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.
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
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.
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.
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.