Dr. Alan Jeffrey , University at Newcastle Upon Tyne, United Kingdom

Handbook Of Mathematical Formulas and Integrals, 3rd Edition

ISBN 0-12-382256-4 ・ Paperback ・ 890 Pages
Academic Press ・ Forthcoming Title (October 2003)

The updated Handbook is an essential reference for researchers and students in applied mathematics, engineering, and physics. It provides quick access to important formulas, relations, and methods from algebra, trigonometric and exponential functions, combinatorics, probability, matrix theory, calculus and vector calculus, ordinary and partial differential equations, Fourier series, orthogonal polynomials, and Laplace transforms. Many of the entries are based upon the updated sixth edition of Gradshteyn and Ryzhik's Table of Integrals, Series, and Products and other important reference works.

The Second Edition has new chapters covering solutions of elliptic, parabolic and hyperbolic equations and qualitative properties of the heat and Laplace equation.

Features

Key Features:
Comprehensive coverage of frequently used integrals, functions and fundamental mathematical results
Contents selected and organized to suit the needs of students, scientists, and engineers
Contains tables of Laplace and Fourier transform pairs
New section on numerical approximation
New section on the z-transform
Easy reference system

Contents

Preface. Index of Special Functions and Notations. Quick Reference List of Frequently Used Data. Numerical, Algebraic, and Analytical Results for Series and Calculus. Functions and Identities. Derivatives of Elementary Functions. Indefinite Integrals of Algebraic Functions. Indefinite Integrals of Exponential Functions. Indefinite Integrals of Logarithmic Functions. Indefinite Integrals of Hyperbolic Functions. Indefinite Integrals Involving Inverse Hyperbolic Functions. Indefinite Integrals of Trigonometric Functions. Indefinite Integrals of Inverse Trigonometric Functions. The Gamma, Beta, Pi, and Psi Functions. Elliptic Integrals and Functions. Probability Integrals and the Error Function. Fresnel Integrals, Sine and Cosine Integrals. Definite Integrals. Different Forms of Fourier Series. Bessel Functions. Orthogonal Polynomials. Laplace Transformation. Fourier Transforms. Numerical Integration. Solutions of Standard Ordinary Differential Equations. Vector Analysis. Systems of Orthogonal Coordinates. Partial Differential Equations and Special Functions. The z-Transform. Numerical Approximation. Short Classified Reference List. Solutions of Elliptic, Parabolic and Hyperbolic Equations. Qualitative Properties of the Heat and Laplace Equation. Index.

Robert Zipf , Scarsdale, New York, U.S.A.

Fixed Income Mathematics

ISBN 0-12-781721-2 ・ Hardback ・ 366 Pages
Academic Press ・ June 2003

An introduction to common fixed income instruments and mathematics, this book offers explanations, exercises, and examples without demanding sophisticated mathematics. Not only does the author use his business and teaching experience to highlight the fundamentals of investment and management decision-making, but he also offers questions and exercises that suggest the applicability of fixed income mathematics. Written for the reader with a general mathematics background, this self-teaching book is suffused with examples that also make it a handy reference guide. It should serve as a gateway to financial mathematics and to increased competence in business analysis.

Features

Accessible to readers with basic skills who are looking for applications to the finance environment
No calculus will be included and the author will review probability, statistics, and the basics of the Black-Scholes model
Uses international comparisons to illustrate how interest is compounded

Contents

Introduction
Interest
Compound Interest
Present Value]
Annuities Certain
Bond Price Calculation
Future Value of Annuity
Accrued Interest
Discount Securities
Calculations for Other Securities
Quotations
Types of Yields
Sources of Return
Volatility and Its Measures
Duration
Convexity
Calculus Derivation
Probability Applications
Term Structure of Interest Rates
Uncertain and Variable Cash Flows
Mortgage Backed Securities
Futures
Options
Bibliography

Edited by Titu Andreescu, Zuming Feng, George Lee

Mathematical Olympiads 2000-2001
Problems and Solutions from Around the World

Publication is planned for July 2003 | Paperback | ISBN: 0-88385-810-X

This book is a continuation of Mathematical Olympiads 1999?2000: Problems and Solutions From Around the World, published by the Mathematical Association of America. It contains solutions to the problems from 27 national and regional contests featured in the earlier book, together with selected problems (without solutions) from national and regional contests given during 2001. In many cases multiple solutions are provided in order to encourage students to compare different problem-solving strategies. The editors have tried to present a wide variety of problems, especially from those countries that have often done well at the IMO. The problems themselves should provide much enjoyment for all those fascinated by solving challenging mathematics questions.

Contents
1. 2000 national contests: problems and solutions; 2. 2000 regional contests: problems and solutions; 3. 2001 national contests: problems; 4. 2001 regional contests: problems.

