Complex analysis, complex variables Books
Legare Street Press Mathematische Abhandlungen besonders aus dem Gebiete der höhern Arithmetik und der elliptischen Functionen. Mit einer Vorrede von C.F. Gauss
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£25.60
Legare Street Press Mathematische Abhandlungen besonders aus dem Gebiete der höhern Arithmetik und der elliptischen Functionen. Mit einer Vorrede von C.F. Gauss
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£18.95
LEGARE STREET PR Orders of Infinity the Infinitärcalcül of Paul Du BoisReymond
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£22.75
LEGARE STREET PR Théorie Des Fonctions Analytiques
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£28.45
LEGARE STREET PR The Applications of Elliptic Functions
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£19.95
LEGARE STREET PR Théorie Des Fonctions Analytiques
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£19.90
LEGARE STREET PR Orders of Infinity the Infinitärcalcül of Paul Du BoisReymond
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£14.09
LEGARE STREET PR Answers to Exercises in An Introduction to Mathematical Analysis
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£21.80
LEGARE STREET PR Answers to Exercises in An Introduction to Mathematical Analysis
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£13.22
MP-AMM American Mathematical Nonlinear Dynamics and Time Series Building a
Book SynopsisA collection of research and expository papers reflecting the interfacing of two fields: nonlinear dynamics and statistics. It presents the proceedings of a workshop entitled 'Nonlinear Dynamics and Time Series: Building a Bridge Between the Natural and Statistical Sciences' held at the Centre de Recherches Mathematiques in Montreal in July 1995.Table of ContentsOpening lectures: Tools for the analysis of chaotic data by H. I. Abarbanel Some comments on nonlinear time series analysis by H. Tong Embeddings, dimension, and system reconstruction: A general approach to predictive and fractal scaling dimensions in discrete-index time series by C. D. Cutler Statistics for continuity and differentiability: An application to attractor reconstruction from time series by L. M. Pecora, T. L. Carroll, and J. F. Heagy Reconstruction of integrate-and-fire dynamics by T. Sauer Surrogate data methodology: On the validity of the method of surrogate data by K.-S. Chan Using "surrogate surrogate data" to calibrate the actual rate of false positives in tests for nonlinearity in time series by J. Theiler and D. Prichard Local Lyapunov exponents: Chaos with confidence: Asymptotics and applications of local Lyapunov exponents by B. A. Bailey, S. Ellner, and D. W. Nychka Estimating local Lyapunov exponents by Z.-Q. Lu and R. L. Smith Long-range dependence: Defining and measuring long-range dependence by P. Hall Modelling nonlinearity and long memory in time series by P. M. Robinson and P. Zaffaroni Data analysis and applications: Ergodic distributions of random dynamical systems by L. M. Berliner, S. N. MacEachern, and C. S. Forbes Detecting structure in noise by L. Borland Characterizing nonlinearity in weather and epilepsy data: A personal view by M. C. Casdagli Assessment of linear and nonlinear correlations between neural firing events by A. Longtin and D. M. Racicot Markov chain methods in the analysis of heart rate variability by S. J. Merrill and J. R. Cochran.
£81.00
Society for Industrial & Applied Mathematics,U.S. A Software Repository for Gaussian Quadratures
Book SynopsisThis companion piece to the author’s 2018 book, A Software Repository for Orthogonal Polynomials, focuses on Gaussian quadrature and the related Christoffel function. The book makes Gauss quadrature rules of any order easily accessible for a large variety of weight functions and for arbitrary precision. It also documents and illustrates known as well as original approximations for Gauss quadrature weights and Christoffel functions.The repository contains 60 datasets, each dealing with a particular weight function. Included are classical, quasi-classical, and, most of all, nonclassical weight functions and associated orthogonal polynomials.
£51.85
Society for Industrial & Applied Mathematics,U.S. Numerical Linear Algebra
Book SynopsisSince its original appearance in 1997, Numerical Linear Algebra has been a leading textbook in its field, used in universities around the world. It is noted for its 40 lecture-sized short chapters and its clear and inviting style. It is reissued here with a new foreword by James Nagy and a new afterword by Yuji Nakatsukasa about subsequent developments.Trade ReviewA beautifully written textbook offering a distinctive and original treatment.""- Nicholas J. Higham, University of Manchester""Offers a rarely seen integration of computation and theory, illuminated by judiciously chosen examples.""- Ilse Ipsen, North Carolina State University""Almost the perfect text to introduce graduate students to the subject.""- Daniel Szyld, Temple University""An ideal book for a graduate course in numerical linear algebra.""- Suely Oliveira, University of Iowa
£32.36
Society for Industrial & Applied Mathematics,U.S. The Theory of Composites
Book SynopsisComposites have been studied for more than 150 years, and interest in their properties has been growing. This classic volume provides the foundations for understanding a broad range of composite properties, including electrical, magnetic, electromagnetic, elastic and viscoelastic, piezoelectric, thermal, fluid flow through porous materials, thermoelectric, pyroelectric, magnetoelectric, and conduction in the presence of a magnetic field (Hall effect). Exact solutions of the PDEs in model geometries provide one avenue of understanding composites; other avenues include microstructure-independent exact relations satisfied by effective moduli, for which the general theory is reviewed; approximation formulae for effective moduli; and series expansions for the fields and effective moduli that are the basis of numerical methods for computing these fields and moduli. The range of properties that composites can exhibit can be explored either through the model geometries or through microstructure-independent bounds on the properties. These bounds are obtained through variational principles, analytic methods, and Hilbert space approaches. Most interesting is when the properties of the composite are unlike those of the constituent materials, and there has been an explosion of interest in such composites, now known as metamaterials. The Theory of Composites surveys these aspects, among others, and complements the new body of literature that has emerged since the book was written. It remains relevant today by providing historical background, a compendium of numerous results, and through elucidating many of the tools still used today in the analysis of composite properties. This book is intended for applied mathematicians, physicists, and electrical and mechanical engineers. It will also be of interest to graduate students.
