Series: Universitext
Translation of the 3rd edition of "Numerische Behandlung partieller Differentialgleichungen" published by Teubner, 2005.
2007, Softcover
ISBN: 978-3-540-71582-5
Due: September 2007
About this textbook
This book deals with discretization techniques for elliptic, parabolic and hyperbolic partial differential equations. It provides an introduction to the main principles of discretization and presents the reader the ideas and analysis of advanced numerical methods in this area.
The main motivation is to give mathematically interested students, scientists and engineers a textbook which contains all basic discretization techniques for the fundamental types of partial differential equations and in which the reader can find analytical tools, properties of the discretization techniques and hints to algorithmic aspects. It also covers current research developments. For instance, it provides introductions to a posteriori error estimation, discontinuous Galerkin methods and optimal control with partial differential equations, very recent subjects rarely found in other books. The book is mainly dedicated to finite element methods, but also discusses difference methods and finite volume techniques.
Further, basic tools are provided for solving the generated
discrete problems, while chapters on singularly perturbed problems, variational inequalities and optimal control illuminate special
topics reflecting the research interests of the authors.
Series: Springer Monographs in Mathematics
2007, Approx. 145 p., Hardcover
ISBN: 978-0-387-72473-7
Due: October 2007
About this textbook
Author writes in a clear and engaging style
Contains never before published elementary proofs
Author provides new results and detailed exposition
Self-contained, and suitable for use in a classroom setting or for self-study
A highly creative contribution to the theory of modular forms and dirichlet series
The main topics of the book are the critical values of Dirichlet L-functions and Hecke L-functions of an imaginary quadratic field, and various problems on elliptic modular forms. As to the values of Dirichlet L-functions, all previous papers and books reiterate a single old result with a single old method. After a review of elementary Fourier analysis, the author presents completely new results with new methods, though old results will also be proved. No advanced knowledge of number theory is required up to this point. As applications, new formulas for the second factor of the class number of a cyclotomic field will be given.
The second half of the book assumes familiarity with basic knowledge of modular forms. However, all definitions and facts are clearly stated, and precise references are given. The notion of nearly holomorphic modular forms is introduced and applied to the determination of the critical values of Hecke L-functions of an imaginary quadratic field. Other notable features of the book are: (1) some new results on classical Eisenstein series; (2) the discussion of isomorphism classes of elliptic curves with complex multiplication in connection with their zeta function and periods; (3) a new class of holomorphic differential operators that send modular forms to those of a different weight.
The book will be of interest to graduate students and researchers who are interested in special values of L-functions, class number formulae, arithmetic properties of modular forms (especially their values), and the arithmetic properties of Dirichlet series. It treats in detail, from an elementary viewpoint, the simplest cases of a fundamental area of ongoing research, the only prerequisite being a basic course in algebraic number theory.
Table of contents
Preface.- Introduction.- Preliminaries on Modular Forms and Dirichlet Series.- Critical Values of Dirichlet L-functions.- The Case of Imaginary Quadratic Fields and Nearly Holomorphic Modular Forms.- Eisenstein Series.- Critical Values of Dirichlet Series Associated with Imaginary Quadratic Fields.- Supplementary Results.- Appendix.- References.- Index.-
Series: Universitext
2007, Approx. 300 p., 30 illus., Softcover
ISBN: 978-0-387-72489-8
Due: November 2007
About this book
Traditional approach, but cleaner and more streamlined than most others
Accessible introduction to class field theory
Lots of challenging exercises
Class field theory, the study of abelian extensions of algebraic number fields, is one of the largest branches of algebraic number theory. It brings together the quadratic and higher reciprocity laws of Gauss, Legendre, and others, and vastly generalizes them. Some of its consequences (e.g., the Chebotarev density theorem) apply even to nonabelian extensions.
This book is an accessible introduction to class field theory. It takes a traditional approach in that it attempts to present the material using the original techniques of proof (global to local), but in a fashion which is cleaner and more streamlined than most other books on this topic. It could be used for a graduate course on algebraic number theory, as well as for students who are interested in self-study. The book has been class-tested, and the author has included exercises throughout the text.
Table of contents
Preface.- A Brief Review.- Dirichlet's Theorem on Primes in Arithmetic Progressions.- Ray Class Groups.- The Idelic Theory.- Artin Reciprocity.- The Existence Theorem, Consequences and Applications.- Local Class Field Theory.- Bibliography.- Index
Version: p+eRef (book + online access)
2008
ISBN: 978-0-387-36061-4
Due: July 2008
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About this book
"No similar reference work on Algorithms is currently available"
"Comprehensive A-Z coverage of this complex subject area makes this volume easily accessible to professionals and researchers in all fields who are interested in a particular aspect of Algorithms"
"Targeted literature references provide additional value for researchers looking to study a topic in more detail"
"Entries are cross-linked with journal articles"
The Encyclopedia of Algorithms will provide a comprehensive set of solutions to important algorithmic problems for students and researchers interested in quickly locating useful information. The first edition of the reference will focus on high-impact solutions from the most recent decade; later editions will widen the scope of the work.
Nearly 500 entries will be organized alphabetically by problem, with subentries allowing for distinct solutions and special cases to be listed by the year. An entry will include:
a description of the basic algorithmic problem
the input and output specifications
the key results
examples of applications
citations to the key literature
Open problems, links to downloadable code, experimental results, data sets, and illustrations may be provided. All entries will be written by experts with links to Internet sites that outline their research work will be provided. The entries will be peer-reviewed.
This defining reference will be published in print and on line. The print publication will include an index of subjects and authors as well as a chronology for locating recent solutions. The online edition will supplement this index with hyperlinks as well as include hyperlinks in the text of the entries to related entries, xRefer citations, and other useful URLs mentioned above.
Written for:
Entries in this reference will appeal significantly to computer scientists working in a wide range of areas such as Bioinformatics, Cryptography, Data Compression, Medical Informatics, Network and Communication Protocols, Artificial Intelligence, and Pattern Recognition.
The title will also be useful for scholars, students, and professionals who work in fields such as mathematics, statistics, computational biology, economics, finance and stochastics, medical informatics, data mining, industrial engineering, and decision science.