Mathematics springer.com/NEWSonline 18 T. Andreescu, The University of Texas at Dallas, Richardson, TX, USA; D. Andrica, Babeş-Bolyai University, Cluj-Napoca, Romania Complex Numbers from A to ... Z It is impossible to imagine modern mathematics without complex numbers. e second edition of Complex Numbers from A to … Z introduces the reader to this fascinating subject that from the time of L. Euler has become one of the most utilized ideas in mathematics. e exposition concentrates on key concepts and then elementary results concerning these numbers. e reader learns how complex numbers can be used to solve algebraic equations and to understand the geo- metric interpretation of complex numbers and the operations involving them. e theoretical parts of the book are augmented with rich exercises and problems at various levels of difficulty. Features 7 Learn how complex numbers may be used to solve algebraic equations as well as their geo- metric interpretation 7 eoretical aspects are augmented with rich exercises and problems at various levels of difficulty 7 A special feature is a selection of outstanding Olympiad problems solved by employing the methods present- ed 7 May serve as an engaging supplemental text for an introductory undergrad course on complex numbers or number theory Contents Preface.- Complex Numbers in Algebraic Form.- Complex Numbers in Trigonometric Form.- Com- plex Numbers and Geometry.- More on Complex Numbers and Geometry.- Olympiad-Caliber Problems.- Answers, Hints and Solutions to Proposed Problems.- Glossary.- References.- Index of Authors. Fields of interest Number eory; Algebraic Geometry; Geometry Target groups Lower undergraduate Product category Undergraduate textbook Due January 2014 2nd ed. 2014. X, 435 p. 81 illus. Softcover 7 * € (D) 48,14 | € (A) 49,49 | sFr 60,00 7 € 44,99 | £40.99 ISBN 978-0-8176-8414-3 9<HTLIMH=giebed> S. Chatterjee, Stanford University, Stanford, CA, USA Superconcentration and Related Topics A certain curious feature of random objects, introduced by the author as “super concentration,” and two related topics, “chaos” and “multiple val- leys,” are highlighted in this book. Although super concentration has established itself as a recognized feature in a number of areas of probability theory in the last twenty years (under a variety of names), the author was the first to discover and explore its connections with chaos and multiple valleys. He achieves a substantial degree of simplification and clarity in the presentation of these findings by using the spectral approach. Features 7 First book devoted to the topic of super con- centration, chaos and multiple valleys 7 Presents a wide array of examples on the subject 7 In- tegrates new concepts and gives a systematic account of the history and development of the features of random objects Contents Preface.- 1.Introduction.- 2.Markov semigroups.- 3.Super concentration and chaos.- 4.Multiple valleys.- 5.Talagrand’s method for proving super concentration.- 6.e spectral method for proving super concentration.- 7.Independent flips.- 8.Ex- tremal fields.- 9.Further applications of hyper- contractivity.- 10.e interpolation method for proving chaos.- 11.Variance lower bounds.- 12.Di- mensions of level sets.- Appendix A. Gaussian random variables.- Appendix B. Hypercontractiv- ity.- Bibliography.- Indices. Fields of interest Probability eory and Stochastic Processes; Mathematical Physics; Statistical Physics, Dynami- cal Systems and Complexity Target groups Research Product category Monograph Due May 2014 2014. X, 140 p. (Springer Monographs in Mathematics) Hardcover 7 approx. * € (D) 90,94 | € (A) 93,49 | sFr 113,50 7 approx. € 84,99 | £76.50 ISBN 978-3-319-03885-8 9<HTODMJ=adiifi> A. Contin, P. Paolini, R. Salerno, Politecnico di Milano, Milano, Italy (Eds) Innovative Technologies in Urban Mapping Built Space and Mental Space e book presents a comprehensive vision of the impact of ICT on the contemporary city, heritage, public spaces and meta-cities on both urban and metropolitan scales, not only in produc- ing innovative perspectives but also related to newly discovered scientific methods, which can be used to stimulate the emerging reciprocal relations between cities and information technologies. Features 7 Multidisciplinary and innovative use of ICT in urban studies and fast growing cities 7 Present- ing new and original research in both theoretical and practical fields 7 Presenting newly discov- ered scientific methods Contents Part I e Academic Question of Research.- Part II e institution’s claim.- Part III Technologies for communicating architecture and urban spaces.- Part IV Modelling tool soſtware, Processing lan- guage and environment methodology, urban sim- ulation and projects evaluation.- Part V Advanced digital design and manufacturing technologies and Architectonic and Urban design project.- Part VI Critical reactions: A bridge between academic core concepts and new PhD researches. Fields of interest Mathematical Soſtware; Computer Systems Organization and Communication Networks; Multimedia Information Systems Target groups Research Product category Contributed volume Due December 2013 2014. Approx. 200 p. (SxI - Springer for Innovation / SxI - Springer per l’Innovazione, Volume 10) Softcover 7 * € (D) 90,94 | € (A) 93,49 | sFr 113,50 7 € 84,99 | £76.50 ISBN 978-3-319-03797-4 9<HTODMJ=adhjhe>
Transcript
Mathematics springer.com/NEWSonline
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T. Andreescu, The University of Texas at Dallas, Richardson, TX, USA; D. Andrica, Babeş-Bolyai University, Cluj-Napoca, Romania
Complex Numbers from A to ... ZIt is impossible to imagine modern mathematics without complex numbers. The second edition of Complex Numbers from A to … Z introduces the reader to this fascinating subject that from the time of L. Euler has become one of the most utilized ideas in mathematics. The exposition concentrates on key concepts and then elementary results concerning these numbers. The reader learns how complex numbers can be used to solve algebraic equations and to understand the geo-metric interpretation of complex numbers and the operations involving them. The theoretical parts of the book are augmented with rich exercises and problems at various levels of difficulty.
