field of category theory, that make it possible to tackle until now unsolvable representation problems (determination of the range of a given functor). The basic idea is: if a functor lifts many objects, then it also lifts many (poset-indexed) diagrams.

Features7 The book is centered on two statements: namely, CLL, and its main precursor, the Armature Lemma, which are results of category theory, with hard proofs, which appear here for the first time. Most of the book is aimed at applications outside category theory, and is thus written as a toolbox 7 The results of the book illustrate how certain representation problems have counterexamples of different cardinalities such as aleph zero, one, two, and explain why 7 CLL and the Armature Lemma have a wide application range, which we illustrate with examples in lattice theory, universal algebra, and ring theory 7 We also give pointers to solutions, made possible by our results, to previ-ously intractable representation problems, with respect to various functors

Contents1 Background.- 2 Boolean Algebras Scaled with Respect to a Poset.- 3 The Condensate Lifting Lemma (CLL).- 4 Larders from First-order Struc-tures.- 5 Congruence-Preserving Extensions.- 6 Larders from von Neumann Regular Rings.- 7 Discussion.

Fields of interestAlgebra; Category Theory, Homological Algebra; General Algebraic Systems


I. G. Graham, T. Y. Hou, O. Lakkis, R. Scheichl (Eds.)

Numerical Analysis of Multiscale Problems

The 91st London Mathematical Society Durham Symposium on “Numerical Analysis of Multiscale Problems’’ was held at Durham, UK, from July 5th to 15th 2010, with more than 100 international participants attending. This book contains 10 invited articles from the meeting’s key speakers, including all those who gave the six short courses of three lectures each. The articles cover a range of topics of contemporary interest in the numerical analysis of multiscale problems, including analysis of forward and inverse PDE problems in hetero-geneous media, of high frequency wave propaga-tion, of atomistic-continuum modelling and of high-dimensional problems arising in modelling uncertainty. Novel upscaling and preconditioning techniques, applications to turbulent multi-phase flow, and to problems of current interest in mate-rials science are all dealt with in the articles.

Fields of interestComputational Mathematics and Numerical Analysis; Computational Science and Engineering


F. Hirsch, University of Evry, France; C. Profeta, B. Roynette, University of Nancy, France; M. Yor, Institut Universitaire de France, Paris

Peacocks and Associated Martingales, with Explicit Constructions

We call peacock an integrable process which is increasing in the convex order; such a notion plays an important role in Mathematical Finance. A deep theorem due to Kellerer states that a process is a peacock if and only if it has the same one-dimen-sional marginals as a martingale. Such a martingale is then said to be associated to this peacock. In this monograph, we exhibit numerous examples of peacocks and associated martingales with the help of different methods: construction of sheets, time reversal, time inversion, self-decomposability, SDE, Skorokhod embeddings. They are devel-oped in eight chapters, with about a hundred of exercises.

Features7 First book on this topic 7 A remarkable range of probabilistic tools 7 Numerous exercises with hints

ContentsSome Examples of Peacocks.- The Sheet Method.- The Time Reversal Method.- The Time Inver-sion Method.- The Sato Process Method.- The Stochastic Differential Equation Method.- The Skorokhod Embedding (SE) Method. Comparison of Multidimensional Marginals.

Fields of interestProbability Theory and Stochastic Processes; Quantitative Finance



Due August 2011


7 € 34,95 | £31.997 * € (D) 37,40 | € (A) 38,45 | sFr 50,50ISBN 978-3-642-21773-9

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Type of publicationContributed volume

Due September 2011

2011. X, 360 p. 50 illus., 10 in color. (Lecture Notes in Computational Science and Engineering, Volume 83) Hardcover

7 € 109,95 | £99.007 * € (D) 117,65 | € (A) 120,95 | sFr 158,00ISBN 978-3-642-22060-9

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Available

2011. 430 p. 11 illus., 6 in color. (Bocconi & Springer Series) Hardcover

7 € 89,95 | £81.007 * € (D) 96,25 | € (A) 98,95 | sFr 129,00ISBN 978-88-470-1907-2

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T. Insperger, G. Stépán, Budapest University of Technology and Economics, Hungary

Semi-Discretization for Time-Delay SystemsStability and Engineering Applications

This book presents the recently introduced and already widely referred semi-discretization method for the stability analysis of delayed dynamical systems. Delay differential equations often come up in different fields of engineering, like feed-back control systems, machine tool vibrations, balancing/stabilization with reflex delay. The behavior of such systems is often counter-intuitive and closed form analytical formulas can rarely be given even for the linear stability conditions. If parametric excitation is coupled with the delay effect, then the governing equation is a delay differential equation with time periodic coeffi-cients, and the stability properties are even more intriguing. The semi-discretization method is a simple but efficient method that is based on the discretization with respect to the delayed term and the periodic coefficients only. The method can effectively be used to construct stability diagrams in the space of system parameters.

