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This textbook by respected authors helps students foster
computational skills and intuitive understanding with a careful
balance of theory, applications, historical development and
optional materials.
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.
The purpose of this book is to provide core material in nonlinear
analysis for mathematicians, physicists, engineers, and
mathematical biologists. The main goal is to provide a working
knowledge of manifolds, dynamical systems, tensors, and
differential forms. Some applications to Hamiltonian mechanics,
fluid me chanics, electromagnetism, plasma dynamics and control
thcory arc given in Chapter 8, using both invariant and index
notation. The current edition of the book does not deal with
Riemannian geometry in much detail, and it does not treat Lie
groups, principal bundles, or Morse theory. Some of this is planned
for a subsequent edition. Meanwhile, the authors will make
available to interested readers supplementary chapters on Lie
Groups and Differential Topology and invite comments on the book's
contents and development. Throughout the text supplementary topics
are given, marked with the symbols ~ and {l:;J. This device enables
the reader to skip various topics without disturbing the main flow
of the text. Some of these provide additional background material
intended for completeness, to minimize the necessity of consulting
too many outside references. We treat finite and
infinite-dimensional manifolds simultaneously. This is partly for
efficiency of exposition. Without advanced applications, using
manifolds of mappings, the study of infinite-dimensional manifolds
can be hard to motivate.
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Vladimir I. Arnold - Collected Works - Representations of Functions, Celestial Mechanics, and KAM Theory 1957-1965 (English, Russian, Paperback, 2010 ed.)
Vladimir I. Arnold; Edited by Alexander B. Givental, Boris Khesin, Jerrold E. Marsden, Alexander N. Varchenko, …
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R5,335
Discovery Miles 53 350
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Ships in 10 - 15 working days
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Vladimir Igorevich Arnold is one of the most influential
mathematicians of our time. V. I. Arnold launched several
mathematical domains (such as modern geometric mechanics,
symplectic topology, and topological fluid dynamics) and
contributed, in a fundamental way, to the foundations and methods
in many subjects, from ordinary differential equations and
celestial mechanics to singularity theory and real algebraic
geometry. Even a quick look at a partial list of notions named
after Arnold already gives an overview of the variety of such
theories and domains: KAM (Kolmogorov-Arnold-Moser) theory, The
Arnold conjectures in symplectic topology, The Hilbert-Arnold
problem for the number of zeros of abelian integrals, Arnold's
inequality, comparison, and complexification method in real
algebraic geometry, Arnold-Kolmogorov solution of Hilbert's 13th
problem, Arnold's spectral sequence in singularity theory, Arnold
diffusion, The Euler-Poincare-Arnold equations for geodesics on Lie
groups, Arnold's stability criterion in hydrodynamics, ABC
(Arnold-Beltrami-Childress) ?ows in ?uid dynamics, The
Arnold-Korkina dynamo, Arnold's cat map, The Arnold-Liouville
theorem in integrable systems, Arnold's continued fractions,
Arnold's interpretation of the Maslov index, Arnold's relation in
cohomology of braid groups, Arnold tongues in bifurcation theory,
The Jordan-Arnold normal forms for families of matrices, The Arnold
invariants of plane curves. Arnold wrote some 700 papers, and many
books, including 10 university textbooks. He is known for his lucid
writing style, which combines mathematical rigour with physical and
geometric intuition. Arnold's books on
Ordinarydifferentialequations and Mathematical
methodsofclassicalmechanics became mathematical bestsellers and
integral parts of the mathematical education of students throughout
the world."
A development of the basic theory and applications of mechanics
with an emphasis on the role of symmetry. The book includes
numerous specific applications, making it beneficial to physicists
and engineers. Specific examples and applications show how the
theory works, backed by up-to-date techniques, all of which make
the text accessible to a wide variety of readers, especially senior
undergraduates and graduates in mathematics, physics and
engineering. This second edition has been rewritten and updated for
clarity throughout, with a major revamping and expansion of the
exercises. Internet supplements containing additional material are
also available.
