ISBN: 0-471-17976-0
Hardcover
Projected Pub Date: Jan 2000
A novel, practical introduction to functional analysis
In the twenty years since the first edition of Applied Functional
Analysis was published, there has been an explosion in the number
of books on functional analysis.
Yet none of these offers the unique perspective of this new
edition. Jean-Pierre Aubin updates his popular
reference on functional analysis with new insights and recent
discoveries紡dding three new chapters on set-valued analysis and
convex analysis, viability kernels and capture basins, and
first-order partial differential equations.
He presents, for the first time at an introductory level, the
extension of differential calculus in the framework of both the
theory of distributions and set-valued analysis, and discusses
their application for studying boundary-value problems for
elliptic and parabolic partial differential equations and for
systems of first-order partial differential equations.
To keep the presentation concise and accessible, Jean-Pierre
Aubin introduces functional analysis through the simple
Hilbertian structure. He seamlessly blends pure mathematics with
applied areas that illustrate the theory, incorporating a broad
range of examples from numerical analysis, systems theory,
calculus of variations, control and optimization theory, convex
and nonsmooth analysis, and more.
Finally, a summary of the essential theorems as well as exercises
reinforcing key concepts are provided. Applied Functional
Analysis, Second Edition is an excellent and timely resource for
both pure and applied mathematicians.
Series Title:
"Pure and Applied Mathematics: A Wiley-Interscience Series
of Texts, Monographs and Tracts
Contents
The Projection Theorem.
Theorems on Extension and Separation.
Dual Spaces and Transposed Operators.
The Banach Theorem and the Banach-Steinhaus Theorem.
Construction of Hilbert Spaces.
L2 Spaces and Convolution Operators.
Sobolev Spaces of Functions of One Variable.
Some Approximation Procedures in Spaces of Functions.
Sobolev Spaces of Functions of Several Variables and the Fourier
Transform.
Elementary Convex Analysis.
Elementary Spectral Theory.
Hilbert-Schmidt Operators and Tensor Products.
Boundary Value Problems.
Differential-Operational Equations and Semigroups of Operators.
Introduction to Nonlinear Analysis.
Selection of Results.
Exercises.
Index.
ISBN: 0-471-32233-4
Hardcover
Projected Pub Date: Feb 2000
Following up the acclaimed Five Golden Rules, another quintet of
gleaming math discoveries
With Five More Golden Rules, readers are treated to another
fascinating set of theoretical gems from acclaimed popular
science author John Casti. Injecting all-new ingredients into his
trademark recipe of real-world examples, historical anecdotes,
and straightforward explanations, Casti once again brings math to
thrilling life. All who enjoyed the unique pleasures of the
original will love this follow-up survey highlighting the cr?me
de la cr?me of math in the last century.
Explores how knot theory informs the classic tale of Alexander
the Great and the Gordian Knot Considers how the Shannon Coding
Theory applies to decoding the human genome
Subject:
Mathematics / General & Introductory Mathematics / Popular
Interest
Contents:
The Alexander Polynomial.
The Hopf Bifurcation Theorem.
The Kalman Filter.
The Hahn-Banach Theorem.
The Shannon Coding Theorem.
Bibliography.
Index.
ISBN: 0-471-98723-9
Hardcover
Projected Pub Date: Jun 2000
The new generation of credit risk management techniques.
Traditionally, investment and retail banks managed credit risk by
setting credit limits. But as financial instruments become more
and morecomplex, traditional credit risk management techniques
fall short of the task. Investment and retail banks everywhere
are scrambling forup-to-the-minute information on the new
generation of credit risk management techniques. Advanced Credit
Risk Analysis explores thelatest thinking and practices worldwide
in the areas of credit risk pricing and management.
Arms finance professionals with detailed technical information on
cutting-edge credit risk mathematical modeling techniques.
Didier Cossin (Lausanne, Switzerland) is with the International
Institute for Management Development in Lausanne. He has worked
for numerous financial institutions, including Goldman Sachs,
Associates en France, and Roussel Uclaf, and has held teaching
positions at Harvard, MIT, and the Sorbonne. Hughes Pirotte
(Lausanne, Switzerland) is his teaching and research assistant.
Subject:
Finance & Investments / Institutional /
ISBN: 0-471-37910-7
Paperback
Projected Pub Date: Feb 2000
An insightful and timely guide to the new technologies that are
shaping our lives.
Which new technologies will have the biggest impact on our lives
in the years ahead? Find out in Who Gives a Gigabyte?, as Senior
Editor of Scientific American takes readers on a fascinating
journey through the brave new world of gene therapy, virtual
corporations, recyclable cars, and a fast-paced look at the most
important recent developments in genetics, medicine, robotics,
environmental cleanup, energy, and more. Based on interviews with
today's leading technology developers as well as extensive
research of the scientific literature, the book
explains, in plain English, what the new technologies are, how
they work, how they will most likely evolve in the near future,
and how they will affect our lives in the next century.
