Series: Cambridge Mathematical Library
Paperback (ISBN-13: 9780521134200)
Page extent: 304 pages
Size: 228 x 152 mm
Now back in print, this highly regarded book has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces, which include moduli spaces in positive characteristic, moduli spaces of principal bundles and of complexes, Hilbert schemes of points on surfaces, derived categories of coherent sheaves, and moduli spaces of sheaves on Calabi*Yau threefolds. The authors review changes in the field since the publication of the original edition in 1997 and point the reader towards further literature. References have been brought up to date and errors removed. Developed from the authors' lectures, this book is ideal as a text for graduate students as well as a valuable resource for any mathematician with a background in algebraic geometry who wants to learn more about Grothendieck's approach.
* A widely-cited classic finally brought back into print * Material originally class-tested by the authors * Now contains fully-updated references and reviews of the latest results in the field
Preface to the second edition; Preface to the first edition; Introduction; Part I. General Theory: 1. Preliminaries; 2. Families of sheaves; 3. The Grauert*Mullich Theorem; 4. Moduli spaces; Part II. Sheaves on Surfaces: 5. Construction methods; 6. Moduli spaces on K3 surfaces; 7. Restriction of sheaves to curves; 8. Line bundles on the moduli space; 9. Irreducibility and smoothness; 10. Symplectic structures; 11. Birational properties; Glossary of notations; References; Index.
Hardback (ISBN-13: 9780521192255)
Paperback (ISBN-13: 9780521140638)
422 colour illus. 100 tables
Page extent: 966 pages
Size: 279 x 215 mm
Modern developments in theoretical and applied science depend on knowledge of the properties of mathematical functions, from elementary trigonometric functions to the multitude of special functions. These functions appear whenever natural phenomena are studied, engineering problems are formulated, and numerical simulations are performed. They also crop up in statistics, financial models, and economic analysis. Using them effectively requires practitioners to have ready access to a reliable collection of their properties. This handbook results from a 10-year project conducted by the National Institute of Standards and Technology with an international group of expert authors and validators. Printed in full colour, it is destined to replace its predecessor, the classic but long-outdated Handbook of Mathematical Functions, edited by Abramowitz and Stegun. Includes a DVD with a searchable PDF of each chapter.
* Compendium of properties of mathematical special functions * Developed by expert authors, editors, and validators * Carefully edited for uniform treatment of technical content
Contents
1. Algebraic and analytic methods Ranjan Roy, Frank W. J. Olver, Richard A. Askey and Roderick S. C. Wong; 2. Asymptotic approximations Frank W. J. Olver and Roderick S. C. Wong; 3. Numerical methods Nico M. Temme; 4. Elementary functions Ranjan Roy and Frank W. J. Olver; 5. Gamma function Richard A. Askey and Ranjan Roy; 6. Exponential, logarithmic, sine and cosine integrals Nico M. Temme; 7. Error functions, Dawson's and Fresnel integrals Nico M. Temme; 8. Incomplete gamma and related functions Richard B. Paris; 9. Airy and related functions Frank W. J. Olver; 10. Bessel functions Frank W. J. Olver and Leonard C. Maximon; 11. Struve and related functions Richard B. Paris; 12. Parabolic cylinder functions Nico M. Temme; 13. Confluent hypergeometric functions Adri B. Olde Daalhuis; 14. Legendre and related functions T. Mark Dunster; 15. Hypergeometric function Adri B. Olde Daalhuis; 16. Generalized hypergeometric functions and Meijer G-function Richard A. Askey and Adri B. Olde Daalhuis; 17. q-Hypergeometric and related functions George E. Andrews; 18. Orthogonal polynomials Tom H. Koornwinder, Roderick S. C. Wong, Roelof Koekoek and Rene F. Swarttouw; 19. Elliptic integrals Bille C. Carlson; 20. Theta functions William P. Reinhardt and Peter L. Walker; 21. Multidimensional theta functions Bernard Deconinck; 22. Jacobian elliptic functions William P. Reinhardt and Peter L. Walker; 23. Weierstrass elliptic and modular functions William P. Reinhardt and Peter L. Walker; 24. Bernoulli and Euler polynomials Karl Dilcher; 25. Zeta and related functions Tom M. Apostol; 26. Combinatorial analysis David M. Bressoud; 27. Functions of number theory Tom M. Apostol; 28. Mathieu functions and Hill's equation Gerhard Wolf; 29. Lame functions Hans Volkmer; 30. Spheroidal wave functions Hans Volkmer; 31. Heun functions Brian D. Sleeman and Vadim Kuznetsov; 32. Painleve transcendents Peter A. Clarkson; 33. Coulomb functions Ian J. Thompson; 34. 3j,6j,9j symbols Leonard C. Maximon; 35. Functions of matrix argument Donald St. P. Richards; 36. Integrals with coalescing saddles Michael V. Berry and Chris Howls.
