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This volume is dedicated to the memory of Shoshichi Kobayashi, and
gathers contributions from distinguished researchers working on
topics close to his research areas. The book is organized into
three parts, with the first part presenting an overview of
Professor Shoshichi Kobayashi's career. This is followed by two
expository course lectures (the second part) on recent topics in
extremal Kahler metrics and value distribution theory, which will
be helpful for graduate students in mathematics interested in new
topics in complex geometry and complex analysis. Lastly, the third
part of the volume collects authoritative research papers on
differential geometry and complex analysis. Professor Shoshichi
Kobayashi was a recognized international leader in the areas of
differential and complex geometry. He contributed crucial ideas
that are still considered fundamental in these fields. The book
will be of interest to researchers in the fields of differential
geometry, complex geometry, and several complex variables geometry,
as well as to graduate students in mathematics.
This volume is dedicated to the memory of Shoshichi Kobayashi, and
gathers contributions from distinguished researchers working on
topics close to his research areas. The book is organized into
three parts, with the first part presenting an overview of
Professor Shoshichi Kobayashi's career. This is followed by two
expository course lectures (the second part) on recent topics in
extremal Kahler metrics and value distribution theory, which will
be helpful for graduate students in mathematics interested in new
topics in complex geometry and complex analysis. Lastly, the third
part of the volume collects authoritative research papers on
differential geometry and complex analysis. Professor Shoshichi
Kobayashi was a recognized international leader in the areas of
differential and complex geometry. He contributed crucial ideas
that are still considered fundamental in these fields. The book
will be of interest to researchers in the fields of differential
geometry, complex geometry, and several complex variables geometry,
as well as to graduate students in mathematics.
The papers in this volume are based on lectures given during the
meeting of the Seminaire Sud Rhodanien de Geometrie which we
organized at MSRI from May 22 to June 2, 1989, as part of a
year-long program on Symplectic Geometry and Mechanics. The
Seminaire Sud Rhodanien de Geometrie (SSRG) was established in 1982
by geometers and mathematical physicists at the Universities of
Avignon, Lyon, Marseille, and Montpellier, with the aim of
developing and coordinating research in symplectic geometry and its
applications to analysis and mathematical physics. It has been
designated by the Centre N ationale de la Recherche Scientifique as
a "Groupement de Recherche" (G.D.R. 144), centered at the
Universite Claude Bernard (Lyon I). From the beginning, the SSRG
has involved the cooperation of colleagues from other universities
inside and outside France; in addition to the editors of this
volume, its Scientific Committee consists of D. Bennequin, P.
Libermann, A. Lichnerowicz, C.-M. MarIe, J.-M. Morvan, P. Molino,
and J.-M. Souriau. In particular, there have always been strong
connections with the University of California at Berkeley, making
this other "UCB" into a virtual fifth pole of the SSRG. Through its
international meetings, of which the first five were held at Lyon,
Montpellier, and Marseille, the SSRG has become an important cen
ter of exchange for the latest developments in symplectic geometry
and its applications. It seemed natural, therefore, to have this
sixth meeting at MSRI in Berkeley in conjunction with the
"symplectic year" 1988-89."
Jerry Marsden, one of the world's pre-eminent mechanicians and
applied mathematicians, celebrated his 60th birthday in August
2002. The event was marked by a workshop on "Geometry, Mechanics,
and Dynamics"at the Fields Institute for Research in the
Mathematical Sciences, of which he wasthefoundingDirector.
Ratherthanmerelyproduceaconventionalp- ceedings, with relatively
brief accounts of research and technical advances presented at the
meeting, we wished to acknowledge Jerry's in?uence as a teacher, a
propagator of new ideas, and a mentor of young talent. Con-
quently, starting in 1999, we sought to collect articles that might
be used as entry points by students interested in ?elds that have
been shaped by Jerry's work. At the same time we hoped to give
experts engrossed in their own technical niches an indication of
the wonderful breadth and depth of their subjects as a whole. This
book is an outcome of the e?orts of those who accepted our in-
tations to contribute. It presents both survey and research
articles in the several ?elds that represent the main themes of
Jerry's work, including elasticity and analysis, ?uid mechanics,
dynamical systems theory, g- metric mechanics, geometric control
theory, and relativity and quantum mechanics. The common thread
running through this broad tapestry is the use of geometric methods
that serve to unify diverse disciplines and bring a
widevarietyofscientistsandmathematicianstogether, speakingalanguage
which enhances dialogue and encourages cross-fertilization.
Andreas Floer died on May 15, 1991 an untimely and tragic death.
His visions and far-reaching contributions have significantly
influenced the developments of mathematics. His main interests
centered on the fields of dynamical systems, symplectic geometry,
Yang-Mills theory and low dimensional topology. Motivated by the
global existence problem of periodic solutions for Hamiltonian
systems and starting from ideas of Conley, Gromov and Witten, he
developed his Floer homology, providing new, powerful methods which
can be applied to problems inaccessible only a few years ago. This
volume opens with a short biography and three hitherto unpublished
papers of Andreas Floer. It then presents a collection of invited
contributions, and survey articles as well as research papers on
his fields of interest, bearing testimony of the high esteem and
appreciation this brilliant mathematician enjoyed among his
colleagues. Authors include: A. Floer, V.I. Arnold, M. Atiyah, M.
Audin, D.M. Austin, S.M. Bates, P.J. Braam, M. Chaperon, R.L.