Features 7 Learn how complex numbers may be used to solve algebraic equations as well as their geo-metric interpretation 7 Theoretical aspects are augmented with rich exercises and problems at various levels of difficulty 7 A special feature is a selection of outstanding Olympiad problems solved by employing the methods present-ed 7 May serve as an engaging supplemental text for an introductory undergrad course on complex numbers or number theory
Contents Preface.- Complex Numbers in Algebraic Form.- Complex Numbers in Trigonometric Form.- Com-plex Numbers and Geometry.- More on Complex Numbers and Geometry.- Olympiad-Caliber Problems.- Answers, Hints and Solutions to Proposed Problems.- Glossary.- References.- Index of Authors.
Fields of interestNumber Theory; Algebraic Geometry; Geometry
S. Chatterjee, Stanford University, Stanford, CA, USA
Superconcentration and Related TopicsA certain curious feature of random objects, introduced by the author as “super concentration,” and two related topics, “chaos” and “multiple val-leys,” are highlighted in this book. Although super concentration has established itself as a recognized feature in a number of areas of probability theory in the last twenty years (under a variety of names), the author was the first to discover and explore its connections with chaos and multiple valleys. He achieves a substantial degree of simplification and clarity in the presentation of these findings by using the spectral approach.
Features 7 First book devoted to the topic of super con-centration, chaos and multiple valleys 7 Presents a wide array of examples on the subject 7 In-tegrates new concepts and gives a systematic account of the history and development of the features of random objects
Contents Preface.- 1.Introduction.- 2.Markov semigroups.- 3.Super concentration and chaos.- 4.Multiple valleys.- 5.Talagrand’s method for proving super concentration.- 6.The spectral method for proving super concentration.- 7.Independent flips.- 8.Ex-tremal fields.- 9.Further applications of hyper-contractivity.- 10.The interpolation method for proving chaos.- 11.Variance lower bounds.- 12.Di-mensions of level sets.- Appendix A. Gaussian random variables.- Appendix B. Hypercontractiv-ity.- Bibliography.- Indices.
Fields of interestProbability Theory and Stochastic Processes; Mathematical Physics; Statistical Physics, Dynami-cal Systems and Complexity
A. Contin, P. Paolini, R. Salerno, Politecnico di Milano, Milano, Italy (Eds)
Innovative Technologies in Urban MappingBuilt Space and Mental Space
The book presents a comprehensive vision of the impact of ICT on the contemporary city, heritage, public spaces and meta-cities on both urban and metropolitan scales, not only in produc-ing innovative perspectives but also related to newly discovered scientific methods, which can be used to stimulate the emerging reciprocal relations between cities and information technologies.
Features 7 Multidisciplinary and innovative use of ICT in urban studies and fast growing cities 7 Present-ing new and original research in both theoretical and practical fields 7 Presenting newly discov-ered scientific methods
Contents Part I The Academic Question of Research.- Part II The institution’s claim.- Part III Technologies for communicating architecture and urban spaces.- Part IV Modelling tool software, Processing lan-guage and environment methodology, urban sim-ulation and projects evaluation.- Part V Advanced digital design and manufacturing technologies and Architectonic and Urban design project.- Part VI Critical reactions: A bridge between academic core concepts and new PhD researches.