Features7 Stability diagrams for some basic delay systems appearing in engineering problems are summa-rized in the introduction 7 The semi-discreti-zation method is presented in a simple and clear way with examples 7 Different approaches for the application of the semi-discretization method is presented considering the rate convergence and numerical efficiency

ContentsIntroducing delay.- Basic delay differential equa-tions.- Newtonian examples.- Engineering applica-tions.- Summary.- References.

Fields of interestDynamical Systems and Ergodic Theory; Control; Mechanical Engineering


J. Jost, Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany

Riemannian Geometry and Geometric Analysis

This established reference work continues to lead its readers to some of the hottest topics of contemporary mathematical research. The previous edition introduced and explained the ideas of the parabolic methods that had found a spectacular success in the work of Perelman at the examples of closed geodesics and harmonic forms. It also discussed further examples of geometric variational problems from quantum field theory, another source of profound new ideas and methods in geometry. The 6th edition includes a systematic treatment of eigenvalues of Rieman-nian manifolds and several other additions. Also, the entire material has been reorganized in order to improve the coherence of the book.

From the reviews 7 “This book provides a very readable introduction to Riemannian geometry and geometric analysis. ... With the vast development of the mathematical subject of geometric analysis, the present textbook is most welcome.” Mathematical Reviews”...the mate-rial ... is self-contained. Each chapter ends with a set of exercises. Most of the paragraphs have a section ‘Perspectives’, written with the aim to place the material in a broader context and explain further results and directions” 7 Zentralblatt MATH

Features7 Continues to lead its readers to some of the hottest topics of contemporary mathematical research 7 Each chapter ends with a set of exercises 7 The 6th edition includes a systematic treatment of eigenvalues of Riemannian manifolds and several other addition

Fields of interestDifferential Geometry; Theoretical, Mathematical and Computational Physics

Target groupsGraduate

S. Jung, Hongik University, Jochiwon, Republic of South Korea

Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis

No books dealing with a comprehensive illustra-tion of the fast developing field of nonlinear analysis had been published for the mathemati-cians interested in this field for more than a half century until D. H. Hyers, G. Isac and Th. M. Rassias published their book, “Stability of Functional Equations in Several Variables”. This book will complement the books of Hyers, Isac and Rassias and of Czerwik (Functional Equa-tions and Inequalities in Several Variables) by presenting mainly the results applying to the Hyers-Ulam-Rassias stability. Many mathemati-cians have extensively investigated the subjects on the Hyers-Ulam-Rassias stability. This book covers and offers almost all classical results on the Hyers-Ulam-Rassias stability in an integrated and self-contained fashion.

Features7 Organized such that highly advanced under-graduate as well as graduate level students will be able to follow the materials 7 Contains unified notation and refined formulaeAll the necessary materials and information are included in this book 7 Offers almost all classical results on the Hyers—Ulam—Rassias stability in an integrated and self-contained fashion

Fields of interestDifference and Functional Equations; Analysis; Functional Analysis



Due July 2011

2011. X, 170 p. 50 illus. (Applied Mathematical Sciences, Volume 178) Hardcover


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Due August 2011

6th ed. 2011. XIII, 612 p. (Universitext) Softcover

7 € 64,95 | £49.997 * € (D) 69,50 | € (A) 71,45 | sFr 93,50ISBN 978-3-642-21297-0

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Available

2011. XVI, 364 p. 1 illus. (Springer Optimization and Its Applications, Volume 48) Hardcover

7 € 59,95 | £53.997 * € (D) 64,15 | € (A) 65,95 | sFr 86,00ISBN 978-1-4419-9636-7

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M. Kano, Ibaraki University, Hitachi, Japan; J. Akiyama, Tokai University, Shibuya-ku, Japan

Factors and Factorizations of GraphsProof Techniques in Factor Theory

This book chronicles the development of graph factors and factorizations. It pursues a comprehen-sive approach, addressing most of the important results from hundreds of findings over the last century. One of the main themes is the observa-tion that many theorems can be proved using only a few standard proof techniques. This stands in marked contrast to the seemingly countless, complex proof techniques offered by the extant body of papers and books. In addition to covering the history and development of this area, the book offers conjectures and discusses open problems. It also includes numerous explanatory figures that enable readers to progressively and intuitively understand the most important notions and proofs in the area of factors and factorization.

