ISBN: 978-1-119-12150-3
544 pages
September 2016
A new edition of this classic work, comprehensively revised to present exciting new developments in this important subject
The study of numerical methods for solving ordinary differential equations is constantly developing and regenerating, and this third edition of a popular classic volume, written by one of the worldfs leading experts in the field, presents an account of the subject which reflects both its historical and well-established place in computational science and its vital role as a cornerstone of modern applied mathematics.
In addition to serving as a broad and comprehensive study of numerical methods for initial value problems, this book contains a special emphasis on Runge-Kutta methods by the mathematician who transformed the subject into its modern form dating from his classic 1963 and 1972 papers. A second feature is general linear methods which have now matured and grown from being a framework for a unified theory of a wide range of diverse numerical schemes to a source of new and practical algorithms in their own right. As the founder of general linear method research, John Butcher has been a leading contributor to its development; his special role is reflected in the text. The book is written in the lucid style characteristic of the author, and combines enlightening explanations with rigorous and precise analysis. In addition to these anticipated features, the book breaks new ground by including the latest results on the highly efficient G-symplectic methods which compete strongly with the well-known symplectic Runge-Kutta methods for long-term integration of conservative mechanical systems.
This third edition of Numerical Methods for Ordinary Differential Equations will serve as a key text for senior
Preface to the first edition xi
Preface to the second edition xv
Preface to the third edition xvii
1 Differential and Difference Equations 1
10 Differential Equation Problems 1
and more
ISBN: 978-0-470-69962-1
472 pages
September 2016
A thoroughly revised and updated edition of this introduction to modern statistical methods for shape analysis
Shape analysis is an important tool in the many disciplines where objects are compared using geometrical features. Examples include comparing brain shape in schizophrenia; investigating protein molecules in bioinformatics; and describing growth of organisms in biology.
This book is a significant update of the highly-regarded `Statistical Shape Analysisf by the same authors. The new edition lays the foundations of landmark shape analysis, including geometrical concepts and statistical techniques, and extends to include analysis of curves, surfaces, images and other types of object data. Key definitions and concepts are discussed throughout, and the relative merits of different approaches are presented.
The authors have included substantial new material on recent statistical developments and offer numerous examples throughout the text. Concepts are introduced in an accessible manner, while retaining sufficient detail for more specialist statisticians to appreciate the challenges and opportunities of this new field. Computer code has been included for instructional use, along with exercises to enable readers to implement the applications themselves in R and to follow the key ideas by hands-on analysis.
Statistical Shape Analysis: with Applications in R will offer a valuable introduction to this fast-moving research area for statisticians and other applied scientists working in diverse areas, including archaeology, bioinformatics, biology, chemistry, computer science, medicine, morphometics and image analysis
1 Introduction 1
1.1 Definition and Motivation 1
1.2 Landmarks 3
1.3 The shapes package in R 6
1.4 Practical Applications 8
and more
Series: Springer Biographies
1st ed. 2016, XIII, 348 p. 54 illus., 3 illus. in color.
Hardcover
ISBN 978-1-4939-3531-4
* Follows young Enrico Fermi's research itineraries, starting from his
first paper in 1921, where he deals with some problems in general
relativity, until 1933, when he publishes his fundamental theory of
the beta decay
* Analyzes Fermi's research from 1933 to 1954, underlining his
involvement in developing the atomic bomb and his central role in
the beginning of the big science
* Includes sections of unpublished notes and letters
* Provides a timeline of Fermifs life achievements as well as a separate
timeline for the physics field throughout the early 20th century
* Contains an extensive bibliography and index for easy reference
This biography explores the life and career of the Italian physicist Enrico Fermi, which
is also the story of thirty years that transformed physics and forever changed our
understanding of matter and the universe: nuclear physics and elementary particle
physics were born, nuclear fission was discovered, the Manhattan Project was developed,
the atomic bombs were dropped, and the era of gbig scienceh began. It would be
impossible to capture the full essence of this revolutionary period without first
understanding Fermi, without whom it would not have been possible.
Enrico Fermi: The Obedient Genius attempts to shed light on all aspects of Fermifs life -
his work, motivation, influences, achievements, and personal thoughts - beginning with
the publication of his first paper in 1921 through his death in 1954. During this time,
Fermi demonstrated that he was indeed following in the footsteps of Galileo, excelling in
his work both theoretically and experimentally by deepening our understanding of the
Pauli exclusion principle, winning the Nobel Prize for his discovery of the fundamental
properties of slow neutrons, developing the theory of beta decay, building the first
nuclear reactor, and playing a central role in the development of the atomic bomb.
