Series: Modern Birkhauser Classics
Originally published as volume 127 in the series: Progress in
Mathematics
1st ed. 1994. 2nd printing, 2007, VIII, 414 p., Softcover
ISBN: 978-0-8176-4584-7
About this book
The first two chapters of this book are devoted to convexity in
the classical sense, for functions of one and several real
variables respectively. This gives a background for the study in
the following chapters of related notions which occur in the
theory of linear partial differential equations and complex
analysis such as (pluri-)subharmonic functions, pseudoconvex
sets, and sets which are convex for supports or singular supports
with respect to a differential operator. In addition, the
convexity conditions which are relevant for local or global
existence of holomorphic differential equations are discussed,
leading up to Trepreaufs theorem on sufficiency of condition (capital
Greek letter Psi) for microlocal solvability in the analytic
category.
At the beginning of the book, no prerequisites are assumed beyond
calculus and linear algebra. Later on, basic facts from
distribution theory and functional analysis are needed. In a few
places, a more extensive background in differential geometry or
pseudodifferential calculus is required, but these sections can
be bypassed with no loss of continuity. The major part of the
book should therefore be accessible to graduate students so that
it can serve as an introduction to complex analysis in one and
several variables. The last sections, however, are written mainly
for readers familiar with microlocal analysis.
Table of contents
Preface.- Convex Functions of one Variable.- Convexity in A
Finite-Dimensional Vector Space.- Subharmonic Functions.-
Plurisubharmonic Functions.- Convexity with Respect to A Linear
Group.-Convexity with Respect to Differential Operators.-
Convexity and Condition.- Appendix.- Notes.- References.- Index
of Notation.- Index
Originally published by Prentice Hall, 1987
4th ed., 2007, XXII, 778 p., 79 illus., Hardcover
ISBN: 978-0-8176-4393-5
About this textbook
One of the most fundamental and active areas in mathematics, the
theory of partial differential equations (PDEs) is essential in
the modeling of natural phenomena. PDEs have a wide range of
interesting and important applications in every branch of applied
mathematics, physics, and engineering, including fluid dynamics,
elasticity, and optics.
This significantly expanded fourth edition is designed as an
introduction to the theory and applications of linear PDEs. The
authors provide fundamental concepts, underlying principles, a
wide range of applications, and various methods of solutions to
PDEs. In addition to essential standard material on the subject,
the book contains new material that is not usually covered in
similar texts and reference books, including conservation laws,
the spherical wave equation, the cylindrical wave equation,
higher-dimensional boundary-value problems, the finite element
method, fractional partial differential equations, and nonlinear
partial differential equations with applications
Table of contents
Preface to the Fourth Edition
Preface to the Third Edition
Introduction
First-Order, Quasi-Linear Equations and Method of Characteristics
Mathematical Models
Classification of Second-Order Linear Equations
The Cauchy Problem and Wave Equations
Fourier Series and Integrals with Applications
Method of Separation of Variables
Eigenvalue Problems and Special Functions
Boundary-Value Problems and Applications
Higher-Dimensional Boundary-Value Problems
Green's Functions and Boundary-Value Problems
Integral Transform Methods with Applications
Nonlinear Partial Differential Equations with Applications
Numerical and Approximation Methods
Tables of Integral Transforms
Answers and Hints to Selected Exercises
Appendix: Some Special Functions and Their Properties
Bibliography
Index
Series: Cambridge Series in Statistical and Probabilistic
Mathematics
Hardback (ISBN-13: 9780521868426)
This book is about the coordinate-free, or geometric, approach to
the theory of linear models; more precisely, Model I ANOVA and
linear regression models with non-random predictors in a finite-dimensional
setting. This approach is more insightful, more elegant, more
direct, and simpler than the more common matrix approach to
linear regression, analysis of variance, and analysis of
covariance models in statistics. The book discusses the intuition
behind and optimal properties of various methods of estimating
and testing hypotheses about unknown parameters in the models.
Topics covered range from linear algebra, such as inner product
spaces, orthogonal projections, book orthogonal spaces, Tjur
experimental designs, basic distribution theory, the geometric
version of the Gauss-Markov theorem, optimal and non-optimal
properties of Gauss-Markov, Bayes, and shrinkage estimators under
assumption of normality, the optimal properties of F-test, and
the analysis of covariance and missing observations.
* Geometric approach to linear statistical models
* Optimality theory
* Many exercises and problems; detailed index
Contents
1. Introduction; 2. Topics in linear algebra; 3. Random vectors;
4. Gauss-Markov estimation; 5. Normal theory: estimation; 6.
Normal theory: testing; 7. Analysis of covariance; 8. Missing
observations.
Ces trois volumes dfoeuvres choisies rassemblent une
selection dfarticles et de monographies representatifs des
travaux de recherche de Jacques-Louis Lions, regroupes par grands
themes.
Jacques-Louis Lions a ete professeur au College de France,
professeur a lfEcole polytechnique, president de lfINRIA,
president du CNES et president de lfAcademie des Sciences. Il
est decede le 17 mai 2001.
Son influence sur les mathematiques appliquees a ete considerable
en France et dans le monde. Il a publie plus de 20 livres et pres
de 600 articles dans les principales revues internationales de
mathematiques. La SMAI (Societe de Mathematiques Appliquees et
Industrielles) a pris lfinitiative de publier ses oeuvres
choisies, et la SMF (Societe Mathematique de France) sfest
associee a cette publication, qui a recu le soutien du Ministere
de la Recherche.
Chaque volume est precede dfune breve introduction redigee par
un membre du Comite Scientifique (Alain Bensoussan, Philippe G.
Ciarlet, Roland Glowinski et Roger Temam) qui a selectionne les
oeuvres retenues.
Les oeuvres choisies sont publiees par EDP Sciences en 3 volumes
:
|
|
|
Equations aux derivees partielles Interpolation
(740 p) ISBN 2-86883-661-5
Controle Homogeneisation
(874 p) ISBN 2-86883-662-3
Analyse numerique Calcul scientifique Applications
(828 p) ISBN 2-86883-663-1