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This book is intended to help advanced undergraduate, graduate, and
postdoctoral students in their daily work by offering them a
compendium of numerical methods. The choice of methods pays
significant attention to error estimates, stability and convergence
issues, as well as optimization of program execution speeds.
Numerous examples are given throughout the chapters, followed by
comprehensive end-of-chapter problems with a more pronounced
physics background, while less stress is given to the explanation
of individual algorithms. The readers are encouraged to develop a
certain amount of skepticism and scrutiny instead of blindly
following readily available commercial tools. The second edition
has been enriched by a chapter on inverse problems dealing with the
solution of integral equations, inverse Sturm-Liouville problems,
as well as retrospective and recovery problems for partial
differential equations. The revised text now includes an
introduction to sparse matrix methods, the solution of matrix
equations, and pseudospectra of matrices; it discusses the sparse
Fourier, non-uniform Fourier and discrete wavelet transformations,
the basics of non-linear regression and the Kolmogorov-Smirnov
test; it demonstrates the key concepts in solving stiff
differential equations and the asymptotics of Sturm-Liouville
eigenvalues and eigenfunctions. Among other updates, it also
presents the techniques of state-space reconstruction, methods to
calculate the matrix exponential, generate random permutations and
compute stable derivatives.
This book is designed as a practical and intuitive introduction to
probability, statistics and random quantities for physicists. The
book aims at getting to the main points by a clear, hands-on
exposition supported by well-illustrated and worked-out examples. A
strong focus on applications in physics and other natural sciences
is maintained throughout. In addition to basic concepts of random
variables, distributions, expected values and statistics, the book
discusses the notions of entropy, Markov processes, and
fundamentals of random number generation and Monte-Carlo methods.
This book is designed as a practical and intuitive introduction to
probability, statistics and random quantities for physicists. The
book aims at getting to the main points by a clear, hands-on
exposition supported by well-illustrated and worked-out examples. A
strong focus on applications in physics and other natural sciences
is maintained throughout. In addition to basic concepts of random
variables, distributions, expected values and statistics, the book
discusses the notions of entropy, Markov processes, and
fundamentals of random number generation and Monte-Carlo methods.
This book helps advanced undergraduate, graduate and postdoctoral
students in their daily work by offering them a compendium of
numerical methods. The choice of methods pays significant attention
to error estimates, stability and convergence issues as well as to
the ways to optimize program execution speeds. Many examples are
given throughout the chapters, and each chapter is followed by at
least a handful of more comprehensive problems which may be dealt
with, for example, on a weekly basis in a one- or two-semester
course. In these end-of-chapter problems the physics background is
pronounced, and the main text preceding them is intended as an
introduction or as a later reference. Less stress is given to the
explanation of individual algorithms. It is tried to induce in the
reader an own independent thinking and a certain amount of
scepticism and scrutiny instead of blindly following readily
available commercial tools.
In this Supplement we have collected the invited and contributed
talks pre sented at the XVIII European Conference on Few-Body
Problems in Physics, organised by the Jozef Stefan Institute and
the University of Ljubljana, Slove nia. The Conference, sponsored
by the European Physical Society, took place at the lakeside resort
of Bled from 8 to 14 September, 2002. This meeting was a part of
the series of European Few-Body Conferences, previously held in
Evora/Portugal (2000), Autrans/France (1998), Peniscola/Spain
(1995), ... Our aim was to emphasise, to a larger extent than at
previous Conferences, the interdisciplinarity of research fields of
the Few-Body community. To pro mote a richer exchange of ideas, we
therefore strived to avoid parallel sessions as much as possible.
On the other hand, to promote the participation of young scientists
who we feel will eventually shape the future of Few-Body Physics,
we wished to give almost all attendees the opportunity to speak."
This book is intended to help advanced undergraduate, graduate, and
postdoctoral students in their daily work by offering them a
compendium of numerical methods. The choice of methods pays
significant attention to error estimates, stability and convergence
issues, as well as optimization of program execution speeds.
Numerous examples are given throughout the chapters, followed by
comprehensive end-of-chapter problems with a more pronounced
physics background, while less stress is given to the explanation
of individual algorithms. The readers are encouraged to develop a
certain amount of skepticism and scrutiny instead of blindly
following readily available commercial tools. The second edition
has been enriched by a chapter on inverse problems dealing with the
solution of integral equations, inverse Sturm-Liouville problems,
as well as retrospective and recovery problems for partial
differential equations. The revised text now includes an
introduction to sparse matrix methods, the solution of matrix
equations, and pseudospectra of matrices; it discusses the sparse
Fourier, non-uniform Fourier and discrete wavelet transformations,
the basics of non-linear regression and the Kolmogorov-Smirnov
test; it demonstrates the key concepts in solving stiff
differential equations and the asymptotics of Sturm-Liouville
eigenvalues and eigenfunctions. Among other updates, it also
presents the techniques of state-space reconstruction, methods to
calculate the matrix exponential, generate random permutations and
compute stable derivatives.
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