Interwoven with this fascinating story, the book details the major developments in physics
and provides the necessary background material to fully appreciate the dramatic changes
that were taking place.
Also included are appendices that provide a timeline of Fermifs life, several primary source
documents from the period, and an extensive bibliography. This book will enlighten
anyone interested in Fermifs work or the scientific events that led to the physics revolution
of the first half of the twentieth century.
Series: SpringerBriefs in Mathematics
1st ed. 2016, XIII, 157 p. 79 illus.
Softcover
ISBN 978-3-319-30516-5
* Assembles the latest research on chromatic graph theory, vertex
colorings, edge colorings, binomial colorings, kaleidoscopic colorings
and majestic colorings
* Contains detailed proofs and illustrations
* Provides a number of new problems and topics to study
This book describes kaleidoscopic topics that have developed in the area of graph
colorings. Unifying current material on graph coloring, this book describes current
information on vertex and edge colorings in graph theory, including harmonious
colorings, majestic colorings, kaleidoscopic colorings and binomial colorings. Recently
there have been a number of breakthroughs in vertex colorings that give rise to other
colorings in a graph, such as graceful labelings of graphs that have been reconsidered
under the language of colorings.
The topics presented in this book include sample detailed proofs and illustrations, which
depicts elements that are often overlooked. This book is ideal for graduate students and
researchers in graph theory, as it covers a broad range of topics and makes connections
between recent developments and well-known areas in graph theory.
1st ed. 2016, XII, 274 p.
Hardcover
ISBN 978-3-319-30742-8
* Written by one of the leading scholars in the field Includes a novel
presentation of differentiation and absolute continuity using a local
maximum function, resulting in an exposition that is both simpler
and more general than the traditional approach
* Theorems are stated for Lebesgue and Borel measures, with a note
indicating when the same proof works only for Lebesgue measures
* Appendices cover additional material, including theorems for higher
dimensions and a short introduction to nonstandard analysis
This textbook is designed for a year-long course in real analysis taken by beginning
graduate and advanced undergraduate students in mathematics and other areas such as
statistics, engineering, and economics. Written by one of the leading scholars in the field,
it elegantly explores the core concepts in real analysis and introduces new, accessible
methods for both students and instructors.
The first half of the book develops both Lebesgue measure and, with essentially no
additional work for the student, general Borel measures for the real line. Notation
indicates when a result holds only for Lebesgue measure. Differentiation and absolute
continuity are presented using a local maximal function, resulting in an exposition that is
both simpler and more general than the traditional approach.
The second half deals with general measures and functional analysis, including Hilbert
spaces, Fourier series, and the Riesz representation theorem for positive linear functionals
on continuous functions with compact support. To correctly discuss weak limits of
measures, one needs the notion of a topological space rather than just a metric space,
so general topology is introduced in terms of a base of neighborhoods at a point. The
development of results then proceeds in parallel with results for metric spaces, where
the base is generated by balls centered at a point. The text concludes with appendices
on covering theorems for higher dimensions and a short introduction to nonstandard
analysis including important applications to probability theory and mathematical Economics.
1st ed. 2016, X, 267 p.
Hardcover
ISBN 978-3-319-30950-7
Series: Algebra and Applications, Vol. 21
* Presents a new cohomology theory for varieties over local function
fields, taking values in the category of overconvergent (Ó,Þ)-modules
* Introduces coefficient objects for this newly developed cohomology
theory, providing a bridge between the local and global pictures
* Proves a p-adic weight monodromy conjecture in equicharacteristic p
In this monograph, the authors develop a new theory of p-adic cohomology for
varieties over Laurent series fields in positive characteristic, based on Berthelot's
theory of rigid cohomology. Many major fundamental properties of these cohomology
groups are proven, such as finite dimensionality and cohomological descent, as
well as interpretations in terms of Monsky-Washnitzer cohomology and Le Stum's
overconvergent site. Applications of this new theory to arithmetic questions, such as lindependence
and the weight monodromy conjecture, are also discussed.
The construction of these cohomology groups, analogous to the Galois representations
associated to varieties over local fields in mixed characteristic, fills a major gap in the study
of arithmetic cohomology theories over function fields. By extending the scope of existing
methods, the results presented here also serve as a first step towards a more general
theory of p-adic cohomology over non-perfect ground fields.
Rigid Cohomology over Laurent Series Fields will provide a useful tool for anyone interested
in the arithmetic of varieties over local fields of positive characteristic. Appendices on
important background material such as rigid cohomology and adic spaces make it as
self-contained as possible, and an ideal starting point for graduate students looking to
explore aspects of the classical theory of rigid cohomology and with an eye towards future
research in the subject.