Paperback (ISBN-13: 9780521532761)
Page extent: 147 pages
Size: 246 x 189 mm
Thoroughly revised for its second edition, this advanced textbook provides an introduction to the basic methods of computational physics, and an overview of progress in several areas of scientific computing by relying on free software available from CERN. The book begins by dealing with basic computational tools and routines, covering approximating functions, differential equations, spectral analysis, and matrix operations. Important concepts are illustrated by relevant examples at each stage. The author also discusses more advanced topics, such as molecular dynamics, modeling continuous systems, Monte Carlo methods, genetic algorithm and programming, and numerical renormalization. It includes many more exercises. This can be used as a textbook for either undergraduate or first-year graduate courses on computational physics or scientific computation. It will also be a useful reference for anyone involved in computational research.
* Detailed descriptions of the traditional computational methods * Concise introductions to the newest developments in scientific computing * Vivid and practical examples from contemporary physics and related fields, useful to students and researchers. Includes extensive exercises * Programs written in Java
Preface to first edition; Preface; Acknowledgements; 1. Introduction; 2. Approximation of a function; 3. Numerical calculus; 4. Ordinary differential equations; 5. Numerical methods for matrices; 6. Spectral analysis; 7. Partial differential equations; 8. Molecular dynamics simulations; 9. Modeling continuous systems; 10. Monte Carlo simulations; 11. Genetic algorithm and programming; 12. Numerical renormalization; References; Index.
Series: London Mathematical Society Lecture Note Series (No. 371)
Paperback (ISBN-13: 9780521438001)
26 b/w illus. 90 exercises
Page extent: 368 pages
Size: 228 x 152 mm
This is a one-stop introduction to the methods of ergodic theory applied to holomorphic iteration. The authors begin with introductory chapters presenting the necessary tools from ergodic theory thermodynamical formalism, and then focus on recent developments in the field of 1-dimensional holomorphic iterations and underlying fractal sets, from the point of view of geometric measure theory and rigidity. Detailed proofs are included. Developed from university courses taught by the authors, this book is ideal for graduate students. Researchers will also find it a valuable source of reference to a large and rapidly expanding field. It eases the reader into the subject and provides a vital springboard for those beginning their own research. Many helpful exercises are also included to aid understanding of the material presented and the authors provide links to further reading and related areas of research.
* A self-contained introduction suitable for graduate students, including exercises * Brings together a wide variety of methods and results previously scattered throughout the literature * Provides pointers to further reading and links to related areas of research
Introduction; Basic examples and definitions; 1. Measure preserving endomorphisms; 2. Compact metric spaces; 3. Distance expanding maps; 4. Thermodynamical formalism; 5. Expanding repellers in manifolds and in the Riemann sphere, preliminaries; 6. Cantor repellers in the line, Sullivan's scaling function, application in Feigenbaum universality; 7. Fractal dimensions; 8. Conformal expanding repellers; 9. Sullivan's classification of conformal expanding repellers; 10. Holomorphic maps with invariant probability measures of positive Lyapunov exponent; 11. Conformal measures; References; Index.