Features7 The book is self-contained and comprehen-sive, allowing readers to rely on it exclusively to understand the entire history and development of this area 7 Unlike other books, in which difficult proof techniques are simply lifted from earlier sources, in this book, the contents of each proof technique is analyzed and streamlined 7 Each chapter features conjectures and open problems, inspiring readers to further their own study

Contents1 Basic Terminology.- 2 Matchings and 1-Factors.- 3 Regular Factors and f-Factors.- 4 (g, f)-Factors and [a, b]-Factors.- 5 [a, b]-Factorizations.- 6 Parity Factors.- 7 Component Factors.- 8 Spanning Trees.

Fields of interestMathematics, general; Programming Techniques


P. S. Knopov, Department of Mathematical Methods of Operation Research, V.M. Glushkov Institute of Cybernetics, National Academy of Science of Ukraine, 03187 Kiev, Ukraine; A. S. Korkhin, Department of Economical Cybernetics and Information Technology, National Mining University, 49005 Dnepropetrovsk, Ukraine

Regression Analysis Under A Priori Parameter Restrictions

This monograph focuses on the construction of regression models with linear and non-linear constrain inequalities from the theoretical point of view. Unlike previous publications, this volume analyses the properties of regression with inequality constrains, investigating the flexibility of inequality constrains and their ability to adapt in the presence of additional a priori information The implementation of inequality constrains improves the accuracy of models, and decreases the likelihood of errors. Based on the obtained theoretical results, a computational technique for estimation and prognostication problems is suggested. This approach lends itself to numerous applications in various practical problems, several of which are discussed in detail The book is useful resource for graduate students, PhD students, as well as for researchers who specialize in applied statistics and optimization. This book may also be useful to specialists in other branches of applied mathematics, technology, econometrics and finance

Features7 Presents four central topics in stochastic opti-mization: calculation of parameter estimates, the asymptotic theory of estimates, estimation theory for small samples, and prediction theory 7 Describes applications to practical problems from various areas of study including economet-rics, clinical medicine, and several other experi-mental sciences 7 Considers the problems of prediction by means of linear regression in the context of small samples

Fields of interestOperations Research, Management Science; Statis-tical Theory and Methods; Probability Theory and Stochastic Processes


V. Koltchinskii, Georgia Institute of Technology, Atlanta GA, USA

Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery ProblemsEcole d’Eté de Probabilités de Saint-FlourXXXVIII-2008

The purpose of these lecture notes is to provide an introduction to the general theory of empirical risk minimization with an emphasis on excess risk bounds and oracle inequalities in penalized prob-lems. In recent years, there have been new devel-opments in this area motivated by the study of new classes of methods in machine learning such as large margin classification methods (boosting, kernel machines). The main probabilistic tools involved in the analysis of these problems are concentration and deviation inequalities by Talagrand along with other methods of empirical processes theory (symmetrization inequalities, contraction inequality for Rademacher sums, entropy and generic chaining bounds). Sparse recovery based on l_1-type penalization and low rank matrix recovery based on the nuclear norm penalization are other active areas of research, where the main problems can be stated in the framework of penalized empirical risk minimiza-tion, and concentration inequalities and empirical processes tools have proved to be very useful.

Features7 Provides a unified framework for machine learning problems (such as large margin clas-sification), sparse recovery and low rank matrix problems 7 Develops a variety of probabilistic inequalities for empirical processes needed to obtain error bounds in machine learning and sparse recovery 7 Develops a comprehensive theory of excess risk bounds and oracle inequali-ties for penalized empirical risk minimization

Field of interestProbability Theory and Stochastic Processes



Due July 2011


7 € 69,95 | £62.997 * € (D) 74,85 | € (A) 76,95 | sFr 100,50ISBN 978-3-642-21918-4

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Due October 2011

2011. XIV, 282 p. 4 illus. (Springer Optimization and Its Applications, Volume 54) Hardcover


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Due August 2011

2011. X, 230 p. (Lecture Notes in Mathematics / École d’Été de Probabilités de Saint-Flour, Volume 2033) Softcover

7 € 44,95 | £40.997 * € (D) 48,10 | € (A) 49,45 | sFr 64,50ISBN 978-3-642-22146-0

