Estrada, R., Universidad de Costa Rica, San Jose, Costa Rica,
Kanwal, R.P., Pennsylvania State University, USA

A Distributional Approach to Asymptotics
Theory and Applications, 2nd Edition

Birkhauser Advanced Texts
2002. Approx. 464 pages. Hardcover
ISBN 3-7643-4142-4
English

Key features of this significantly expanded second edition:
- addition of several new chapters and sections, including a presentation of time-domain asymptotics needed for the understanding of wavelet theory
- extensive examples and problem sets
- useful bibliography and index.

This book is a modern introduction to asymptotic analysis intended not only for mathematicians, but for physicists, engineers, and graduate students as well. Written by two of the leading experts in the field, the text provides readers with a firm grasp of mathematical theory, and at the same time demonstrates applications in areas such as differential equations, quantum mechanics, noncommutative geometry, and number theory.

"...The authors of this remarkable book are among the very few who have faced up to the challenge of explaining what an asymptotic expansion is, and of systematizing the handling of asymptotic series. The idea of using distributions is an original one, and we recommend that you read the book...[it] should be on your bookshelf if you are at all interested in knowing what an asymptotic series is." ? "The Bulletin of Mathematics Books" (Review of the 1st edition)

"...The book is a valuable one, one that many applied mathematicians may want to buy. The authors are undeniably experts in their field...most of the material has appeared in no other book." ? "SIAM News" (Review of the 1st edition)

Table of contents
Preface
1. Basic Results in Asymptotics
2. Introduction to the Theory of Distributions
3. A Distributional Theory for Asymptotic Expansions
4. The Asymptotic Expansion of Multi-Dimensional Generalized Functions
5. The Asymptotic Expansion of Certain Series Considered by Ramamujan
6. The Cesaro Behavior of Distributions
7. Series of Dirac Delta Functions
References
Index

Fang, K.-T., Hong Kong Baptist University, China; Hickernell, F.J., Hong Kong Baptist University, China; Niederreiter, H., National University of Singapore (Eds.)

Monte Carlo and Quasi-Monte Carlo Methods 2000
Proceedings of a Conference held at Hong Kong Baptist University,
Hong Kong SAR, China, Nov. 27-Dec.1, 2000

2002. XXII, 548 pp. Softcover
3-540-42718-X
Recommended Retail Price: DM 189,90 *

This book represents the refereed proceedings of the Fourth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing which was held at Hong Kong Baptist University in 2000. An important feature are invited surveys of the state-of-the-art in key areas such as multidimensional numerical integration, low-discrepancy point sets, random number generation, and applications of Monte Carlo and quasi-Monte Carlo methods. These proceedings include also carefully selected contributed papers on all aspects of Monte Carlo and quasi-Monte Carlo methods. The reader will be informed about current research in this very active field.

Keywords: Monte Carlo methods, Quasi-Monte Carlo methods, simulation methods, random number generation, numerical integration

Apostol, T.M., Caltech, Pasadena, CA, USA

Early History of Mathematics
VHS/NTSC

NTSC-Version

2002. VHS/NTSC video tape, duration: 30 minutes.
3-540-92648-8

The film explains with easy-accessible examples and in Tom Apostol's characteristically perfect presentation major events in the history of early mathematics. Everybody interested in mathematics will be able to understand the film, and even experts will learn something new from it.

Keywords: history of mathematics, geometry, algebra

Contents: 1. Introduction.- 2. From Euclid to the Seventeenth Century.- 3. From Scratch Marks to Number Systems.- 4. From Numerology to Number Theory.- 5. The Pythagorean Theorem.- 6. A Shocking Discovery.- 7. pi Through the Ages.- 8. From Astronomy to Trigonometry.- 9. From Archimedes to Fermat and Descartes.- 10. The Race for the Calculus

Series: Springer VideoMATH.

Accardi, L., University of Rome, Italy; Lu, Y.G., Universita degli Studi di Bari, Italy; Volovich, I., Steklov Mathematical Institute, Moscow, Russia

Quantum Theory and Its Stochastic Limit

2002. XVI, 502 pp. Hardcover
3-540-41928-4

The subject of this book is a new mathematical technique, the stochastic limit, developed for solving nonlinear problems in quantum theory involving systems with infinitely many degrees of freedom (typically quantum fields or gases in the thermodynamic limit). This technique is condensed into some easily applied rules (called "stochastic golden rules"), which allow us to single out the dominating contributions to the dynamical evolution of systems in regimes involving long times and small effects. In the stochastic limit the original Hamiltonian theory is approximated using a new Hamiltonian theory which is singular. These singular Hamiltonians still define a unitary evolution, and the new equations give much more insight into the relevant physical phenomena than the original Hamiltonian equations. Especially, one can explicitly compute multi-time correlations (e.g. photon statistics) or coherent vectors, which are beyond the reach of typical asymptotic techniques.

Keywords: Stochastic Limit, Quantum Probability, Interacting Fock Space, QED, Stochastic Golden Rule, Quantum Noise, Collection Phenomena .

Contents: I. Notations and Statement of the Problem: Quantum Fields. Those Kinds of Fields We Call Noises. Open Systems. The Stochastic Resonance Principle. Measurements and Filtering Theory. Idea of the Proof and Causal Normal Order. Chronological Product Approach to the Stochastic Limit. Functional Integral Approach to the Stochastic Limit. Low-Density Limit: Basic Idea. Six Basic Principles of the Stochastic Limit.- II. Strongly Nonlinear Regimes: Particles Interacting with a Bose Field. Particles Interacting with a Fermi Field. Field--Field Interactions.- III. Estimates and Proofs: Analytical Theory of Feynman Diagrams. Term by Term Convergence.