Forty simple illustrations show readers how things work?from
satellites to DNA.
Gary Stix (New York, NY) is a Senior Editor for Scientific
American. Miriam Lacob is a freelance journalist who has written
for Scientific American, Data Communications, Computer Decision,
and other publications.
Subject: Life Sciences / General & Introductory Life Sciences
series: Pure and Applied Mathematics volume:
229
02/01/2000 In Press
Hardcover, 310 Pages, Illustrated
ISBN: 0-8247-0320-0
description:
Presents counterexamples to apparently true mathematical
statements, yielding numerous counterintuitive results in
constructions of strange functions.
This remarkable reference explores the fundamental operations of
real analysis that are closely connected with pathological
functions?demonstratingmuch-needed revisions, generalizations, or
extensions of differentiation, integration, convergence, and
other basic concepts of analysis.
Thoroughly discusses applications of the Baire category method,
the Zermelo-Fraenkel set theory, Cantor and Peano type functions,
and the continuumhypothesis.
Presenting numerous new?and surprising?results, Strange Functions
in Real Analysis analyzes examples and constructions of strange
functions, especially those acting from the real line into itself
explores the Axiom of Dependent Choice and demonstrates its
sufficiency for most domains of classical mathematics highlights
the general theory of stochastic processes investigates functions
associated with a Hamel basis of the real line evaluates the
relationship between the Sierpinski partition of the plane and
Fubini type theorems introduces applications of sup-measurable
and weakly sup-measurable functions in the theory of ordinary
differential equations addresses functions with bad descriptive
structure, such as those that lack the Baire property or are
nonmeasurable in the Lebesgue sense compares and contrasts
everywhere differentiable nowhere monotone functions and Jarnik痴
nowhere approximately differentiable functions and more!
Containing over 1400 equations, Strange Functions in Real
Analysis is an exceptional resource for mathematicians working in
general set theory,
descriptive set theory, optimization, ordinary differential
equations, and functional equations; and for graduate students
specializing in real analysis, classical
measure theory, and point set theory.
contents:
Introduction: Preliminary Facts
Cantor and Peano Type Functions
Singular Monotone Functions
Everywhere Differentiable Nowhere Monotone Functions
Nowhere Approximately Differentiable Functions
Blumberg痴 Theorem and Sierpinski-Zygmund Function
Lebesgue Nonmeasurable Functions and Functions Without the Baire
Property
Hamel Basis and Cauchy Functional Equation
Luzin Sets, Sierpinski Sets and Their Applications
Egorov Type Theorems
Sierpinski痴 Partition of the Euclidean Plane
Sup-Measurable and Weakly Sup-Measurable Functions
Ordinary Differential Equations with Bad Right-Hand Sides
Nondifferentiable Functions from the Point of View of Category
and Measure
Bibliography
Published July 1999 by Prentice Hall Business Publishing
Copyright 2000, 698 pp.
Cloth
ISBN 0-13-022444-8
For undergraduate and graduate courses in Options and Futures,
Financial Engineering and Risk Management, typically found in
business, finance, economics and mathematics departments. Also
suitable for practitioners who want to acquire a working
knowledge of how derivatives can be analyzed.
This best seller represents how academia and real-world practice
have come together with a common respect and focus of theory and
practice. It provides a unifying approach to the valuation of all
derivatives?not just futures and options. It assumes that the
reader has taken an introductory course in finance and an
introductory course in probability and statistics. No prior
knowledge of options, futures contracts, swaps, and so on is
assumed.
Contents:
1. Introduction.
2. Futures Markets and the Use of Futures for Hedging.
3. Forward and Futures Prices.
4. Interest Rates and Duration.
5. Swaps.
6. Options Markets.
7. Properties of Stock Option Prices.
8. Trading Strategies Involving Options.
9. Introduction to Binomial Trees.
10. Model of the Behavior of Stock Prices.
11. The Black-Scholes Model.
12. Options on Stock Indices, Currencies, and Futures.
13. The Greek Letters.
14. Value at Risk.
15. Estimating Volatilities and Correlations.
16. Numerical Procedures.
17. Volatility Smiles and Alternatives to Black-Scholes.
18. Exotic Options.
19. Extensions of the Theoretical Framework for Pricing
Derivatives: Martingales and Measures.
20. Interest Rate Derivatives: The Standard Market Models.
21. Interest Rate Derivatives: Models of the Short Rate.
22. Interest Rate Derivatives: More Advanced Models.
23. Credit Risk.