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H. P. Langtangen, Simula Research Laboratory, Lysaker, Norway

Python Scripting for Computational Science

Now in its revised and updated 4th edition, this book teaches computational scientists how to develop tailored, flexible, and human-efficient working environments built from small programs written in the easy-to-learn, high-level Python language.As in the previous edition, the focus is on highly relevant examples and applications. These include binding together existing applications and tools, for example, for automating simulation, data analysis, and visualization.The book also covers steering simulations and computational experi-ments; equipping old programs with graphical user interfaces; making computational Web applica-tions; and creating interactive interfaces with a Maple/Matlab-like syntax to numerical applica-tions in C/C++ or Fortran.The highly regarded author, Hans Petter Langtangen, demonstrates that scripting with Python helps the programmer achieve much greater productivity, increases the reliability of scientific work and lets programmers have more fun - on Unix, Windows and Macintosh.

Features7 Shows how to develop tailored, flexible, and human-efficient working environments using the easy-to-learn, high-level Python language 7 Focuses on examples and applications of prac-tical use to computational scientists 7 Compatible with the new NumPy implementation and features updated information, correction of errors, and improved associated software tools 7 Updated information on many new and revised Python tools

Contents

Fields of interestComputational Science and Engineering; Numerical and Computational Physics ; Software Engineering/Programming and Operating Systems


J. Neuberger, Department of Mathematics, University of North Texas, Denton, TX, USA

A Sequence of Problems on Semigroups

This text consists of a sequence of problems which develop a variety of aspects in the field of semigroupsof operators. Many of the problems are not found easily in other books. Written in the Socratic/Moore method, this is a problem book without the answers presented. To get the most out of the content requires high motivation from the reader to work out the exercises. The reader is given the opportunity to discover important developments of the subject and to quickly arrive at the point of independent research. The compact-ness of the volume and the reputation of the author lends this consider set of problems to be a ‘classic’ in the making. This text is highly recom-mended for us as supplementary material for 3 graduate level courses.

Features7 Written in the Socratic/Moore method style and provision of references, enables the motivated student to arrive at the point of independent research 7 Student who works through the prob-lems will have a range of introduction to aspects of one-parameter semigroups of transformations 7 Problems include wide applicability to prob-ability and the Heat equation

ContentsPreface.-1. Introduction.-2. The idea of a semi-group.-3. Translation semigroups.-4. Linear contin-uous semigroups.-5.Strongly continuous linear semigroups.-6. An Application to the Heat Equa-tion.-7. Some Problems in Analysis.-8.Semigroups of steepest descent.-9. Numerics of semigroups of steepest descent.-10. Nonlinear semigroups studied by linear methods.-11. Measures and linear exten-sion of nonlinear semigroups.

Fields of interestOrder, Lattices, Ordered Algebraic Structures; Category Theory, Homological Algebra; General Algebraic Systems


C. A. Oliveira, Bloomberg LP, New York, NY, USA; P. M. Pardalos, University of Florida, Gainesville, FL, USA

Mathematical Aspects of Network Routing Optimization

Before the appearance of broadband links and wireless systems, networks have been used to connect people in new ways. Now, the modern world is connected through large-scale, compu-tational networked systems such as the Internet. Because of the ever-advancing technology of networking, efficient algorithms have become increasingly necessary to solve some of the problems developing in this area.”Mathematical Aspects of Network Routing Optimization” focuses on computational issues arising from the process of optimizing network routes, such as quality of the resulting links and their reliability. Algorithms are a cornerstone for the understanding of the protocols underlying multicast routing. The main objective in the text is to derive efficient algo-rithms, with or without guarantee of approxima-tion. Notes have been provided for basic topics such as graph theory and linear programming to assist those who are not fully acquainted with the mathematical topics presented throughout the book.” Mathematical Aspects of Network Routing Optimization” provides a thorough introduction to the subject of algorithms for network routing, and focuses especially on multicast and wireless ad hoc systems.