£83.30
Springer International Publishing AG Algebraic Curves and Riemann Surfaces for
Book SynopsisThe theory relating algebraic curves and Riemann surfaces exhibits the unity of mathematics: topology, complex analysis, algebra and geometry all interact in a deep way. This textbook offers an elementary introduction to this beautiful theory for an undergraduate audience. At the heart of the subject is the theory of elliptic functions and elliptic curves. A complex torus (or “donut”) is both an abelian group and a Riemann surface. It is obtained by identifying points on the complex plane. At the same time, it can be viewed as a complex algebraic curve, with addition of points given by a geometric “chord-and-tangent” method. This book carefully develops all of the tools necessary to make sense of this isomorphism. The exposition is kept as elementary as possible and frequently draws on familiar notions in calculus and algebra to motivate new concepts. Based on a capstone course given to senior undergraduates, this book is intended as a textbook for courses at this level and includes a large number of class-tested exercises. The prerequisites for using the book are familiarity with abstract algebra, calculus and analysis, as covered in standard undergraduate courses.Table of Contents1 Introduction.- Part I Algebraic curves.- 2 Algebra.- 3 Affine space.- 4 Projective space.- 5 Tangents.- 6 Bézout’s theorem.- 7 The elliptic group.- Part II Riemann Surfaces.- 8 Quasi-Euclidean spaces.- 9 Connectedness, smooth and simple.- 10 Path integrals.- 11 Complex differentiation.- 12 Riemann surfaces.- Part III Curves and surfaces.- 13 Curves are surfaces.- 14 Elliptic functions and the isomorphism theorem.- 15 Puiseux theory.- 16 A brief history of elliptic functions.
£999.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Theory of Stein Spaces
Book SynopsisFrom the reviews: "Theory of Stein Spaces provides a rich variety of methods, results, and motivations - a book with masterful mathematical care and judgement. It is a pleasure to have this fundamental material now readily accessible to any serious mathematician." --J. Eells in Bulletin of the London Mathematical Society (1980)Trade Review"Theory of Stein Spaces provides a rich variety of methods, results, and motivations - a book with masterful mathematical care and judgement. It is a pleasure to have this fundamental material now readily accessible to any serious mathematician."J. Eells in Bulletin of the London Mathematical Society (1980) "Written by two mathematicians who played a crucial role in the development of the modern theory of several complex variables, this is an important book."J.B. Cooper in Internationale Mathematische Nachrichten (1979)Table of ContentsA. Sheaf Theory.- B. Cohomology Theory.- I. Coherence Theory for Finite Holomorphic Maps.- II. Differential Forms and Dolbeault Theory.- III. Theorems A and B for Compact Blocks ?m.- IV. Stein Spaces.- V. Applications of Theorems A and B.- VI. The Finiteness Theorem.- VII. Compact Riemann Surfaces.- Table of Symbols.- Addendum.- Errors and Misprints.
£999.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Complex Manifolds and Deformation of Complex
Book SynopsisKodaira is a Fields Medal Prize Winner. (In the absence of a Nobel prize in mathematics, they are regarded as the highest professional honour a mathematician can attain.) Kodaira is an honorary member of the London Mathematical Society. Affordable softcover edition of 1986 classicTable of ContentsHolomorphic Functions.- Complex Manifolds.- Differential Forms, Vector Bundles, Sheaves.- Infinitesimal Deformation.- Theorem of Existence.- Theorem of Completeness.- Theorem of Stability.