Fields of interestMathematical Software; Computer Systems Organization and Communication Networks; Multimedia Information Systems
F. Fujie, Nagoya University, Nagoya, Japan; P. Zhang, Western Michigan University, Kalamazoo, MI, USA
Covering Walks in GraphsCovering Walks in Graphs is aimed at research-ers and graduate students in the graph theory community and provides a comprehensive treat-ment on measures of two well studied graphical properties, namely Hamiltonicity and travers-ability in graphs. This text looks into the famous Kӧnigsberg Bridge Problem, the Chinese Postman Problem, the Icosian Game and the Traveling Salesman Problem as well as well-known math-ematicians who were involved in these problems. The concepts of different spanning walks with examples and present classical results on Hamil-tonian numbers and upper Hamiltonian numbers of graphs are described; in some cases, the authors provide proofs of these results to illustrate the beauty and complexity of this area of research. Two new concepts of traceable numbers of graphs and traceable numbers of vertices of a graph which were inspired by and closely related to Hamiltonian numbers are introduced. Results are illustrated on these two concepts and the relation-ship between traceable concepts and Hamiltonian concepts are examined.
Features 7 Provides a comprehensive treatment on measures of Hamiltonicity and traversability in graphs 7 Contains intriguing open problems and conjectures on spanning walks in graphs 7 De-scribes new frame works for several well-known Hamiltonian concepts with interesting new results
Fields of interestGraph Theory; Combinatorics; Applications of Mathematics
Target groupsResearch
Product categoryBrief
Due January 2014
2014. X, 118 p. 37 illus., 11 in color. (SpringerBriefs in Mathematics) Softcover7 * € (D) 53,49 | € (A) 54,99 | sFr 67,007 € 49,99 | £44.99ISBN 978-1-4939-0304-7
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G. N. Gatica, Universidad de Concepcion, Concepcion, Chile
A Simple Introduction to the Mixed Finite Element MethodTheory and Applications
The main purpose of this book is to provide a simple and accessible introduction to the mixed finite element method as a fundamental tool to numerically solve a wide class of boundary value problems arising in physics and engineer-ing sciences. The book is based on material that was taught in corresponding undergraduate and graduate courses at the Universidad de Concep-cion, Concepcion, Chile, during the last 7 years. As compared with several other classical books in the subject, the main features of the present one have to do, on one hand, with an attempt of pre-senting and explaining most of the details in the proofs and in the different applications. In particu-lar several results and aspects of the corresponding analysis that are usually available only in papers or proceedings are included here.
Features 7 Presentation and explanation of most of the details in the proofs and in the different applica-tions 7 Inclusion of results that are usually available only in papers or proceedings 7 Em-phasis on core concepts and fundamental results that need to be understood previously by thesis students and young researchers
Contents Introduction.- The Babuska-Brezzi Theory.- Raviart-Thomas Spaces.- Mixed Finite Element Methods.
Fields of interestNumerical Analysis; Partial Differential Equations; Several Complex Variables and Analytic Spaces
K. Ito, Kyoto University RIMS, Kyoto, Japan D. Stroock, S. Varadhan (Eds)
Selected PapersKiyosi Itô (1915 - 2008) was one of the pioneers of probability theory, and the originator of Ito Calculus. First published in 1942 in Japanese, this epoch-making theory of stochastic differential equations describes nondeterministic and random evolutions. The Ito formula has found applica-tions in other branches of mathematics as well as in various other fields including e.g., conformal field theory in physics, stochastic control theory in engineering, population genetics in biology and mathematical finance in economics. Besides being renowned for his brilliant mathematical achievements during a long and productive career spanning over sixty years, Itô has been a truly inspirational teacher to many mathematicians. He has received numerous awards and honors, including the 1987 Wolf Foundation Prize in Mathematics, the 1998 Kyoto Prize in Basic Sci-ences and the 2003 Japanese Cultural Merit Prize. In 2006, Itô was awarded the first Carl Friedrich Gauss Prize for Applications of Mathematics. This book contains a selection of 38 papers published between 1941 and 1983.