Features7 Provides an overview of network routing optimization, and acts as an introduction to algorithms that can be used to solve optimization problems that arise from networks 7 Describes many of the problems for those who may not have been introduced to the more advanced math 7 Is a solid introduction to network routing optimization, but also presents topics for further advanced research

Fields of interestOptimization; Algorithms; Computer Communi-cation Networks



Due September 2011

4th ed. 2011. XXVI, 760 p. 70 illus. in color. (Texts in Computational Science and Engineering, Volume 3) Hardcover


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Due August 2011

2011. VI, 146 p. (Problem Books in Mathematics) Hardcover


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Due September 2011

2011. XXIV, 218 p. 47 illus. (Springer Optimization and Its Applications, Volume 53) Hardcover

7 € 79,95 | £72.007 * € (D) 85,55 | € (A) 87,95 | sFr 115,00ISBN 978-1-4614-0310-4

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M. Pietikäinen, A. Hadid, G. Zhao, Machine Vision Group, Department of Computer Science and Engineering, University of Oulu, Oulu, Finland; T. Ahonen, Visual Computing and Ubiquitous Imaging Research Team, Nokia Research Center, Palo Alto, CA, USA

Computer Vision Using Local Binary Patterns

The recent emergence of Local Binary Patterns (LBP) has led to significant progress in applying texture methods to various computer vision problems and applications. The focus of this research has broadened from 2D textures to 3D textures and spatiotemporal (dynamic) textures. Also, where texture was once utilized for applica-tions such as remote sensing, industrial inspection and biomedical image analysis, the introduc-tion of LBP-based approaches have provided outstanding results in problems relating to face and activity analysis, with future scope for face and facial expression recognition, biometrics, visual surveillance and video analysis. Computer Vision Using Local Binary Patterns provides a detailed description of the LBP methods and their variants both in spatial and spatiotemporal domains. This comprehensive reference also provides an excellent overview as to how texture methods can be utilized for solving different kinds of computer vision and image analysis problems. Source codes of the basic LBP algorithms, demonstrations, some databases and a comprehensive LBP bibliography can be found from an accompanying web site.

Features7 Written by pioneers in the topic of Local Binary Patterns Contains a wealth of illustrations to aid a deeper understanding of the subject 7 Offers those working with LBPs a single point of refer-ence by providing a comprehensive coverage of the uses of Local Binary Pattern methodology

Fields of interestMathematics, general; Computer Imaging, Vision, Pattern Recognition and Graphics; Image Processing and Computer Vision


L. Robbiano, Università di Genova, Italia

Álgebra LinearPara todos

O objetivo deste livro é o de fornecer as primeiras ferramentas matemáticas associadas à Álgebra Linear. O texto foi elaborado por um matemático que procurou “sair do seu personagem” para vir ao encontro de um público amplo. O desafio é o de tornar acessível a todos, os primeiros fundamentos e as primeiras técnicas de um saber fundamental para a ciência e a tecnologia. Com esse intuito, o autor escolheu escrevê-lo em um estilo não tradicional e o enriqueceu não somente com exer-cícios, mas também com frases de auto-referência, aforismos, citações, palíndromos e problemas para serem resolvidos com a ajuda do computador. O livro é para todos, mas tem uma dedicação espe-cial aos estudantes dos cursos de graduação em disciplinas científicas e aos professores cujo texto poderá ser útil também como material de consulta.

Features7 Fornecer as primeiras ferramentas matemáticas associadas à Álgebra Linear 7 Render acessível a todos os primeiros fundamentos e as primeiras técnicas de um saber fundamental para a ciência e a tecnologia 7 Livro de fácil compreensão que pode ser utilizado por qualquer pessoa com interesse em entender fatos básicos da matemática associados à Álgebra Linear

Fields of interestAlgebra; Linear and Multilinear Algebras, Matrix Theory

Target groupsLower undergraduate

B. Straughan, Durham University, Durham, United Kingdom

Heat WavesThis book surveys significant modern contribu-tions to the mathematical theories of generalized heat wave equations. The first three chapters form a comprehensive survey of most modern contribu-tions also describing in detail the mathematical properties of each model. Acceleration waves and shock waves are the focus in the next two chapters. Numerical techniques, continuous data depen-dence, and spatial stability of the solution in a cylinder, feature prominently among other topics treated in the following two chapters. The final two chapters are devoted to a description of selected applications and the corresponding formation of mathematical models. Illustrations are taken from a broad range that includes nanofluids, porous media, thin films, nuclear reactors, traffic flow, biology, and medicine, all of contemporary active technological importance and interest. This book will be of value to applied mathematicians, theoretical engineers and other practitioners who wish to know both the theory and its relevance to diverse applications.