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Vladimir I. Arnold - Collected Works - Representations of Functions, Celestial Mechanics, and KAM Theory 1957-1965 (English, Russian, Hardcover, 2010 ed.)
Vladimir I. Arnold; Edited by Alexander B. Givental, Boris Khesin, Jerrold E. Marsden, Alexander N. Varchenko, …
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R5,373
Discovery Miles 53 730
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Ships in 10 - 15 working days
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Vladimir Igorevich Arnold is one of the most influential
mathematicians of our time. V. I. Arnold launched several
mathematical domains (such as modern geometric mechanics,
symplectic topology, and topological fluid dynamics) and
contributed, in a fundamental way, to the foundations and methods
in many subjects, from ordinary differential equations and
celestial mechanics to singularity theory and real algebraic
geometry. Even a quick look at a partial list of notions named
after Arnold already gives an overview of the variety of such
theories and domains: KAM (Kolmogorov-Arnold-Moser) theory, The
Arnold conjectures in symplectic topology, The Hilbert-Arnold
problem for the number of zeros of abelian integrals, Arnold's
inequality, comparison, and complexification method in real
algebraic geometry, Arnold-Kolmogorov solution of Hilbert's 13th
problem, Arnold's spectral sequence in singularity theory, Arnold
diffusion, The Euler-Poincare-Arnold equations for geodesics on Lie
groups, Arnold's stability criterion in hydrodynamics, ABC
(Arnold-Beltrami-Childress) ?ows in ?uid dynamics, The
Arnold-Korkina dynamo, Arnold's cat map, The Arnold-Liouville
theorem in integrable systems, Arnold's continued fractions,
Arnold's interpretation of the Maslov index, Arnold's relation in
cohomology of braid groups, Arnold tongues in bifurcation theory,
The Jordan-Arnold normal forms for families of matrices, The Arnold
invariants of plane curves. Arnold wrote some 700 papers, and many
books, including 10 university textbooks. He is known for his lucid
writing style, which combines mathematical rigour with physical and
geometric intuition. Arnold's books on
Ordinarydifferentialequations and Mathematical
methodsofclassicalmechanics became mathematical bestsellers and
integral parts of the mathematical education of students throughout
the world.
In this volume readers will find for the first time a detailed
account of the theory of symplectic reduction by stages, along with
numerous illustrations of the theory. Special emphasis is given to
group extensions, including a detailed discussion of the Euclidean
group, the oscillator group, the Bott-Virasoro group and other
groups of matrices. Ample background theory on symplectic reduction
and cotangent bundle reduction in particular is provided. Novel
features of the book are the inclusion of a systematic treatment of
the cotangent bundle case, including the identification of cocycles
with magnetic terms, as well as the general theory of singular
reduction by stages.
One of the worlds foremost geometers, Alan Weinstein has made deep
contributions to symplectic and differential geometry, Lie theory,
mechanics, and related fields. Written in his honor, the invited
papers in this volume reflect the active and vibrant research in
these areas and are a tribute to Weinsteins ongoing influence. The
well-recognized contributors to this text cover a broad range of
topics: Induction and reduction for systems with symmetry,
symplectic geometry and topology, geometric quantization, the
Weinstein Conjecture, Poisson algebra and geometry, Dirac
structures, deformations for Lie group actions, Kahler geometry of
moduli spaces, theory and applications of Lagrangian and
Hamiltonian mechanics and dynamics, symplectic and Poisson
groupoids, and quantum representations.Intended for graduate
students and working mathematicians in symplectic and Poisson
geometry as well as mechanics, this text is a distillation of
prominent research and an indication of the future trends and
directions in geometry, mechanics, and mathematical physics.
This volume is a collection of fourteen papers, written by well-known authors, on aspects of applied mathematics, fluid dynamics, combustion, kinetic theory, condensed matter physics, computational neuroscience, biophysics and closely related areas. There are two uniting themes. First, the papers celebrate the long and durable contributions of Professor Lawrence Sirovich on the occasion of his turning seventy. Second, the threads of nonlinearity weave through all the problems discussed. The papers combine original research with expository style and make a fascinating reading for a diverse readership in applied mathematics and science.