F. Klein, Universität Göttingen Mathematisches Institut, Göttingen, Germany; A. Sommerfeld, Universität München Fak. Mathematik, München, Germany
The Theory of the Top. Volume IVTechnical Applications of the Theory of the Top
Translated by: R. J. Nagem, G. Sandri, Boston University, Boston, MA, USA
The Theory of the Top. Volume IV. Techni-cal Applications of the Theory of the Top is the fourth and final volume in a series of self-contained English translations of the classic and definitive treatment of rigid body motion. Key features: * Complete and unabridged presentation with recent advances and additional notes; * An-notations by the translators provide insights into the nature of science and mathematics in the late 19th century; * Each volume interweaves theory and applications. The Theory of the Top was origi-nally presented by Felix Klein as an 1895 lecture at Göttingen University that was broadened in scope and clarified as a result of collaboration with Arnold Sommerfeld. Graduate students and researchers interested in theoretical and applied mechanics will find this series of books a thorough and insightful account.
Features 7 Provides insights into kinematic theo-ry 7 Discusses practical uses of applied theoreti-cal mechanics 7 Incorporates both historical matter and recent advances
Contents Chapter IX: Technical applications.
Fields of interestHistory of Mathematical Sciences; Mathematical Methods in Physics; Mechanics
New SeriesSpringerBriefs in OptimizationSeries editors: P. M. Pardalos, S. M. Robinson
SpringerBriefs present concise summaries of cutting-edge research and practical applica-tions across a wide spectrum of fields. Featuring compact volumes of 50 to 125 pages, the series covers a range of content from professional to academic. Briefs are characterized by fast, global electronic dissemination, standard publishing con-tracts, standardized manuscript preparation and formatting guidelines, and expedited production schedules. Typical topics might include: A timely report of state-of-the art techniques A bridge between new research results, as published in journal articles, and a contextual literature review A snapshot of a hot or emerging topic An in-depth case study A presentation of core concepts that students must understand in order to make independent contributions SpringerBriefs in Op-timization showcase algorithmic and theoretical techniques, case studies, and applications within the broad-based field of optimization. Manu-scripts related to the ever-growing applications of optimization in applied mathematics, engineering, medicine, economics, and other applied sciences are encouraged. Series Editors Panos M. Pardalos, University of Florida János D. Pintér, PCS Inc. Stephen M. Robinson,University of Wisconsin-Madison Tamás Terlaky, Lehigh University My T. Thai, University of Florida
I. S. Kotsireas, Wilfrid Laurier University, Waterloo, ON, Canada; S. N. Mujahid, P. Pardalos, University of Florida, Gainesville, FL, USA
D-Optimal MatricesThis is the first book devoted to the computa-tional aspects of D-optimal matrices. The mono-graph presents a compendium of known algo-rithmic techniques used to search for D-optimal matrices of a specific type and a unique approach in searching for D-optimal matrices as combi-natorial optimization problems. The application of each algorithm is illustrated with fully worked examples. New results on D-optimal matrices are also stated and proven.
Features 7 There is no book devoted to the computa-tional aspects of D-optimal matrices 7 Most algorithms used to look for D-optimal matrices are scattered in research papers 7 Phrasing the problem of searching for D-optimal matrices as a Combinatorial Optimization problem has never been done before in the literature
Contents 1. Introduction (statement of the problem, basic definitions, PAF). -2. Properties of D-optimal matrices (determinant, Ehlich’s two-circulant construction, symmetries). -3. Algorithms for searching for D-optimal matrices (power spectral density, supplementary difference sets, string sorting, combinatorial optimization). -4. Features of the objective function landscapes for D-optimal matrices. -5. Applications of D-optimal matrices. -6. Bibliographical references. -7. Subject Index.
Fields of interestMathematical Modeling and Industrial Mathemat-ics; Quality Control, Reliability, Safety and Risk; Statistics, general
Target groupsResearch
Product categoryBrief
Due September 2014
2014. IV, 104 p. 20 illus. (SpringerBriefs in Optimization) Softcover7 approx. * € (D) 53,45 | € (A) 54,95 | sFr 72,007 approx. € 49,95 | £44.99ISBN 978-1-4419-9343-4
H. Koch, University of Bonn, Bonn, Germany; D. Tataru, University of California, Berkeley, CA, USA; M. Visan, University of California, Los Angeles, CA, USA
Dispersive Equations and Nonlinear WavesGeneralized Korteweg–de Vries, Nonlinear Schrödinger, Wave and Schrödinger Maps
The first part of the book provides an introduc-tion to key tools and techniques in dispersive equations: Strichartz estimates, bilinear estimates, modulation and adapted function spaces, with an application to the generalized Korteweg-de Vries equation and the Kadomtsev-Petviashvili equa-tion. The energy-critical nonlinear Schrödinger equation, global solutions to the defocusing prob-lem, and scattering are the focus of the second part. Using this concrete example, it walks the reader through the induction on energy technique, which has become the essential methodology for tackling large data critical problems.
