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Problems and Solutions
Author: Willi-Hans Steeb
Publisher: World Scientific Publishing Company
ISBN: 9813109947
Pages: 252
Year: 2016-03-02
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This book presents a collection of problems for nonlinear dynamics, chaos theory and fractals. Besides the solved problems, supplementary problems are also added. Each chapter contains an introduction with suitable definitions and explanations to tackle the problems. The material is self-contained, and the topics range in difficulty from elementary to advanced. While students can learn important principles and strategies required for problem solving, lecturers will also find this text useful, either as a supplement or text, since concepts and techniques are developed in the problems.
Nonlinear Dynamics and Chaos
Author: Steven H. Strogatz
Publisher: Hachette UK
ISBN: 0813349117
Pages: 500
Year: 2014-08-26
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This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors. A unique feature of the book is its emphasis on applications. These include mechanical vibrations, lasers, biological rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic control systems, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with mathematical theory. In the twenty years since the first edition of this book appeared, the ideas and techniques of nonlinear dynamics and chaos have found application to such exciting new fields as systems biology, evolutionary game theory, and sociophysics. This second edition includes new exercises on these cutting-edge developments, on topics as varied as the curiosities of visual perception and the tumultuous love dynamics in Gone With the Wind.
Handbook of Nonlinear Partial Differential Equations, Second Edition
Author: Andrei D. Polyanin, Valentin F. Zaitsev
Publisher: CRC Press
ISBN: 142008724X
Pages: 1912
Year: 2016-04-19
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New to the Second Edition More than 1,000 pages with over 1,500 new first-, second-, third-, fourth-, and higher-order nonlinear equations with solutions Parabolic, hyperbolic, elliptic, and other systems of equations with solutions Some exact methods and transformations Symbolic and numerical methods for solving nonlinear PDEs with MapleTM, Mathematica®, and MATLAB® Many new illustrative examples and tables A large list of references consisting of over 1,300 sources To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology. They outline the methods in a schematic, simplified manner and arrange the material in increasing order of complexity.
Who's Who in Fluorescence 2009
Author: Chris D. Geddes
Publisher: Springer Science & Business Media
ISBN: 1441901914
Pages: 234
Year: 2009-04-02
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th The Who’s Who in Fluorescence 2009 is the 7 volume of the Who’s who series. The previous six volumes (2003 – 2008) have been very well received by the fluorescence community, with 1000’s of copies being distributed around the world, through conferences and workshops, as well as through internet book sites. In addition, the Institute of Fluorescence ( mailed 100’s of copies of the 2008 volume to contributors around the world. This new 2009 volume features some 419 entries from no fewer than 41 countries worldwide, as compared to 418 entries (38 different countries) in 2008 and 405 entries in the 2007 volume, respectively. We have received 29 new entries this year, and deleted 25 entries that were not updated by contributors from past years. In 2008, 129 AIM numbers were submitted as compared to 106 in 2007. This year the number has risen again to 136 AIM numbers submitted. This year we also see the introduction of the h-index number listing, a publication statistic provided by the Thompson’s ISI Web of Science. Some 42 contributors provided their h-numbers. In 2009 we also see a continued and strong company support, in light of the current world economic climate, which will enable us to further disseminate the volume in 2009– 2010. In this regard we especially thank the instrumentation companies for their continued support, where without their financial contributions, it is likely that the volume would not be the success it is today.
On Growth and Form
Author: D'Arcy Wentworth Thompson
Publisher: Prabhat Prakashan
Year: 2018-01-01
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It is not the biologist with an inkling of mathematics, but the skilled and learned mathematician who must ultimately deal with such problems as are merely sketched and adumbrated here. I pretend to no math­e­mat­i­cal skill, but I have made what use I could of what tools I had; I have dealt with simple cases, and the math­e­mat­i­cal methods which I have introduced are of the easiest and simplest kind. Elementary as they are, my book has not been written without the help—the indispensable help—of many friends. Like Mr Pope translating Homer, when I felt myself deficient I sought assistance! And the experience which Johnson attributed to Pope has been mine also, that men of learning did not refuse to help me.
Random Graphs and Complex Networks
Author: Remco van der Hofstad
Publisher: Cambridge University Press
ISBN: 110717287X
Pages: 375
Year: 2016-12-22
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This classroom-tested text is the definitive introduction to the mathematics of network science, featuring examples and numerous exercises.