£999.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Complex Analysis
Book SynopsisAll needed notions are developed within the book: with the exception of fundamentals which are presented in introductory lectures, no other knowledge is assumed Provides a more in-depth introduction to the subject than other existing books in this area Over 400 exercises including hints for solutions are includedTrade ReviewFrom the reviews: "The guiding principle of the presentation of classical complex analysis is to proceed as quickly as possible to the central results while using a small number of notions and concepts from other fields. Thus the prerequisites for understanding this book are minimal; only elementary facts of calculus and algebra are required. … Motivating introductions, more than four hundred exercises of all levels of difficulty with hints or solutions, historical annotations, and over 120 figures make the overall presentation very attractive." (L’Enseignement Mathematique, Vol. 52 (2), 2006) "The first four chapters cover the essential core of complex analysis … . The second part of the book is devoted to an extensive representation of the theory of elliptic functions … . Interesting introductions, over four hundred exercises with hints or solutions, historical remarks, and over 120 figures make this book very appropriate and attractive for students at all levels." (F. Haslinger, Monatshefte für Mathematik, Vol. 149 (3), 2006) "It is, in fact, a massive introduction to complex analysis, covering a very wide range of topics. … This is the material that I like to cover in an undergraduate course. … Theorems and proofs are clearly delimited, which many students find helpful. … There are problems at the end of each section, and sketches of solutions are given … . Overall, this is quite an attractive book." (Fernando Q. Gouvêa, MathDL, February, 2006) From the reviews of the second edition: "This introduction to complex analysis is fairly special, and … unique within the existing related textbook literature. … The authors present, apart from the standard material, a wide range of topics that are usually not covered by introductory texts … . No doubt, this excellent, comprehensive, and nearly self-contained textbook on complex analysis deserves a wide international audience of readers, who will profit a great deal from studying it." (Werner Kleinert, Zentralblatt MATH, Vol. 1167, 2009)Table of ContentsDifferential Calculus in the Complex Plane C.- Integral Calculus in the Complex Plane C.- Sequences and Series of Analytic Functions, the Residue Theorem.- Construction of Analytic Functions.- Elliptic Functions.- Elliptic Modular Forms.- Analytic Number Theory.- Solutions to the Exercises.
£59.99
Elsevier Science Complex Numbers in n Dimensions
Book Synopsis
£60.99
LEGARE STREET PR Institutiones Calculi Differentialis...
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£43.60
Springer International Publishing AG Decomposition of Jacobians by Prym Varieties
Book SynopsisThis monograph studies decompositions of the Jacobian of a smooth projective curve, induced by the action of a finite group, into a product of abelian subvarieties. The authors give a general theorem on how to decompose the Jacobian which works in many cases and apply it for several groups, as for groups of small order and some series of groups. In many cases, these components are given by Prym varieties of pairs of subcovers. As a consequence, new proofs are obtained for the classical bigonal and trigonal constructions which have the advantage to generalize to more general situations. Several isogenies between Prym varieties also result.Trade Review“The book is very well written, and gives a number of results, and of examples, interesting in some fields of Algebraic Geometry, specially those concerning algebraic curves, or equivalently, Riemann surfaces. Also, it serves to recall the work of Sevín Recillas Pishmish, whose untimely death prevented him from continuing working on these topics.” (José Javier Etayo, zbMATH 1514.14001, 2023)Table of ContentsIntroduction.- Preliminaries and basic results.- Finite covers of curves.- Covers of degree 2 and 3.- Covers of degree 4.- Some special groups and complete decomposabality.- Bibliography.- Index.
£999.99
Springer Elliptic Functions and Modular Forms
Book Synopsis
£999.99
Springer New York Classical Fourier Analysis 2014
Book SynopsisThe coverage of topics and exposition style are designed to leave no gaps in understanding and stimulate further study.This third edition includes new Sections 3.5, 4.4, 4.5 as well as a new chapter on “Weighted Inequalities,” which has been moved from GTM 250, 2nd Edition.Trade Review“The most up-to-date account of the most important developments in the area. … It has to be pointed out that the hard ones usually come with a good hint, which makes the book suitable for self-study, especially for more motivated students. That being said, the book provides a good reference point for seasoned researchers as well” (Atanas G. Stefanov, Mathematical Reviews, August, 2015)Table of ContentsPreface.- 1. Lp Spaces and Interpolation.- 2. Maximal Functions, Fourier Transform, and Distributions.- 3. Fourier Series.- 4. Topics on Fourier Series.- 5. Singular Integrals of Convolution Type.- 6. Littlewood–Paley Theory and Multipliers.- 7. Weighted Inequalities.- A. Gamma and Beta Functions.- B. Bessel Functions.- C. Rademacher Functions.- D. Spherical Coordinates.- E. Some Trigonometric Identities and Inequalities.- F. Summation by Parts.- G. Basic Functional Analysis.- H. The Minimax Lemma.- I. Taylor's and Mean Value Theorem in Several Variables.- J. The Whitney Decomposition of Open Sets in Rn.- Glossary.- References.- Index.