Features 7 Exposition of central ideas in dispersive equations 7 Basic techniques and function spaces 7 Coherent introduction to induction on energy, minimal blowup solutions and interaction Morawetz estimates 7 Introduction to gauge transform, choice of functions spaces, and control of interacting waves
Contents Local existence of solutions to the initial value problem for dispersive equations.- The energy critical nonlinear Schrödinger equation.- Wave maps and Schrödinger maps.
M. Kriele, Hoboken, NJ, USA; J. Wolf, Fachbereich Mathematik und Technik, Remagen, Germany
Value- Oriented Risk Management of Insurance CompaniesValue- and risk-oriented management is a holistic method of managing businesses. In this book both actuarial methods and methods pertain-ing to classical internal control and classical risk management are used. Therefore the approach taken is necessarily interdisciplinary. Indeed, there is a new dynamically developing field for actuaries as a result of the emphasis now on the measure-ment of risk. This book provides the required basic knowledge for this subject from an actuarial perspective. It enables the reader to implement in practice a risk management system that is based on quantitative methods.
Features 7 Combines a discussion of practical methods for risk management with a precise presentation of the mathematical concepts on which these meth-ods are based 7 Contains R-scripts which can be used as a starting point for an implementation of the methods presented 7 Prepares the reader for modern risk management, which is consistent with the guidelines of the international association of insurance supervisors, and in particular with Solvency II
Contents The Process of Risk Management.- Risk Mea-sures.- Dependencies.- Risk Capital.- Allocation of Capital.- Performance Measurement.- Value-oriented Company Management.- Solvency and Regulatory Questions.
Fields of interestActuarial Sciences; Insurance; Statistics for Busi-ness/Economics/Mathematical Finance/Insurance
W. E. Langlois, San Jose City College Division of Science and Mathematics, San Jose, CA, USA; M. Deville, EPFL STI DO MXD 130, Lausanne, Switzerland
Slow Viscous FlowLeonardo wrote, ‘Mechanics is the paradise of the mathematical sciences, because by means of it one comes to the fruits of mathematics’ ; replace ‘Me-chanics’ by ‘Fluid mechanics’ and here we are.
Features 7 New edition of a classic text, incorporating nearly 50 years of progress and innovation since the first edition 7 Teaches the basic principles of fluid mechanics and solves fluid flow problems where viscous effects are the dominant physical phenomena 7 Updated and expanded coverage of topics relevant to nanotechnology and thin film hydrodynamics, hydromagnetic effects, radiative heat transfer and more 7 The basic equations of fluid dynamics are developed in more detail than in other texts 7 A variety of fluid flow problems are treated in a way that supplements the existing literature
Contents Cartesian Tensors.- The Equations of Viscous Flow.- Curvilinear Coordinates.- Exact Solutions to the Equations of Viscous Flow.- Pipe Flow.- Flow Past a Sphere.- Plane Flow.- Rotary Flow.- Lubrication Theory.- Introduction to the Finite Element Method.- Variational Principle, Weak Formulation and Finite Elements.- Stokes Ow and Corner Eddies.- References.- Index.
Fields of interestApproximations and Expansions; Applications of Mathematics; Computational Mathematics and Numerical Analysis
G. V. Milovanovic, Serbian Academy of Sciences and Arts, Belgrade, Serbia; M. T. Rassias, ETH Zürich, Zürich, Switzerland (Eds)
Analytic Number Theory, Approximation Theory, and Special FunctionsIn Honor of Hari M. Srivastava
Contents Part I. Analytic Number Theory, Combinatorics, and Special Sequences of Numbers and Polynomi-als.- The mean values of the Riemann Zeta func-tion on the critical line (A. Ivić).- Explicit bounds concerning non-trivial zeros of the Riemann Zeta function (M. Hassani).- On the value-distribution of logarithmic derivatives of Dirichlet L-functions (Y. Ihara, K. Matsumoto).- Multiple Gamma functions and their applications (J. Choi).- On partition functions of hyperbolic three-geometry and associated Hilbert schemes (A.A. Bytsenko and E. Elizalde).- Families of twisted Bernoulli numbers, twisted Bernoulli polynomials and their applications (Y. Simsek).- Combinatorial interpre-tation of a generalized basic series (A.K. Agarwal, M. Rana).- Identities for reciprocal binomials (A. Sofo).- A note on q-Stirling numbers (M. Merca).- Part II. Analytic Inequalities and Applications.- A survey on Cauchy–Bunyakovsky–Schwarz inequality for power series (A. Ibrahim, S.S. Dragomir).- Topics in special functions III (G.D. Anderson, M. Vuorinen, X. Zhang).- Completely monotone functions—a digest (M. Merkle).- New applications of superquadracity (S. Abramovich).- Green’s operator and differential forms (S. Ding, Y. Xing).- Multidimensional discrete Hilbert-type in-equalities, operators and compositions (B. Yang).- The function (bx-ax)/x: Ratio’s properties (F. Qi, Q.-M. Luo, B.-N. Guo).- On the approximation and bounds of the Gini mean difference (P. [...]