Problems and Solutions in Differential Geometry, Lie Series, Differential Forms, Relativity and Applications
Publisher: World Scientific Publishing Company
ISBN: 9813230843
Pages: 296
Year: 2017-10-20
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This volume presents a collection of problems and solutions in differential geometry with applications. Both introductory and advanced topics are introduced in an easy-to-digest manner, with the materials of the volume being self-contained. In particular, curves, surfaces, Riemannian and pseudo-Riemannian manifolds, Hodge duality operator, vector fields and Lie series, differential forms, matrix-valued differential forms, Maurer–Cartan form, and the Lie derivative are covered. Readers will find useful applications to special and general relativity, Yang–Mills theory, hydrodynamics and field theory. Besides the solved problems, each chapter contains stimulating supplementary problems and software implementations are also included. The volume will not only benefit students in mathematics, applied mathematics and theoretical physics, but also researchers in the field of differential geometry. Request Inspection Copy
European Congress of Mathematics, Barcelona, July 10-14, 2000
Author: Carles Casacuberta
Publisher: Springer Science & Business Media
ISBN: 3764364173
Pages: 582
Year: 2001-12-01
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The Third European Congress of Mathematics (3ecm) took place from July 10th to July 14th, 2000 in Barcelona. It was organised by the Societat Catalana de Matematiques (Catalan Mathematical Society), under the auspices of the Euro­ pean Mathematical Society (EMS). As foreseen by the EMS and the International Mathematical Union, this Congress was a major event in World Mathematical Year 2000. In addition to reviewing outstanding research achievements, important aspects of the life of European mathematics were discussed. Mathematics is undergoing a period of rapid changes. Effective computation and applications in science and technology go ever more hand in hand with con­ ceptual developments. It was one of the aims of 3ecm to reflect this mutual enrich­ ment, while steering present and future trends of mathematical sciences. In fact, the motto of the Congress, Shaping the 21st Century, was meant to capture these views. Nearly 1400 people from 87 countries gathered together in the Palau de Con­ gressos of Barcelona in order to take part in the activities of the 3ecm scientific programme: Nine plenary lectures, thirty invited lectures in parallel sessions, lec­ tures given by EMS prize winners, ten mini-symposia on special topics, seven round tables, poster sessions, presentations of mathematical software and video exhibitions. Twenty events were satellites of 3ecm in various countries.
Dynamics and Control of Hybrid Mechanical Systems
Author: Gennady Leonov, Ilʹi︠a︡ Izrailevich Blekhman
Publisher: World Scientific
ISBN: 9814282324
Pages: 242
Year: 2010
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The papers in this edited volume aim to provide a better understanding of the dynamics and control of a large class of hybrid dynamical systems that are described by different models in different state space domains. They not only cover important aspects and tools for hybrid systems analysis and control, but also a number of experimental realizations. Special attention is given to synchronization a universal phenomenon in nonlinear science that gained tremendous significance since its discovery by Huygens in the 17th century. Possible applications of the results introduced in the book include control of mobile robots, control of CD/DVD players, flexible manufacturing lines, and complex networks of interacting agents. The book is based on the material presented at a similarly entitled minisymposium at the 6th European Nonlinear Dynamics Conference held in St Petersburg in 2008. It is unique in that it contains results of several international and interdisciplinary collaborations in the field, and reflects state-of-the-art technological development in the area of hybrid mechanical systems at the forefront of the 21st century.
Problems and Solutions in Introductory and Advanced Matrix Calculus
Author: Willi-Hans Steeb, Yorick Hardy
Publisher: World Scientific Publishing Company
ISBN: 9813143819
Pages: 568
Year: 2016-07-14
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This book provides an extensive collection of problems with detailed solutions in introductory and advanced matrix calculus. Supplementary problems in each chapter will challenge and excite the reader, ideal for both graduate and undergraduate mathematics and theoretical physics students. The coverage includes systems of linear equations, linear differential equations, integration and matrices, Kronecker product and vec-operation as well as functions of matrices. Furthermore, specialized topics such as spectral theorem, nonnormal matrices and mutually unbiased bases are included. Many of the problems are related to applications for group theory, Lie algebra theory, wavelets, graph theory and matrix-valued differential forms, benefitting physics and engineering students and researchers alike. It also branches out to problems with tensors and the hyperdeterminant. Computer algebra programs in Maxima and SymbolicC++ have also been provided.
The inverse problem of scattering theory
Author: Z. S. Agranovich, Vladimir Aleksandrovich Marchenko
Pages: 290
Year: 1964
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Problems and Solutions in Quantum Computing and Quantum Information
Publisher: World Scientific Publishing Company
ISBN: 9813238429
Pages: 556
Year: 2018-02-13
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Quantum computing and quantum information are two of the fastest growing and most exciting research fields in physics. Entanglement, teleportation and the possibility of using the non-local behavior of quantum mechanics to factor integers in random polynomial time have also added to this new interest. This book presents a huge collection of problems in quantum computing and quantum information together with their detailed solutions, which will prove to be invaluable to students as well as researchers in these fields. Each chapter gives a comprehensive introduction to the topics. All the important concepts and areas such as quantum gates and quantum circuits, product Hilbert spaces, entanglement and entanglement measures, teleportation, Bell states, Bell measurement, Bell inequality, Schmidt decomposition, quantum Fourier transform, magic gate, von Neumann entropy, quantum cryptography, quantum error corrections, quantum games, number states and Bose operators, coherent states, squeezed states, Gaussian states, coherent Bell states, POVM measurement, quantum optics networks, beam splitter, phase shifter and Kerr Hamilton operator are included. A chapter on quantum channels has also been added. Furthermore a chapter on boolean functions and quantum gates with mapping bits to qubits is included. The topics range in difficulty from elementary to advanced. Almost all problems are solved in detail and most of the problems are self-contained. Each chapter also contains supplementary problems to challenge the reader. Programming problems with Maxima and SymbolicC++ implementations are also provided.