£56.69
World Scientific Publishing Europe Ltd Conformal Maps and Geometry
Book Synopsis
£999.99
Imperial College Press Instabilities, Chaos And Turbulence (2nd Edition)
Book SynopsisThis book (2nd edition) is a self-contained introduction to a wide body of knowledge on nonlinear dynamics and chaos. Manneville emphasises the understanding of basic concepts and the nontrivial character of nonlinear response, contrasting it with the intuitively simple linear response. He explains the theoretical framework using pedagogical examples from fluid dynamics, though prior knowledge of this field is not required. Heuristic arguments and worked examples replace most esoteric technicalities. Only basic understanding of mathematics and physics is required, at the level of what is currently known after one or two years of undergraduate training: elementary calculus, basic notions of linear algebra and ordinary differential calculus, and a few fundamental physical equations (specific complements are provided when necessary). Methods presented are of fully general use, which opens up ample windows on topics of contemporary interest. These include complex dynamical processes such as patterning, chaos control, mixing, and even the Earth's climate. Numerical simulations are proposed as a means to obtain deeper understanding of the intricacies induced by nonlinearities in our everyday environment, with hints on adapted modelling strategies and their implementation.Table of ContentsIntroduction and Overview; First Steps in Nonlinear Dynamics; Life and Death of Dissipative Structures; Nonlinear Dynamics: From Simple to Complex; Applications of the Chaos Concept; Nonlinear Dynamics of Patterns; Open Flows; Instability and Transition; Developed Turbulence; Summary and Perspectives.
£93.60
Imperial College Press Mathematical Analysis For Engineers
Book SynopsisThis book follows an advanced course in analysis (vector analysis, complex analysis and Fourier analysis) for engineering students, but can also be useful, as a complement to a more theoretical course, to mathematics and physics students.The first three parts of the book represent the theoretical aspect and are independent of each other. The fourth part gives detailed solutions to all exercises that are proposed in the first three parts.ForewordForeword (71 KB)Table of ContentsVector Analysis: Differential Operators of Mathematical Physics; Line Integrals; Gradient Vector Fields; Green Theorem; Surface Integrals; Divergence Theorem; Stokes Theorem; Appendix; Complex Analysis: Holomorphic Functions; Complex Integration; Laurent Series; Residue Theorem and Applications; Conformal Mapping; Fourier Analysis: Fourier Series; Fourier Transform; Laplace Transform; Applications: ODE; Applications: PDE; Solutions to the Exercises: Differential Operators: Solutions; Line Integrals: Solutions; Gradient Vector Fields: Solutions; Green Theorem: Solutions; Surface Integrals: Solutions; Divergence Theorem: Solutions; Stokes Theorem: Solutions; Holomorphic Functions: Solutions; Complex Integration: Solutions; Laurent Series: Solutions; Residue Theorem: Solutions; Conformal Mapping: Solutions; Fourier Series: Solutions; Fourier Transform: Solutions; Laplace Transform: Solutions; ODE: Solutions; PDE: Solutions.
£45.60
Imperial College Press INTRODUCTION TO THE CALCULUS OF VARIATIONS
Book SynopsisThe book, containing more than seventy exercises with detailed solutions, is well designed for a course both at the undergraduate and graduate levels.Trade Review"This wonderful book is imbued with a marvelous historical perspective so that the reader is taught some very beautiful mathematics fitted in the proper historical perspective ... it is full of terrific hard analysis focused on a general theme that is exemplified by the author's astute and elegant choice of topics ... There are a lot of (outstanding) exercises and these are critical for a deeper understanding of the material. All of Chapter 7 is devoted to their solutions, and this increases the book's already considerable value as a source for self-study ... it's a very beautiful treatment, and will reward the diligent reader with a solid introduction to a great and grand subject and to a lot of beautiful hard analysis." MAA Online Book Review "A great feature is the concluding Chapter 7, presenting complete solutions to all the exercises set earlier in the book ... This is a well thought-out selection, and Dacorogna's expert discussion is everywhere really clear and nicely motivated, with lots of details put in. He obviously cares about actually teaching and not just covering material." SIAM ReviewTable of ContentsPreliminaries; Classical Methods; Direct Methods; Regularity; Minimal Surfaces; Isoperimetric Inequality; Solutions to the Exercises.
£30.40
Springer Braids Conformal Module Entropy and Gromovs Oka
Book Synopsis1. Introduction.- 2. Riemann Surfaces, Braids, Mapping Classes, and Teichmueller Theory.- 3. The entropy of surface homeomorphisms.- 4. Conformal invariants of homotopy classes of curves. The Main theorem.- 5. Reducible pure braids. Irreducible nodal components, irreducible braid components, and the proof of the Main Theorem.- 6. The general case. Irreducible nodal components, irreducible braid components, and the proof of the Main Theorem.- 7. The conformal module and holomorphic families of polynomials.- 8. Gromov's Oka Principle and conformal module.- 9. Gromov's Oka Principle for (g, m)-fiber bundles.- 10. Fundamental groups and bounds for the extremal length.- 11. Counting functions.- 12. Riemann surfaces of second kind and finiteness theorems.- A. Several complex variables.- B. A Lemma on Conjugation.- C. Koebe's Theorem.- Index.- References.