Features7 Timely applications in nanofluidics and biology 7 Well known researcher 7 Analytical and Numerical solutions included

ContentsPreface.-Introduction.- Interaction with elasticity.-Interaction with fluids.-Acceleration waves.-Shock waves.-Numerical solutions.-Qualitative estimates.-Spatial decay.-Nanofluids.-Other applications.-References.

Fields of interestApplications of Mathematics; Classical Continuum Physics; Fluid- and Aerodynamics



Due August 2011

2011. XIV, 210 p. 87 illus., 56 in color. (Computational Imaging and Vision, Volume 40) Hardcover

7 € 79,95 | £69.957 * € (D) 85,55 | € (A) 87,95 | sFr 115,00ISBN 978-0-85729-747-1

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Available

2011. XV, 200 p. Softcover

7 € 30,95 | £27.997 * € (D) 33,12 | € (A) 34,05 | sFr 44,50ISBN 978-88-470-1886-0

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Due July 2011

2011. 340 p. (Applied Mathematical Sciences, Volume 177) Hardcover


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M. Ullah, O. Wolkenhauer, University of Rostock, Rostock, Germany

Stochastic Approaches for Systems Biology

This textbook focuses on stochastic analysis in systems biology containing both the theory and application. While the authors provide a review of probability and random variables, subse-quent notions of biochemical reaction systems and the relevant concepts of probability theory are introduced side by side. This leads to an intui-tive and easy-to-follow presentation of stochastic framework for modeling subcellular biochemical systems. In particular, the authors make an effort to show how the notion of propensity, the chemical master equation and the stochastic simulation algorithm arise as consequences of the Markov property. The text contains many illustrations, examples and exercises to illustrate the ideas and methods that are introduced. Matlab code is also provided where appropriate. Additionally, the cell cycle is introduced as a more complex case study. Senior undergraduate and graduate students in mathematics and physics as well as researchers working in the area of systems biology, bioinformatics and related areas will find this text useful.

Features7 Focuses on both analytical and numer-ical approaches 7 Key Concepts in Stochastic Processes 7 Matlab examples provided 7 Many illustrations and examples included

ContentsPreface.-Acknowledgments.-Acronyms.-Notation.-List of Figures.-List of Tables.-Introduction.-Probability and random variables.-Stochastic modelling.-The 2MA approach.-The 2MA cell cycle model.-Markov processes with both continuous and jump character.-Matlab codes.-Bibliography.

Fields of interestProbability Theory and Stochastic Processes; Systems Biology; Mathematical and Computa-tional Biology


A. Wazwaz, Saint Xavier University, Chicago, IL, USA

Linear and Nonlinear Integral EquationsMethods and Applications

Linear and Nonlinear Integral Equations: Methods and Applications is a self-contained book divided into two parts. Part I offers a comprehensive and systematic treatment of linear integral equations of the first and second kinds. The text brings together newly developed methods to reinforce and complement the existing procedures for solving linear integral equations. The Volterra integral and integro-differential equations, the Fredholm integral and integro-differential equations, the Volterra-Fredholm integral equations, singular and weakly singular integral equations, and systems of these equations, are handled in this part by using many different computational schemes. Selected worked-through examples and exercises will guide readers through the text. Part II provides an extensive exposition on the nonlinear integral equations and their varied applications, presenting in an accessible manner a systematic treatment of ill-posed Fredholm problems, bifurcation points, and singular points. Selected applications are also investigated by using the powerful Padé approximants. This book is intended for scholars and researchers in the fields of physics, applied mathematics and engineering.

Features7 Comprehensively and systematically treats linear and nonlinear integral equations 7 Makes materials on the linear and nonlinear integral equations accessible without depending heavily on abstract theorems 7 Builds a useful bridge between learning and research in mathematics 7 Offers a large number of well-explained exam-ples and practice problems along with answers

Fields of interestIntegral Equations; Theoretical, Mathematical and Computational Physics; Appl.Mathematics/Computational Methods of Engineering



Due August 2011

2011. X, 190 p. Hardcover


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Due September 2011

Distribution rights in China: Higher Education Press

Jointly published with Higher Education Press

2011. XVIII, 639 p. 4 illus. Hardcover

7 € 139,95 | £126.007 * € (D) 149,75 | € (A) 153,94 | sFr 201,00ISBN 978-3-642-21448-6

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Documents

M. Abate F. Tovena M. Abate F. Tovena TX, USA; , Florida ... · M. Abate, Università di Pisa, Italy; F. Tovena, Università di Roma Tor Vergata, Italy Geometria Differenziale L’opera