Fields of interestNumber Theory; Approximations and Expansions; Functional Analysis
Y. Orlov, CICESE Research Center, Ensenada, Mexico; L. T. Aguilar, Instituto Politécnico Nacional, Tijuana, Mexico
Advanced H∞ ControlTowards Nonsmooth Theory and Applications
This compact monograph is focused on distur-bance attenuation in nonsmooth dynamic systems, developing an H∞ approach in the nonsmooth setting.
Features 7 Provides a unique treatment of disturbance attenuation in nonsmooth systems 7 Combines the most popular robust control models (H-infin-ity, backstepping, and sliding mode) 7 Contains electromechanical applications with underac-tuation and complex phenomena 7 Rigorous theoretical development supported by experimen-tal results
Contents Part I Introduction.- 1 Linear H1 control of autonomous systems.- 2 LMI approach in infinite dimensional setting.- 3 Linear H1 control of time-varying systems.- 4 Nonlinear H1 control.- Part II Nonsmooth H1 Control.- 5 Elements of nonsmooth analysis.- 6 Synthesis of nonsmooth systems.- 7 LMI-based H1 boundary control of nonsmooth parabolic and hyperbolic systems.- Part III Benchmark Applications.- 8 Advanced H1 synthesis of fully actuated robot manipulators with frictional joints.- 9 Nonsmooth H1 synthesis in the presence of backlash.- 10 H1 generation of periodic motion.- 11 LMI-based H1 synthesis of the current profile in tokamak plasmas.- Refer-ences.- Index.
Fields of interestSystems Theory, Control; Vibration, Dynamical Systems, Control; Dynamical Systems and Ergodic Theory
M. A. Pons, North Central College, Naperville, IL, USA
Real Analysis for the UndergraduateWith an Invitation to Functional Analysis
This undergraduate textbook introduces students to the basics of real analysis, provides an introduc-tion to more advanced topics including measure theory and Lebesgue integration, and offers an invitation to functional analysis. While these ad-vanced topics are not typically encountered until graduate study, the text is designed for the begin-ner. The author’s engaging style makes advanced topics approachable without sacrificing rigor. The text also consistently encourages the reader to pick up a pencil and take an active part in the learning process. Key features include: - examples to rein-force theory; - thorough explanations preceding definitions, theorems and formal proofs; - illustra-tions to support intuition; - over 450 exercises designed to develop connections between the concrete and abstract. This text takes students on a journey through the basics of real analysis and provides those who wish to delve deeper the opportunity to experience mathematical ideas that are beyond the standard undergraduate curricu-lum.
Features 7 Engaging style makes complex concepts ac-cessible to a broad audience 7 Examples and illustrations accompany formal proofs 7 Over 450 exercises help readers develop connections between the concrete and abstract
Contents The Real Numbers.- Sequences in R.- Numerical Series.- Continuity.- The Derivative.- Sequence and Series of Functions.- The Riemann Integral.- Lebesgue Measure on R.- Lebesgue Integration .
Fields of interestAnalysis; Real Functions; Functional Analysis
A Direct Method for Parabolic PDE Constrained Optimization ProblemsAndreas Potschka discusses a direct multiple shooting method for dynamic optimization problems constrained by nonlinear, possibly time-periodic, parabolic partial differential equations. In contrast to indirect methods, this approach au-tomatically computes adjoint derivatives without requiring the user to formulate adjoint equations, which can be time-consuming and error-prone. The author describes and analyzes in detail a globalized inexact Sequential Quadratic Program-ming method that exploits the mathematical structures of this approach and problem class for fast numerical performance. The book features applications, including results for a real-world chemical engineering separation problem.
Feature 7 Publication in the field of natural sciences
Contents Parabolic PDE Constrained Optimization Prob-lems.- Two-Grid Newton-Picard Inexact SQP.- Structure Exploiting Solution of QPs.- Applica-tions and Numerical Results.