£999.99
Springer Fachmedien Wiesbaden Grundkurs Funktionentheorie
Book SynopsisTable of Contents0 Vorbereitung.- 0.1 Zusammenhang.- 0.2 Reelle Kurvenintegrale.- 1 Die komplexen Zahlen.- 2 Holomorphie und Meromorphie.- 3 Potenzreihen.- 4 Holomorphie und Winkeltreue.- 5 Cauchyscher Satz: konvexe Gebiete.- 6 Konsequenzen der Integralformeln.- 7 Der Cauchysche Integralsatz.- 8 Isolierte Singularitäten.- 9 Umkehrung holomorpher Funktionen.- 10 Folgen und Familien.- 10.1 Eigenschaften der Grenzfunktion.- 10.2 Normale Familien.- 11 Interpolationen.- 12 Einfacher Zusammenhang.- 13 Der Riemannsche Abbildungssatz.- 14 Der Approximationssatz von Runge.- Stichwortverzeichnis.
£42.29
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Complex Analysis 2: Riemann Surfaces, Several
Book SynopsisThe book contains a complete self-contained introduction to highlights of classical complex analysis. New proofs and some new results are included. All needed notions are developed within the book: with the exception of some basic facts which can be found in the ¯rst volume. There is no comparable treatment in the literature.Trade ReviewFrom the reviews:“The book under review is the second volume of the textbook Complex analysis, consisting of 8 chapters. It provides an approach to the theory of Riemann surfaces from complex analysis. … The book is self-contained and, moreover, some notions which might be unfamiliar for the reader are explained in appendices of chapters. … this book is an excellent textbook on Riemann surfaces, especially for graduate students who have taken the first course of complex analysis.” (Hiroshige Shiga, Mathematical Reviews, Issue 2012 f)“The book under review is largely self-contained, pleasantly down-to-earth, remarkably versatile, and highly educating simultaneously. No doubt, this fine textbook provides an excellent source for the further study of more advanced and topical themes in the theory of Riemann surfaces, their Jacobians and moduli spaces, and in the general theory of complex Abelian varieties and modular forms likewise. It is very welcome that the English translation of the German original has been made available so quickly!” (Werner Kleinert, Zentralblatt MATH, Vol. 1234, 2012)“The author provides a (very brief) introduction to fundamental notions of topology, but develops fully the theory of surfaces and covering spaces he needs. … the book includes a proof of the classification of compact orientable surfaces by their genus. … this one is definitely a graduate text. … There is a lot of mathematics in this book, presented efficiently and well. … It is a book I am glad to have, and that I will certainly refer to in the future.” (Fernando Q. Gouvêa, The Mathematical Association of America, May, 2012)Table of ContentsChapter I. Riemann Surfaces.- Chapter II. Harmonic Functions on Riemann Surfaces.- Chapter III. Uniformization.- Chapter IV. Compact Riemann Surfaces.- Appendices to Chapter IV.- Chapter V. Analytic Functions of Several Complex Variables.- Chapter V. Analytic Functions of Several Complex Variable.- Chapter VI. Abelian Functions.- Chapter VII. Modular Forms of Several Variables.- Chapter VIII. Appendix: Algebraic Tools.- References.- Index.
£62.99
World Scientific Publishing Co Pte Ltd Aspects Of Complex Analysis, Differential
Book SynopsisThis volume constitutes the proceedings of a workshop whose main purpose was to exchange information on current topics in complex analysis, differential geometry, mathematical physics and applications, and to group aspects of new mathematics.Table of ContentsPartially ordered topological linear spaces, S. Koshi; bounded analytic functions on Riemann surfaces, M. Hayashi; on one-side holomorphic continuation of CR functions along complex curves, S. Myslivets; remarks on some function theories on a class of almost complex manifolds, S. Dimiev et al; on the integrability conditions for almost contact manifolds, M.J. Hristov; geometry of real hypersurfaces in a complex projective space, S. Maeda; topology and classical gauge theory, G.L. Naber; complex structure and Dirac theory, I.B. Pestov; quantization on closed manifolds, Y. Ohnuki; quantum teleportation and spin echo - a unitary symplectic spinor approach, E. Binz and W. Schempp. (Part contents)
£115.20
World Scientific Publishing Co Pte Ltd Generalized Synchronization And Generalized
Book SynopsisWhat is synchronization? This book will show how the concept of closeness of states or frequencies between two dynamical systems has evolved from synchronization to consensus. Part 1 introduces the concepts and mathematical descriptions of Generalized Synchronization (GS) while Part 2 covers Generalized Consensus (GC).It is suitable for researchers and practitioners undertaking the studies of synchronization and consensus of multi-agent systems, graduate students and senior undergraduate students with the backgrounds in calculus, linear algebra and ordinary differential equations, equipped with computer programming skills, in mathematics, physics, engineering and even social sciences.
£66.50
World Scientific Publishing Co Pte Ltd Simplicial Complexes In Complex Systems: In
Book SynopsisFor the last few decades researchers from different fields gather their findings and knowledge trying to give a shape to the new science of complex systems. To address this problem, new tools and methods have to be established. A new, or more precisely an alternative, framework for the characterization of complex system was proposed. In this book we will introduce the applicability of applicability of simplicial complexes in the science of complex systems. After introducing the main definitions and properties of simplicial complexes necessary for representation and analysis of complex systems, we will illustrate the usefulness and versatility of tools and concepts related to the simplicial complexes.