Jurgen Fuchs, Christoph Schweigert

Symmetries, Lie Algebras and Representations
A Graduate Course for Physicists

Publication is planned for July 2003 | Paperback | 460 pages 36 line diagrams 18 tables 188 exercises | ISBN: 0-521-54119-0

This is an introduction to Lie algebras and their applications in physics. The first three chapters show how Lie algebras arise naturally from symmetries of physical systems and illustrate through examples much of their general structure. Chapters 4 to 13 give a detailed introduction to Lie algebras and their representations, covering the Cartan-Weyl basis, simple and affine Lie algebras, real forms and Lie groups, the Weyl group, automorphisms, loop algebras and highest weight representations. Chapters 14 to 22 cover specific further topics, such as Verma modules, Casimirs, tensor products and Clebsch-Gordan coefficients, invariant tensors, subalgebras and branching rules, Young tableaux, spinors, Clifford algebras and supersymmetry, representations on function spaces, and Hopf algebras and representation rings. A detailed reference list is provided, and many exercises and examples throughout the book illustrate the use of Lie algebras in real physical problems. The text is written at a level accessible to graduate students, but will also provide a comprehensive reference for researchers.

Reviews
‘One finds a striking wealth of material in this book … The reviewer wholeheartedly recommends this text to graduate students as well as to researchers in theoretical physics and related areas.’ Acta. Sci. Math

‘The presentation of material is next to perfect, … this book may be considered as an excellent textbook … I agree with the authors that ‘many readers will even use it as a reference tool for their whole professional life’.’ Vladimir D. Ivashchuk, General Relativity and Gravitation

Contents
Preface; 1. Symmetries and conservation laws; 2. Basic examples; 3. The Lie algebra su(3) and hadron symmetries; 4. Formalization: algebras and Lie algebras; 5. Representations; 6. The Cartan-Weyl basis; 7. Simple and affine Lie algebras; 8. Real Lie algebras and real forms; 9. Lie groups; 10. Symmetries of the root system. The Weyl group; 11. Automorphisms of Lie algebras; 12. Loop algebras and central extensions; 13. Highest weight representations; 14. Verma modules, Casimirs, and the character formula; 15. Tensor products of representations; 16. Clebsch-Gordan coefficients and tensor operators; 17. Invariant tensors; 18. Subalgebras and branching rules; 19. Young tableaux and the symmetric group; 20. Spinors, Clifford algebras, and supersymmetry; 21. Representations on function spaces; 22. Hopf algebras and representation rings; Epilogue; References; Index.

Arieh Iserles

Acta Numerica 2003
Volume 12

Publication is planned for July 2003 | Hardback | 520 pages | ISBN: 0-521-82523-7

Acta Numerica surveys annually the most important developments in numerical mathematics and scientific computing. The subjects and authors of the substantive survey articles are chosen by a distinguished international editorial board so as to report the most important and timely developments in a manner accessible to the wider community of professionals with an interest in scientific computing. Acta Numerica volumes have proved to be a valuable tool not only for researchers and professionals wishing to develop their understanding of numerical techniques and algorithms and follow new developments, but also as an advanced teaching aid at colleges and universities. Many of the original articles have been used as the prime resource for graduate courses.

Reviews
‘Acta Numerica is a fine achievement and I think we can expect to see it for many years to come. It sets itself laudable and important goals and has, to a large extent, achieved them. I believe that the volumes are of enormous benefit to our subject … The editorial board should be applauded for having the vision and drive necessary to create and sustain such a high quality publication … No mathematics library is complete without this annual publication, and I urge everyone working in numerical mathematics and scientific computing to read it.’ Andrew Stuart, SIAM Review

‘Acta Numerica is a fine achievement and I think we can expect to see it for many years to come. No mathematics library is complete without this annual publication, and I urge everyone working in numerical mathematics and scientific computing to read it.’ Andrew Stuart, SIAM Review

Contributors
Ivo Babuvska, John Osborn, Bernardo Cockburn, Bjorn Engquist, Olof Runborg, Roland Freund, Jonathan Goodman, Andreas Griewank, Ernst Hairer, Christian Lubich, Gerhard Wanner, Eitan Tadmor

Contents
1. Meshless methods Ivo Babuvska and John Osborn; 2. Viscosity methods Bernardo Cockburn; 3. Computational optics Bjorn Engquist and Olof Runborg; 4. Model reduction methods Roland Freund; 5. Computational financial mathematics Jonathan Goodman; 6. Automatic differentiation Andreas Griewank; 7. Numerical geometric integration Ernst Hairer, Christian Lubich and Gerhard Wanner; 8. Numerical stability theory for PDEs Eitan Tadmor.