A presentation of some of the basic ideas of fluid mechanics in a mathematically attractive manner. The text illustrates the physical background and motivation for some constructions used in recent mathematical and numerical work on the Navier- Stokes equations and on hyperbolic systems, so as to interest students in this at once beautiful and difficult subject. This third edition incorporates a number of updates and revisions, while retaining the spirit and scope of the original book.
The purpose of this book is to provide core material in nonlinear analysis for mathematicians, physicists, engineers, and mathematical biologists. The main goal is to provide a working knowledge of manifolds, dynamical systems, tensors, and differential forms. Some applications to Hamiltonian mechanics, fluid mechanics, electromagnetism, plasma dynamics and control theory are given using both invariant and index notation. The prerequisites required are solid undergraduate courses in linear algebra and advanced calculus.
Symmetry has always played an important role in mechanics, from fundamental formulations of basic principles to concrete applications. The theme of the book is to develop the basic theory and applications of mechanics with an emphasis on the role of symmetry. In recent times, the interest in mechanics, and in symmetry techniques in particular, has accelerated because of developments in dynamical systems, the use of geometric methods and new applications to integrable and chaotic systems, control systems, stability and bifurcation, and the study of specific rigid, fluid, plasma and elastic systems. Introduction to Mechanics and Symmetry lays the basic foundation for these topics and includes numerous specific applications, making it beneficial to physicists and engineers. This text has specific examples and applications showing how the theory works, and up-to-date techniques, all of which makes it accessible to a wide variety of readers, expecially senior undergraduate and graduate students in mathematics, physics and engineering. For this second edition, the text has been rewritten and updated for clarity throughout, with a major revamping and expansion of the exercises. Internet supplements containing additional material are also available on-line.
Mathematics is playing an ever more important role in the physical
and biological sciences, provoking a blurring of boundaries between
scientific disciplines and a resurgence of interest in the modern
as weil as the clas sical techniques of applied mathematics. This
renewal of interest, bothin research and teaching, has led to the
establishment of the series: Texts in Applied Mathematics (TAM).
The development of new courses is a natural consequence of a high
Ievel of excitement on the research frontier as newer techniques,
such as numerical and symbolic computer systems, dynamical systems,
and chaos, mix with and reinforce the traditional methods of
applied mathematics. Thus, the purpose of this textbook series is
to meet the current and future needs of these advances and
encourage the teaching of new courses. TAM will publish textbooks
suitable for use in advanced undergraduate and beginning graduate
courses, and will complement the Applied Mathematical Seiences
(AMS) series, which will focus on advanced textbooks and research
Ievel monographs. Preface This book is based on a one-term coursein
fluid mechanics originally taught in the Department of Mathematics
of the U niversity of California, Berkeley, during the spring of
1978. The goal of the course was not to provide an exhaustive
account of fluid mechanics, nor to assess the engineering value of
various approximation procedures."
Designed for courses in advanced calculus and introductory real
analysis, the second edition of Elementary Classical Analysis
strikes a careful and thoughtful balance between pure and applied
mathematics, with the emphasis on techniques important to classical
analysis, without vector calculus or complex analysis. As such,
it's a perfect teaching and learning resource for mathematics
undergraduate courses in classical analysis. The book includes
detailed coverage of the foundations of the real number system and
focuses primarily on analysis in Euclidean space with a view
towards application. As well as being suitable for students taking
pure mathematics, it can also be used by students taking
engineering and physical science courses. There's now even more
material on variable calculus, expanding the textbook's already
considerable coverage of the subject.
This book explores connections between control theory and geometric
mechanics. The author links control theory with a geometric view of
classical mechanics in both its Lagrangian and Hamiltonian
formulations, and in particular with the theory of mechanical
systems subject to motion constraints. The synthesis is appropriate
as there is a rich connection between mechanics and nonlinear
control theory. The book provides a unified treatment of nonlinear
control theory and constrained mechanical systems that incorporates
material not available in other recent texts. The book benefits
graduate students and researchers in the area who want to enhance
their understanding and enhance their techniques.