£66.50
World Scientific Publishing Co Pte Ltd Krzyz Conjecture: Theory And Methods, The
Book SynopsisThis book is about one of the beautiful topics in mathematics. It describes an on-going research on bounded analytic functions which are defined on the unit disc. This is a very active topic that belongs to the theory of complex analysis in a single complex variable. Complex analysis is one of the classical chapters in Mathematics. It contains the analytic theory of functions, the geometric function theory among other theoretical areas, as well as many applications. Some applications originate in other fields of mathematics: geometry, topology, arithmetic and number theory in general, algebra etc. Other applications originate in other scientific and engineering disciplines: physics, dynamical systems, electrical engineering etc.The book includes much more than just a review on the Krzyz conjecture. It includes topics on inner functions within the context of problems that are different from the Krzyz conjecture as well as other topics on general bounded analytic functions. Progress in mathematical research is frequently fuelled by efforts to solve open problems. The book also includes a few important open problems and some partial solutions of these.
£139.50
World Scientific Publishing Co Pte Ltd Nevanlinna Theory And Its Relation To Diophantine
Book SynopsisThis book describes the theories and developments in Nevanlinna theory and Diophantine approximation. Although these two subjects belong to the different areas: one in complex analysis and one in number theory, it has been discovered that a number of striking similarities exist between these two subjects. A growing understanding of these connections has led to significant advances in both fields. Outstanding conjectures from decades ago are being solved.Over the past 20 years since the first edition appeared, there have been many new and significant developments. The new edition greatly expands the materials. In addition, three new chapters were added. In particular, the theory of algebraic curves, as well as the algebraic hyperbolicity, which provided the motivation for the Nevanlinna theory.
£121.50
World Scientific Publishing Co Pte Ltd Friendly Approach To Complex Analysis, A
Book SynopsisThe book constitutes a basic, concise, yet rigorous first course in complex analysis, for undergraduate students who have studied multivariable calculus and linear algebra. The textbook should be particularly useful for students of joint programmes with mathematics, as well as engineering students seeking rigour. The aim of the book is to cover the bare bones of the subject with minimal prerequisites. The core content of the book is the three main pillars of complex analysis: the Cauchy-Riemann equations, the Cauchy Integral Theorem, and Taylor and Laurent series. Each section contains several problems, which are not drill exercises, but are meant to reinforce the fundamental concepts. Detailed solutions to all the 243 exercises appear at the end of the book, making the book ideal for self-study. There are many figures illustrating the text.The second edition corrects errors from the first edition, and includes 89 new exercises, some of which cover auxiliary topics that were omitted in the first edition. Two new appendices have been added, one containing a detailed rigorous proof of the Cauchy Integral Theorem, and another providing background in real analysis needed to make the book self-contained.
£76.00
World Scientific Publishing Co Pte Ltd Brownian Motion And Potential Theory Modern And
Book SynopsisIn this book, potential theory is presented in an inclusive and accessible manner, with the emphasis reaching from classical to modern, from analytic to probabilistic, and from Newtonian to abstract or axiomatic potential theory (including Dirichlet spaces). The reader is guided through stochastic analysis featuring Brownian motion in its early chapters to potential theory in its latter sections. This path covers the following themes: martingales, diffusion processes, semigroups and potential operators, analysis of super harmonic functions, Dirichlet problems, balayage, boundaries, and Green functions.The wide range of applications encompasses random walk models, especially reversible Markov processes, and statistical inference in machine learning models. However, the present volume considers the analysis from the point of view of function space theory, using Dirchlet energy as an inner product. This present volume is an expanded and revised version of an original set of lectures in the Aarhus University Mathematics Institute Lecture Note Series.
£85.50
World Scientific Publishing Co Pte Ltd Brownian Motion And Potential Theory Modern And
Book SynopsisIn this book, potential theory is presented in an inclusive and accessible manner, with the emphasis reaching from classical to modern, from analytic to probabilistic, and from Newtonian to abstract or axiomatic potential theory (including Dirichlet spaces). The reader is guided through stochastic analysis featuring Brownian motion in its early chapters to potential theory in its latter sections. This path covers the following themes: martingales, diffusion processes, semigroups and potential operators, analysis of super harmonic functions, Dirichlet problems, balayage, boundaries, and Green functions.The wide range of applications encompasses random walk models, especially reversible Markov processes, and statistical inference in machine learning models. However, the present volume considers the analysis from the point of view of function space theory, using Dirchlet energy as an inner product. This present volume is an expanded and revised version of an original set of lectures in the Aarhus University Mathematics Institute Lecture Note Series.