Fields of interestOptimization; Mathematics, general; Biochemical Engineering
F. Pukelsheim, Universität Ausgburg Institut für Mathematik, Augsburg, Germany
Proportional RepresentationApportionment Methods and Their Applications
The book offers a rigorous description of the pro-cedures that proportional representation systems use to translate vote counts into seat numbers.
Features 7 With a foreword by Andrew Duff, MEP 7 A rigorous study of electoral systems in Europe 7 A detailed compendium of provable quantitative properties in representation sys-tems 7 Examples of method intrinsic properties: seat biases, majorization relations, double propor-tionality, and many more
Contents Exposing Methods: The 2009 European Parlia-ment Elections.- Imposing Constitutionality: The 2009 Bundestag Election.- From Reals to Integers: Rounding Functions, Rounding Rules.- Divisor Methods of Apportionment: Divide and Round.- Quota Methods of Apportionment: Divide and Rank.- Targeting the House Size: Discrepancy Distribution.- Favoring Some at the Expense of Others: Seat Biases.- Preferring Stronger Parties to Weaker Parties: Majorization.- Securing System Consistency: Coherence and Paradoxes.- Ap-praising Electoral Equality: Goodness-of-Fit Criteria.- Tracing Peculiarities: Vote Thresholds and Majority Clauses.- Truncating Seat Ranges: Minimum-Maximum Restrictions.- Proportional-ity and Personalization: BWG 2013.- Representing Districts and Parties: Double Proportionality.
Fields of interestGame Theory, Economics, Social and Behav. Sciences; Statistics for Social Science, Behavorial Science, Education, Public Policy, and Law; Politi-cal Science, general
A. Quarteroni, École Polytechnique Fédérale de Lausanne Chaire de Modelisation, Lausanne, Switzerland; R. Sacco, Politecnico di Milano MOX, Milano, Italy; P. Gervasio, Università di Brescia, Brescia, Italy
Matematica NumericaLa Matematica Numerica è elemento fondante del calcolo scientifico. Punto di contatto di diverse discipline nella matematica e nelle moderne sci-enze applicate, ne diventa strumento di indagine qualitativa e quantitativa. Scopo di questo testo è fornire i fondamenti metodologici della matemat-ica numerica, richiamandone le principali propri-età, quali la stabilità, l’accuratezza e la complessità algoritmica. Nel contesto di ogni specifica classe di problemi vengono illustrati gli algoritmi più ido-nei, ne viene fatta l’analisi teorica e se ne verificano i risultati previsti implementandoli con ausilio di programmi in linguaggio MATLAB. Il volume è indirizzato principalmente agli studenti delle facoltà scientifiche, con particolare attenzione ai corsi di laurea in Ingegneria, Matematica e Scienze dell’Informazione. L’enfasi posta sullo sviluppo di software lo rende interessante auche per ricer-catori e utilizzatori delle tecniche del calcolo scien-tifico nei campi professionali piú disparati.
Features 7 La Matematica Numerica è elemento fondante del calcolo scientifico 7 Fornisce i fondamenti metodologici della matematica numerica 7 Indi-rizzato principalmente agli studenti delle facoltà scientifiche
Fields of interestMathematics, general; Applications of Mathemat-ics; Analysis
R. Sentis, Commissariat Energie tomique, DAM-Ile-de-France and Laborartoire Jacques-Louis-Lions, Université Pierre-et-Marie-Curie, Paris, France
Mathematical Models and Methods for Plasma Physics, Volume 1Fluid Models
This monograph is dedicated to the derivation and analysis of fluid models occurring in plasma phys-ics. It focuses on models involving quasi-neutrality approximation, problems related to laser propaga-tion in a plasma, and coupling plasma waves and electromagnetic waves. Applied mathematicians will find a stimulating introduction to the world of plasma physics and a few open problems that are mathematically rich.
Features 7 Centralizes results that were strewn in differ-ent research papers and inaccessible by physi-cists 7 The derivations of some classical plasma models are explained from a mathematical point of view 7 Rigorous asymptotic analysis tools are used to justify classical physical approximations
Contents Chapter 1. Introduction. Some Plasma charac-teristic quantities.- Chapter 2. Quasi-neutrality. Magneto-hydrodynamics.- Chapter 3. Laser propagation. Coupling with ion acoustic waves.- Chapter 4. Langmuir waves and Zakharov equations.- Chapter 5. Coupling electron waves and laser waves.- Chapter 6. Models with several species.- Appendix.- Bibliography.- Index.