Pattern Formation in Continuous and Coupled Systems
Author: Martin Golubitsky, Dan Luss, Steven H. Strogatz
Publisher: Springer Science & Business Media
ISBN: 1461215587
Pages: 323
Year: 2012-12-06
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This IMA Volume in Mathematics and its Applications PATTERN FORMATION IN CONTINUOUS AND COUPLED SYSTEMS is based on the proceedings of a workshop with the same title, but goes be yond the proceedings by presenting a series of mini-review articles that sur vey, and provide an introduction to, interesting problems in the field. The workshop was an integral part of the 1997-98 IMA program on "EMERG ING APPLICATIONS OF DYNAMICAL SYSTEMS." I would like to thank Martin Golubitsky, University of Houston (Math ematics) Dan Luss, University of Houston (Chemical Engineering), and Steven H. Strogatz, Cornell University (Theoretical and Applied Mechan ics) for their excellent work as organizers of the meeting and for editing the proceedings. I also take this opportunity to thank the National Science Foundation (NSF), and the Army Research Office (ARO), whose financial support made the workshop possible. Willard Miller, Jr., Professor and Director v PREFACE Pattern formation has been studied intensively for most of this cen tury by both experimentalists and theoreticians, and there have been many workshops and conferences devoted to the subject. In the IMA workshop on Pattern Formation in Continuous and Coupled Systems held May 11-15, 1998 we attempted to focus on new directions in the patterns literature.
Functional Equations in Mathematical Analysis
Author: Themistocles M. Rassias, Janusz Brzdek
Publisher: Springer Science & Business Media
ISBN: 1461400554
Pages: 748
Year: 2011-09-18
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The stability problem for approximate homomorphisms, or the Ulam stability problem, was posed by S. M. Ulam in the year 1941. The solution of this problem for various classes of equations is an expanding area of research. In particular, the pursuit of solutions to the Hyers-Ulam and Hyers-Ulam-Rassias stability problems for sets of functional equations and ineqalities has led to an outpouring of recent research. This volume, dedicated to S. M. Ulam, presents the most recent results on the solution to Ulam stability problems for various classes of functional equations and inequalities. Comprised of invited contributions from notable researchers and experts, this volume presents several important types of functional equations and inequalities and their applications to problems in mathematical analysis, geometry, physics and applied mathematics. "Functional Equations in Mathematical Analysis" is intended for researchers and students in mathematics, physics, and other computational and applied sciences.
Perspectives and Problems in Nonlinear Science
Author: Ehud Kaplan, Jerrold E. Marsden, Katepalli R. Sreenivasan
Publisher: Springer Science & Business Media
ISBN: 0387217894
Pages: 444
Year: 2012-12-06
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Lawrence Sirovich will turn seventy on March 1, 2003. Larry's academic life of over 45 years at the Courant Institute, Brown University, Rockefeller University and the Mount Sinai School of Medicine has touched many peo ple and several disciplines, from fluid dynamics to brain theory. His con tributions to the kinetic theory of gases, methods of applied mathematics, theoretical fluid dynamics, hydrodynamic turbulence, the biophysics of vi sion and the dynamics of neuronal populations, represent the creative work of an outstanding scholar who was stimulated mostly by insatiable curios ity. As a scientist, Larry has consistently offered fresh outlooks on classical and difficult subjects, and moved into new fields effortlessly. He delights in what he knows and does, and sets no artificial boundaries to the range of his inquiry. Among the more than fifty or so Ph. D. students and post docs that he has mentored, many continue to make first-rate contributions themselves and hold academic positions in the US and elsewhere. Larry's scientific collaborators are numerous and distinguished. Those of us who have known him well will agree that Larry's charm, above all, is his taste, wit, and grace under fire. Larry has contributed immensely to mathematics publishing. He be gan his career with Springer by founding the Applied Mathematical Sci ences series together with Fritz John and Joe LaSalle some 30 years ago. Later he co-founded the Texts in Applied Mathematics series and more re cently the Interdisciplinary Applied Mathematics series.