£52.25
World Scientific Publishing Company Complex Analysis
Book Synopsis
£108.00
World Scientific Publishing Co Pte Ltd Determining Thresholds Of Complete
Book SynopsisThis book is devoted to the phenomenon of synchronization and its application for determining the values of Lyapunov exponents. In recent years, the idea of synchronization has become an object of great interest in many areas of science, e.g., biology, communication or laser physics. Over the last decade, new types of synchronization have been identified and some interesting new ideas concerning the synchronization have also appeared.This book presents the complete synchronization problem rather than just results from the research. The problem is demonstrated in relation to a kind of coupling applied between dynamical systems, whereby a unique classification of possible couplings is introduced. Another novel feature is the connection presented between synchronization and the problem of determining the Lyapunov exponents, especially for non-differentiable systems. A detailed proposal of such an estimation method and examples of its application are included.Table of ContentsClassification of Couplings between Dynamical Systems: Diffusive and Non-diffusive, Dissipative and Conservative, Common Signal; Methods of Determining the Complete Synchronization Thresholds in Networks of Coupled Oscillators; Synchronizability of Coupled Oscillators: Single and Multiple Synchronous Ranges; Estimation of the Largest Lyapunov Exponent via Complete Synchronization: Discrete-Time Systems, Mechanical Oscillators with Discontinuities, Systems with Time Delay.
£72.20
World Scientific Publishing Co Pte Ltd Elegant Chaos: Algebraically Simple Chaotic Flows
Book SynopsisThis heavily illustrated book collects in one source most of the mathematically simple systems of differential equations whose solutions are chaotic. It includes the historically important systems of van der Pol, Duffing, Ueda, Lorenz, Rössler, and many others, but it goes on to show that there are many other systems that are simpler and more elegant. Many of these systems have been only recently discovered and are not widely known. Most cases include plots of the attractor and calculations of the spectra of Lyapunov exponents. Some important cases include graphs showing the route to chaos. The book includes many cases not previously published as well as examples of simple electronic circuits that exhibit chaos.No existing book thus far focuses on mathematically elegant chaotic systems. This book should therefore be of interest to chaos researchers looking for simple systems to use in their studies, to instructors who want examples to teach and motivate students, and to students doing independent study.Table of ContentsFundamentals; Periodically Forced Systems; Autonomous Dissipative Systems; Autonomous Conservative Systems; Low-Dimensional Systems (D < 3); High-Dimensional Systems (D > 3); Infinite-Dimensional Systems; Chaotic Electrical Circuits.
£86.45
World Scientific Publishing Co Pte Ltd Chua's Circuit Implementations: Yesterday, Today
Book SynopsisSince the birth of the Chua circuit in 1983, a considerable number of fruitful, fascinating and relevant research topics have arisen. In honor of the 25th anniversary of the invention of Chua's circuit, this book presents the 25 years of research on the implementation of Chua's circuit, and also discusses future directions and emerging applications of recent results.The purpose of the book is to provide researchers, PhD students, and undergraduate students a research monograph containing both fundamentals on the topics and advanced results that have been recently obtained. With about 60 illustrations included in the book, it also shows the detailed schematics of several different implementations that can be easily reproduced with a low-cost experimental setup and PC-based measurement instrumentation.
£76.95
World Scientific Publishing Co Pte Ltd Quick Introduction To Complex Analysis, A
Book SynopsisThe aim of the book is to give a smooth analytic continuation from calculus to complex analysis by way of plenty of practical examples and worked-out exercises. The scope ranges from applications in calculus to complex analysis in two different levels.If the reader is in a hurry, he can browse the quickest introduction to complex analysis at the beginning of Chapter 1, which explains the very basics of the theory in an extremely user-friendly way. Those who want to do self-study on complex analysis can concentrate on Chapter 1 in which the two mainstreams of the theory — the power series method due to Weierstrass and the integration method due to Cauchy — are presented in a very concrete way with rich examples. Readers who want to learn more about applied calculus can refer to Chapter 2, where numerous practical applications are provided. They will master the art of problem solving by following the step by step guidance given in the worked-out examples.This book helps the reader to acquire fundamental skills of understanding complex analysis and its applications. It also gives a smooth introduction to Fourier analysis as well as a quick prelude to thermodynamics and fluid mechanics, information theory, and control theory. One of the main features of the book is that it presents different approaches to the same topic that aids the reader to gain a deeper understanding of the subject.
£30.40
World Scientific Publishing Co Pte Ltd Quick Introduction To Complex Analysis, A
Book SynopsisThe aim of the book is to give a smooth analytic continuation from calculus to complex analysis by way of plenty of practical examples and worked-out exercises. The scope ranges from applications in calculus to complex analysis in two different levels.If the reader is in a hurry, he can browse the quickest introduction to complex analysis at the beginning of Chapter 1, which explains the very basics of the theory in an extremely user-friendly way. Those who want to do self-study on complex analysis can concentrate on Chapter 1 in which the two mainstreams of the theory — the power series method due to Weierstrass and the integration method due to Cauchy — are presented in a very concrete way with rich examples. Readers who want to learn more about applied calculus can refer to Chapter 2, where numerous practical applications are provided. They will master the art of problem solving by following the step by step guidance given in the worked-out examples.This book helps the reader to acquire fundamental skills of understanding complex analysis and its applications. It also gives a smooth introduction to Fourier analysis as well as a quick prelude to thermodynamics and fluid mechanics, information theory, and control theory. One of the main features of the book is that it presents different approaches to the same topic that aids the reader to gain a deeper understanding of the subject.