Fields of interestMathematical Applications in the Physical Sci-ences; Plasma Physics; Mathematical Methods in Physics
Target groupsResearch
Product categoryMonograph
Due February 2014
2014. X, 200 p. 15 illus., 10 in color. (Modeling and Simulation in Science, Engineering and Technology) Hardcover7 * € (D) 90,94 | € (A) 93,49 | sFr 113,507 € 84,99 | £76.50ISBN 978-3-319-03803-2
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J. Sesiano, Ecole polytechnique fédérale, Lausanne, Switzerland
Liber MahamelethContents Part I.- 1. The rebirth of mathematics in mediaeval Europe.- 2. The Liber mahameleth.- 3. Manu-scripts of the Liber mahameleth.- 4. Transmission of the Liber mahameleth.- 5. Mathematics in the Liber mahameleth.- 6. The edited Latin text.- Part II.- Translation.- Beginning of the Book (on) ma-hameleth.- A-I. on Numbers.- A-II. on the Prem-isses necessary for practical arithmetic.- A-III. on Multiplication.- A-IV. on Division.- A-V. on the Multiplication of fractions.- A-VI. on the Addition of fractions to fractions.- A-VII. on Subtracting.- A-VIII. on the Division of fractions, with or with-out integers.- A-IX. on the Determination of roots and on their multiplication, division, subtraction, addition and other related subjects.- Beginning of the Second Part.- B-I. on Buying and selling.- B-II. on Profits.- B-III. on Profit in partnership.- B-IV. on Division according to portions.- B-V. on Masses.- B-VI. on Drapery.- B-VIII. on Linens.- B-VIII. on Grinding.- B-IX. on Boiling must.- B-X. on Borrowing.- B-XI. on Hiring.- B-XII. on the Diversity of workers’ wages.- B-XIII on Hiring carriers.- B-XIV. on Hiring stone-cutters.- B-XV. on the Consumption of oil by lamps.- B-XVI. on the Consumption by animals.- B-XVII. on the Consumption of bread by men.- B-XVIII. on the Exchange of morabitini.- B-XIX. on Cisterns.- XX. on Ladders.- B-XXI. on Another topic.- B-XXII. on Messengers.- B-XXIII. on Another topic.- Glossary.- Part III.- Mathematical Commentary.- Book A.- A-I. Numbers.- A-II. Premisses.- A-III. Multiplication of Integers.- A-IV. Division of integers.- A-V. Multiplication of fractions.- A-VI. Addition of fractions.- A-VII. Subtraction of frac-tions.- A-VIII. Division of fractions.- A-IX. [...]
Fields of interestHistory of Mathematical Sciences; Algebra; Se-quences, Series, Summability
Target groupsResearch
Product categoryMonograph
Due January 2014
2014. XCVIII, 1738 p. 465 illus. (Sources and Studies in the History of Mathematics and Physical Sciences) Hardcover7 approx. * € (D) 448,33 | € (A) 460,90 | sFr 551,507 approx. € 419,00 | £373.00ISBN 978-3-319-03939-8
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V. Volpert, Université Claude Bernard Lyon 1, Villeurbanne cedex, France
If we had to formulate in one sentence what this book is about, it might be “How partial differential equations can help to understand heat explosion, tumor growth or evolution of biological species”. These and many other applications are described by reaction-diffusion equations. The theory of reaction-diffusion equations appeared in the first half of the last century.
Features 7 Offers a systematic investigation of reaction-diffusion equations including existence, stability and bifurcations of solutions 7 Presents numer-ous examples and applications from population dynamics, chemical physics, biomedical mod-els 7 Sequel to successful first volume
Contents I. Introduction to the theory of reaction-diffu-sion equations.- Chapter 1. Reaction-diffusion processes, models and applications.- Chapter 2. Methods of analysis.- Chapter 3. Reaction-diffu-sion problems in bounded domains.- Chapter 4. Reaction-diffusion problems on the whole axis.- II. Reaction-diffusion waves in cylinders.- Chapter 5. Monotone systems.- Chapter 6. Reaction-diffusion problems with convection.- Chapter 7. Reaction-diffusion systems with different diffusion coefficients.- Chapter 8. Nonlinear boundary con-ditions.- Chapter 9. Nonlocal reaction-diffusion equations.- Chapter 10. Multi-scale models in biology.- Bibliographical comments.- Concluding remarks.- Acknowledgements.- References.- In-dex.