An extraordinary mathematical conference was held 5-9 August 1990
at the University of California at Berkeley: From Topology to
Computation: Unity and Diversity in the Mathematical Sciences An
International Research Conference in Honor of Stephen Smale's 60th
Birthday The topics of the conference were some of the fields in
which Smale has worked: * Differential Topology * Mathematical
Economics * Dynamical Systems * Theory of Computation * Nonlinear
Functional Analysis * Physical and Biological Applications This
book comprises the proceedings of that conference. The goal of the
conference was to gather in a single meeting mathemati cians
working in the many fields to which Smale has made lasting con
tributions. The theme "Unity and Diversity" is enlarged upon in the
section entitled "Research Themes and Conference Schedule." The
organizers hoped that illuminating connections between seemingly
separate mathematical sub jects would emerge from the conference.
Since such connections are not easily made in formal mathematical
papers, the conference included discussions after each of the
historical reviews of Smale's work in different fields. In
addition, there was a final panel discussion at the end of the
conference.
Basic Multivariable Calculus fills the need for a student-oriented
text devoted exclusively to the third-semester course in
multivariable calculus. In this text, the basic algebraic,
analytic, and geometric concepts of multivariable and vector
calculus are carefully explained, with an emphasis on developing
the student's intuitive understanding and computational technique.
A wealth of figures supports geometrical interpretation, while
exercise sets, review sections, practice exams, and historical
notes keep the students active in, and involved with, the
mathematical ideas. All necessary linear algebra is developed
within the text, and the material can be readily coordinated with
computer laboratories. Basic Multivariable Calculus is the product
of an extensive writing, revising, and class-testing collaboration
by the authors of Calculus III (Springer-Verlag) and Vector
Calculus (W.H. Freeman & Co.). Incorporating many features from
these highly respected texts, it is both a synthesis of the
authors' previous work and a new and original textbook.
This volume presents articles originating from invited talks at an
exciting international conference held at The Fields Institute in
Toronto celebrating the sixtieth birthday of the renowned
mathematician, Vladimir Arnold. Experts from the world over -
including several from 'Arnold's school' - gave illuminating talks
and lively poster sessions. The presentations focussed on Arnold's
main areas of interest: singularity theory, the theory of curves,
symmetry groups, dynamical systems, mechanics, and related areas of
mathematics. The book begins with notes of three lectures by V.
Arnold given in the framework of the Institute's Distinguished
Lecturer program.The topics of the lectures are: From Hilbert's
Superposition Problem to Dynamical Systems; Symplectization,
Complexification, and Mathematical Trinities; and, Topological
Problems in Wave Propagation Theory and Topological Economy
Principle in Algebraic Geometry. Arnold's three articles include
insightful comments on Russian and Western mathematics and science.
Complementing the first is Jurgen Moser's 'Recollections',
concerning some of the history of KAM theory.
The use of geometric methods in classical mechanics has proven to
be a fruitful exercise, with the results being of wide application
to physics and engineering. Here Professor Marsden concentrates on
these geometric aspects, and especially on symmetry techniques. The
main points he covers are: the stability of relative equilibria,
which is analyzed using the block diagonalization technique;
geometric phases, studied using the reduction and reconstruction
technique; and bifurcation of relative equilibria and chaos in
mechanical systems. A unifying theme for these points is provided
by reduction theory, the associated mechanical connection and
techniques from dynamical systems. These methods can be applied to
many control and stabilization situations, and this is illustrated
using rigid bodies with internal rotors, and the use of geometric
phases in mechanical systems. To illustrate the above ideas and the
power of geometric arguments, the author studies a variety of
specific systems, including the double spherical pendulum and the
classical rotating water molecule. This book, based on the 1991 LMS
Invited Lectures, will be valued by pure and applied
mathematicians, physicists and engineers who work in geometry,
nonlinear dynamics, mechanics, and robotics.
A monograph on some of the ways geometry and analysis can be used
in mathematical problems of physical interest. The roles of
symmetry, bifurcation, and Hamiltonian systems in diverse
applications are explored.
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