£58.90
World Scientific Publishing Co Pte Ltd Advanced Courses Of Mathematical Analysis Vi -
Book SynopsisThis volume contains short courses and recent papers by several specialists in different fields of Mathematical Analysis. It offers a wide perspective of the current state of research, and new trends, in areas related to Geometric Analysis, Harmonic Analysis, Complex Analysis, Functional Analysis and History of Mathematics. The contributions are presented with a remarkable expository nature and this makes the discussed topics accessible to a more general audience.
£86.45
World Scientific Publishing Co Pte Ltd Elegant Chaos: Algebraically Simple Chaotic Flows
Book SynopsisThis heavily illustrated book collects in one source most of the mathematically simple systems of differential equations whose solutions are chaotic. It includes the historically important systems of van der Pol, Duffing, Ueda, Lorenz, Rössler, and many others, but it goes on to show that there are many other systems that are simpler and more elegant. Many of these systems have been only recently discovered and are not widely known. Most cases include plots of the attractor and calculations of the spectra of Lyapunov exponents. Some important cases include graphs showing the route to chaos. The book includes many cases not previously published as well as examples of simple electronic circuits that exhibit chaos.No existing book thus far focuses on mathematically elegant chaotic systems. This book should therefore be of interest to chaos researchers looking for simple systems to use in their studies, to instructors who want examples to teach and motivate students, and to students doing independent study.
£45.60
World Scientific Publishing Co Pte Ltd Chaos: From Simple Models To Complex Systems
Book SynopsisChaos: from simple models to complex systems aims to guide science and engineering students through chaos and nonlinear dynamics from classical examples to the most recent fields of research. The first part, intended for undergraduate and graduate students, is a gentle and self-contained introduction to the concepts and main tools for the characterization of deterministic chaotic systems, with emphasis to statistical approaches. The second part can be used as a reference by researchers as it focuses on more advanced topics including the characterization of chaos with tools of information theory and applications encompassing fluid and celestial mechanics, chemistry and biology.The book is novel in devoting attention to a few topics often overlooked in introductory textbooks and which are usually found only in advanced surveys such as: information and algorithmic complexity theory applied to chaos and generalization of Lyapunov exponents to account for spatiotemporal and non-infinitesimal perturbations.The selection of topics, numerous illustrations, exercises and proposals for computer experiments make the book ideal for both introductory and advanced courses.
£45.60
World Scientific Publishing Co Pte Ltd Classical Complex Analysis: A Geometric Approach
Book SynopsisClassical Complex Analysis, available in two volumes, provides a clear, broad and solid introduction to one of the remarkable branches of exact science, with an emphasis on the geometric aspects of analytic functions. Volume 2 begins with analytic continuation. The Riemann mapping theorem is proved and used in solving Dirichlet's problem for an open disk and, hence, a class of general domains via Perron's method. Finally, proof of the uniformization theorem of Riemann surfaces is given.The book is rich in contents, figures, examples and exercises. It is self-contained and is designed for a variety of usages and motivations concerning advanced studies. It can be used both as a textbook for undergraduate and graduate students, and as a reference book in general.Table of ContentsFundamental Theory: Sequences, Series and Infinite Products; Conformal Mapping and Dirichlet's Problem; Riemann Surfaces.
£118.80
World Scientific Publishing Co Pte Ltd Chaos: From Simple Models To Complex Systems
Book SynopsisChaos: from simple models to complex systems aims to guide science and engineering students through chaos and nonlinear dynamics from classical examples to the most recent fields of research. The first part, intended for undergraduate and graduate students, is a gentle and self-contained introduction to the concepts and main tools for the characterization of deterministic chaotic systems, with emphasis to statistical approaches. The second part can be used as a reference by researchers as it focuses on more advanced topics including the characterization of chaos with tools of information theory and applications encompassing fluid and celestial mechanics, chemistry and biology.The book is novel in devoting attention to a few topics often overlooked in introductory textbooks and which are usually found only in advanced surveys such as: information and algorithmic complexity theory applied to chaos and generalization of Lyapunov exponents to account for spatiotemporal and non-infinitesimal perturbations.The selection of topics, numerous illustrations, exercises and proposals for computer experiments make the book ideal for both introductory and advanced courses.Table of ContentsFirst Encounter with Chaos; The Language of Dynamical Systems; Examples of Chaotic Behaviors; Probabilistic Approach to Chaos; Characterization of Chaotic Dynamical Systems; From Order to Chaos in Dissipative Systems; Chaos in Hamiltonian Systems; Chaos and Information Theory; Coarse-Grained Information and Large Scale Predictability; Chaos, Numerical Computations and Experiments; Chaos in Few-Degrees of Freedom Systems; Spatiotemporal Chaos; Turbulence as a Dynamical Systems Problem; Chaos and Statistical Mechanics: Fermi-Pasta-Ulam a Case Study.
£135.00
