Series: Grundlehren der mathematischen Wissenschaften, Vol. 325
2005, XIX, 626 p. 39 illus., Hardcover
ISBN: 3-540-25452-8
About this book
This masterly exposition of the mathematical theory of hyperbolic
system laws brings out the intimate connection with continuum
thermodynamics, emphasizing issues in which the analysis may
reveal something about the physics and, in return, the underlying
physical structure may direct and drive the analysis. The reader
should have a certain mathematical sophistication and be familiar
with the rudiments of the qualitative theory of partial
differential equations, whereas the required notions from
continuum physics are introduced from scratch.
The 2nd edition contains a new chapter recounting the exciting
recent developments on the vanishing viscosity method; numerous
new sections have been incorporated in preexisting chapters, to
introduce newly derived results or present older material,
omitted in the 1st edition. In addition, a substantial portion of
the original text has been reorganized so as to streamline the
exposition, enrich the collection of examples and improve the
notation. The bibliography has been updated and expanded, now
comprising over one thousand titles.
Table of contents
Series: Cornerstones
Set: : Basic Real Analysis and Advanced Real Analysis
2005, XXI, 653 p. 10 illus., Hardcover
ISBN: 0-8176-3250-6
About this textbook
Basic Real Analysis and Advanced Real Analysis systematically
develop those concepts and tools in real analysis that are vital
to every mathematician, whether pure or applied, aspiring or
established. These works present a comprehensive treatment with a
global view of the subject, emphasizing the connections between
real analysis and other branches of mathematics.
Key topics and features of Basic Real Analysis:
* Early chapters treat the fundamentals of real variables,
sequences and series of functions, the theory of Fourier series
for the Riemann integral, metric spaces, and the theoretical
underpinnings of multivariable calculus and differential
equations
* Subsequent chapters develop the Lebesgue theory in Euclidean
and abstract spaces, Fourier series and the Fourier transform for
the Lebesgue integral, point-set topology, measure theory in
locally compact Hausdorff spaces, and the basics of Hilbert and
Banach spaces
* The subjects of Fourier series and harmonic functions are used
as recurring motivation for a number of theoretical developments
* The development proceeds from the particular to the general,
often introducing examples well before a theory that incorporates
them
* The text includes many examples and hundreds of problems, and a
separate 55-page section gives hints or complete solutions for
most of the problems
Basic Real Analysis requires of the reader only familiarity with
some linear algebra and real variable theory, the very beginning
of group theory, and an acquaintance with proofs. It is suitable
as a text in an advanced undergraduate course in real variable
theory and in most basic graduate courses in Lebesgue integration
and related topics. Because it focuses on what every young
mathematician needs to know about real analysis, the book is
ideal both as a course text and for self-study, especially for
graduate students preparing for qualifying examinations. Its
scope and approach will appeal to instructors and professors in
nearly all areas of pure mathematics, as well as applied
mathematicians working in analytic areas such as statistics,
mathematical physics, and differential equations. Indeed, the
clarity and breadth of Basic Real Analysis make it a welcome
addition to the personal library of every mathematician.
Table of contents
Preface.- Dependence among Chapters.- Guide for the Reader.- List
of Figures.- Acknowledgements.- Standard Notation.- Theory of
Calculus in One Real Variable.- Metric Spaces.- Theory of
Calculus in Several Real Variables.- Theory of Ordinary
Differential Equations.- Abstract Measure Theory and Lebesgue
Measure.- Measure Theory for Euclidean Space.- Differentiation of
Lebesgue Integrals on the Line.- Fourier Transform in Euclidean
Space.- Lp Spaces.- Topological Spaces.- Integration of Locally
Compact Spaces.- Hilbert and Banach Spaces.- Appendix.- Hints for
Solutions of Problems.- Selected References.- Index of Notation.-
Index.
Series: Cornerstones
Set: : Basic Real Analysis and Advanced Real Analysis
2005, XXII, 465 p. 6 illus., Hardcover
ISBN: 0-8176-4382-6
About this textbook
Basic Real Analysis and Advanced Real Analysis systematically
develop those concepts and tools in real analysis that are vital
to every mathematician, whether pure or applied, aspiring or
established. These works present a comprehensive treatment with a
global view of the subject, emphasizing the connections between
real analysis and other branches of mathematics.