Cohen, G. Dell' Antonio, S.K. Donaldson, B. D'Onofrio, I. Ekeland,
Y. Eliashberg, K.D. Ernst, R. Finthushel, A.B. Givental, H. Hofer,
J.D.S. Jones, I. McAllister, D. McDuff, Y.-G. Oh, L. Polterovich,
D.A. Salamon, G.B. Segal, R. Stern, C.H. Taubes, C. Viterbo, A.
Weinstein, E. Witten, E. Zehnder
This volume aims to acknowledge J. E. Marsden's influence as a teacher, propagator of new ideas, and mentor of young talent. It presents both survey articles and research articles in the fields that represent the main themes of his work, including elesticity and analysis, fluid mechanics, dynamical systems theory, geometric mechanics, geometric control theory, and relativity and quantum mechanics. The common thread throughout is the use of geometric methods that serve to unify diverse disciplines and bring a wide variety of scientists and mathematicians together in a way that enhances dialogue and encourages cooperation. This book may serve as a guide to rapidly evolving areas as well as a resource both for students who want to work in one of these fields and practitioners who seek a broader view.
The second of a three-volume work, this is the result of the
authors'experience teaching calculus at Berkeley. The book covers
techniques and applications of integration, infinite series, and
differential equations, the whole time motivating the study of
calculus using its applications. The authors include numerous
solved problems, as well as extensive exercises at the end of each
section. In addition, a separate student guide has been prepared.
This book, the third of a three-volume work, is the outgrowth of
the authors' experience teaching calculus at Berkeley. It is
concerned with multivariable calculus, and begins with the
necessary material from analytical geometry. It goes on to cover
partial differention, the gradient and its applications, multiple
integration, and the theorems of Green, Gauss and Stokes.
Throughout the book, the authors motivate the study of calculus
using its applications. Many solved problems are included, and
extensive exercises are given at the end of each section. In
addition, a separate student guide has been prepared.
Andreas Floer died on May 15, 1991 an untimely and tragic death.
His visions and far-reaching contributions have significantly
influenced the developments of mathematics. His main interests
centered on the fields of dynamical systems, symplectic geometry,
Yang-Mills theory and low dimensional topology. Motivated by the
global existence problem of periodic solutions for Hamiltonian
systems and starting from ideas of Conley, Gromov and Witten, he
developed his Floer homology, providing new, powerful methods which
can be applied to problems inaccessible only a few years ago. This
volume opens with a short biography and three hitherto unpublished
papers of Andreas Floer. It then presents a collection of invited
contributions, and survey articles as well as research papers on
his fields of interest, bearing testimony of the high esteem and
appreciation this brilliant mathematician enjoyed among his
colleagues. Authors include: A. Floer, V.I. Arnold, M. Atiyah, M.
Audin, D.M. Austin, S.M. Bates, P.J. Braam, M. Chaperon, R.L.
Cohen, G. Dell' Antonio, S.K. Donaldson, B. D'Onofrio, I. Ekeland,
Y. Eliashberg, K.D. Ernst, R. Finthushel, A.B. Givental, H. Hofer,
J.D.S. Jones, I. McAllister, D. McDuff, Y.-G. Oh, L. Polterovich,
D.A. Salamon, G.B. Segal, R. Stern, C.H. Taubes, C. Viterbo, A.
Weinstein, E. Witten, E. Zehnder
The goal of this text is to help students learn to use calculus
intelligently for solving a wide variety of mathematical and
physical problems. This book is an outgrowth of our teaching of
calculus at Berkeley, and the present edition incorporates many
improvements based on our use of the first edition. We list below
some of the key features of the book. Examples and Exercises The
exercise sets have been carefully constructed to be of maximum use
to the students. With few exceptions we adhere to the following
policies. * The section exercises are graded into three consecutive
groups: (a) The first exercises are routine, modelled almost
exactly on the exam ples; these are intended to give students
confidence. (b) Next come exercises that are still based directly
on the examples and text but which may have variations of wording
or which combine different ideas; these are intended to train
students to think for themselves. (c) The last exercises in each
set are difficult. These are marked with a star (*) and some will
challenge even the best students. Difficult does not necessarily
mean theoretical; often a starred problem is an interesting
application that requires insight into what calculus is really
about. * The exercises come in groups of two and often four similar
ones.
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.
While Applying Social Statistics is "about" social statistics and
includes all of the topics generally covered in similar texts, it
is first and foremost a book about how sociologists use statistics.
Its emphasis is on statistical reasoning in sociology and on
showing how these principles can be applied to numerous problems in
a wide variety of contexts; to answer effectively the question
"what's it for." A main learning objective is to help students
understand how and why social statistics is used. Yet, Weinstein's
style and substance recognize that it is of equal-or even
greater-importance that they begin to learn how to apply these
principles and techniques themselves.
While Applying Social Statistics is 'about' social statistics and
includes all of the topics generally covered in similar texts, it
is first and foremost a book about how sociologists use statistics.
Its emphasis is on statistical reasoning in sociology and on
showing how these principles can be applied to numerous problems in
a wide variety of contexts; to answer effectively the question
'what's it for.' A main learning objective is to help students
understand how and why social statistics is used. Yet, Weinstein's
style and substance recognize that it is of equal-or even
greater-importance that they begin to learn how to apply these
principles and techniques themselves.
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