2004, XVI, 392 p., 106 illus. (92 line art, 14 halftones), 2
tables, plus CD-ROM with MAPLE., Softcover
ISBN: 3-7643-3223-9
About this textbook
Over two hundred novel and innovative computer algebra worksheets
or "recipes" will enable readers in engineering,
physics, and mathematics to easily and rapidly solve and explore
most problems they encounter in their mathematical physics
studies. While the aim of this text is to illustrate
applications, a brief synopsis of the fundamentals for each topic
is presented, the topics being organized to correlate with those
found in traditional mathematical physics texts. The recipes are
presented in the form of stories and anecdotes, a pedagogical
approach that makes a mathematically challenging subject easier
and more fun to learn. Key features: * Uses the MAPLE computer
algebra system to allow the reader to easily and quickly change
the mathematical models and the parameters and then generate new
answers * No prior knowledge of MAPLE is assumed; the relevant
MAPLE commands are introduced on a need-to-know basis * All
recipes are contained on a CD-ROM provided with the text * All
MAPLE commands are indexed for easy reference * A classroom-tested
story/anecdote format is used, accompanied with amusing or
thought-provoking quotations * Study problems, which are
presented as Supplementary Recipes, are fully solved and
annotated and also provided on the CD-ROM This is a self-contained
and standalone text, similar in style and format to Computer
Algebra Recipes: A Gourmet's Guide to Mathematical Models of
Science (ISBN 0-387-95148-2), Springer New York 2001 and Computer
Algebra Recipes for Classical Mechanics (ISBN 0-8176-4291-9),
Birkhauser 2003. Computer Algebra Recipes for Mathematical
Physics may be used in the classroom, for self-study, as a
reference, or as a text for an online course.
Table of contents
* Preface * Introduction * Part I: The Appetizers * Linear ODEs
of Physics * Applications of Series * Vectors and Matrices * Part
II: The Entrees * Linear PDEs of Physics * Complex Variables *
Integral Transform * Calculus of Variations * Part III: The
Desserts * NLODEs & PDEs of Physics * Numerical Methods *
Bibliography * Index
Series : Progress in Mathematics , Vol. 233
2005, Approx. 632 p., Hardcover
ISBN: 3-7643-7182-X
A Birkhauser book
About this book
The Mumford-Shah functional was introduced in the 1980s as a tool
for automatic image segmentation, but it also gave rise to
interesting questions of analysis. This book studies extensively
the singular sets that show up in the minimizers of the
functional. Most of the exciting regularity results and methods
are addressed, in dimensions two and higher, with tools of
classical analysis and geometric measure theory.
Table of contents
Foreword.- Presentation of the Mumford-Shah functional.-
Functions in the Sobolev spaces.- Regularity properties for
quasiminimizers.- Limits of almost-minimizers.- Pieces of C^1
curves for almost-minimizers.- Global Mumford-Shah minimizers in
the plane.- Applications to almost-minimizers (n = 2).- Quasi-
and almost-minimizers in higher dimensions.- Boundary regularity.
2005
1. Ed. 350 S. 20 schw.-w. Zeichn. Gb
3-7643-4363-X
PM - Progress in Mathematics
This work examines in detail the foundations of D-module theory
and its intersection with cohomology groups and representation
theory. This systematic and carefully written exposition begins
with preliminary concepts before focusing on some basic but
important theories that have emerged in the last few decades.
Significant topics that have emerged as studies in their own
right include a treatment of the theory of holonomic D-modules,
perverse sheaves, the Riemann-Hilbert correspondence, Hodge
modules, and Kazhdan-Lusztig polynomials. To further aid the
reader, appendices are provided as reviews for the theory of
derived categories and algebraic varieties.D-modules, Perverse
Sheaves, and Representation Theory is a unique and essential
textbook at the graduate level for classroom use or self-study.
Graduate students and researchers in algebra and representation
theory will benefit greatly from this work. TOC:Introduction -
Part I. D-modules - Preliminary notions - Coherent D-modules -
Holonomic D-modules and its solutions - Theory of meromorphic
connections - Regular holonomic D-modules - Perverse sheaves and
intersection cohomologies - Hodge module - Part II. Algebraic
Groups - Algebraic groups and Lie algebras - Conjugacy classes of
semisimple Lie algebras - Representations of Lie algebras and D-modules
- Character formula of highest weight modules - Hecke algebras
and Hodge modules - A. Algebraic Varieties - B. Derived
categories and derived functors - References - Index
302 pages 133 line diagrams 1 half-tone 50 exercises 138
figures
Paperback available from March 2005
ISBN:0-521-60793-0
This is the second edition of a highly successful and well-respected
textbook on the numerical techniques used to solve partial
differential equations arising from mathematical models in
science, engineering and other fields. The authors maintain an
emphasis on finite difference methods for simple but
representative examples of parabolic, hyperbolic and elliptic
equations from the first edition. However this is augmented by
new sections on finite volume methods, modified equation
analysis, symplectic integration schemes, convection-diffusion
problems, multigrid, and conjugate gradient methods; and several
sections, including that on the energy method of analysis, have
been extensively rewritten to reflect modern developments.
Already an excellent choice for students and teachers in
mathematics, engineering and computer science departments, the
revised text brings the reader up-to-date with the latest
theoretical and industrial developments.
Contents
1. Introduction; 2. Parabolic equations in one space variable; 3.
2-D and 3-D parabolic equations; 4. Hyperbolic equations in one
space dimension; 5. Consistency, convergence and stability; 6.
Linear second order elliptic equations in two dimensions; 7.
Iterative solution of linear algebraic equations; Bibliography;
Index.
512 pages 450 exercises 150 worked examples
Hardback - available from April 2005
ISBN:0-521-85154-8
Number theory and algebra play an increasingly significant role
in computing and communications, as evidenced by the striking
applications of these subjects to such fields as cryptography and
coding theory. This introductory book emphasises algorithms and
applications, such as cryptography and error correcting codes,
and is accessible to a broad audience. The mathematical
prerequisites are minimal: nothing beyond material in a typical
undergraduate course in calculus is presumed, other than some
experience in doing proofs - everything else is developed from
scratch. Thus the book can serve several purposes. It can be used
as a reference and for self-study by readers who want to learn
the mathematical foundations of modern cryptography. It is also
ideal as a textbook for introductory courses in number theory and
algebra, especially those geared towards computer science
students.
Contents
0. Preliminaries; 1. Basic properties of the integers; 2.
Congruences; 3. Computing with large integers; 4. Euclid’s
algorithm; 5. The distribution of primes; 6. Finite and discrete
probability distributions; 7. Probabilistic algorithms; 8.
Abelian groups; 9. Rings; 10. Probabilistic primality testing; 11.
Finding generators and discrete logarithms in Zp*; 12. Quadratic
residues and quadratic reciprocity; 13. Computational problems
related to quadratic residues; 14. Modules and vector spaces; 15.
Matrices; 16. Subexponential-time discrete logarithms and
factoring; 17. More rings; 18. Polynomial arithmetic and
applications; 19. Linearly generated sequences and applications;
20. Finite fields; 21. Algorithms for finite fields; 22.
Deterministic primality testing; Appendix: some useful facts;
Bibliography; Index of notation; Index.