Key topics and features of Advanced Real Analysis:
* Develops Fourier analysis and functional analysis with an eye
toward partial differential equations
* Includes chapters on Sturm?Liouville theory, compact self-adjoint
operators, Euclidean Fourier analysis, topological vector spaces
and distributions, compact and locally compact groups, and
aspects of partial differential equations
* Contains chapters about analysis on manifolds and foundations
of probability
* Proceeds from the particular to the general, often introducing
examples well before a theory that incorporates them
* Includes many examples and nearly two hundred problems, and a
separate 45-page section gives hints or complete solutions for
most of the problems
* Incorporates, in the text and especially in the problems,
material in which real analysis is used in algebra, in topology,
in complex analysis, in probability, in differential geometry,
and in applied mathematics of various kinds
Advanced Real Analysis requires of the reader a first course in
measure theory, including an introduction to the Fourier
transform and to Hilbert and Banach spaces. Some familiarity with
complex analysis is helpful for certain chapters. The book is
suitable as a text in graduate courses such as Fourier and
functional analysis, modern analysis, and partial differential
equations. Because it focuses on what every young mathematician
needs to know about real analysis, the book is ideal both as a
course text and for self-study, especially for graduate students
preparing for qualifying examinations. Its scope and approach
will appeal to instructors and professors in nearly all areas of
pure mathematics, as well as applied mathematicians working in
analytic areas such as statistics, mathematical physics, and
differential equations. Indeed, the clarity and breadth of
Advanced Real Analysis make it a welcome addition to the personal
library of every mathematician.
Table of contents
Preface.- List of Figures.- Dependence among Chapters.- Guide for
the Reader.- Notation and Terminology.- Introduction to Boundary-Value
Problems.- Compact Self-Adjoint Operators.- Topics in Euclidean
Fourier Analysis.- Topics in Functional Analysis.- Distributions.-
Compact and Locally Compact Groups.- Aspects of Partial
Differential Equations.- Analysis on Manifolds.- Foundations of
Probability.- Hints for Solutions of Problems.- Selected
References.- Index of Notation.- Index.
Series: Advances in Mathematics, Vol. 9
2005, XII, 264 p. 38 illus., Hardcover
ISBN: 0-387-27569-X
About this book
Natural duality theory is one of the major growth areas within
general algebra. This text provides a short path to the forefront
of research in duality theory. It presents a coherent approach to
new results in the area, as well as exposing open problems.
Unary algebras play a special role throughout the text.
Individual unary algebras are relatively simple and easy to work
with. But as a class they have a rich and complex entanglement
with dualisability. This combination of local simplicity and
global complexity ensures that, for the study of natural duality
theory, unary algebras are an excellent source of examples and
counterexamples.
A number of results appear here for the first time. In
particular, the text ends with an appendix that provides a new
and definitive approach to the concept of the rank of a finite
algebra and its relationship with strong dualisability.
Table of contents
Preface.- Unary algebras and dualisability.- Binary homomorphisms
and natural dualities.- The complexity of dualisability: three-element
unary algebras.- Full and strong dualisability: three-element
unary algebras.- Dualisability and algebraic constructions.-
Dualisability and clones.- Inherent dualisability.- Epilogue.-
Appendix: Strong dualisability.- References.- Notation.- Index.
Cloth | 2005 | ISBN: 0-691-10287-2
676 pp. | 6 x 9 | 106 line illus.
This self-contained textbook is an informal introduction to
optimization through the use of numerous illustrations and
applications. The focus is on analytically solving optimization
problems with a finite number of continuous variables. In
addition, the authors provide introductions to classical and
modern numerical methods of optimization and to dynamic
optimization.
The book's overarching point is that most problems may be solved
by the direct application of the theorems of Fermat, Lagrange,
and Weierstrass. The authors show how the intuition for each of
the theoretical results can be supported by simple geometric
figures. They include numerous applications through the use of
varied classical and practical problems. Even experts may find
some of these applications truly surprising.
A basic mathematical knowledge is sufficient to understand the
topics covered in this book. More advanced readers, even experts,
will be surprised to see how all main results can be grounded on
the Fermat-Lagrange theorem. The book can be used for courses on
continuous optimization, from introductory to advanced, for any
field for which optimization is relevant.
Jan Brinkhuis is Associate Professor of Finance and Mathematical
Methods and Techniques at the Econometric Institute of Erasmus
University, Rotterdam. Vladimir Tikhomirov holds the Chair of
Optimal Control in the Department of Mechanics and Mathematics at
the Lomonosov Moscow State University.
Endorsements:
"Well written and well organized. The book's examples are
highly varied, interesting and well thought out."--Steinar
Hauan, Carnegie Mellon University
"An extremely interesting introduction to the field of
mathematical optimization. I know of no other book in the field
that offers so many illustrations of the applicability of deep
theoretical issues in optimization. It will command a broad
audience, from beginners to experts."--Kees Roos, Delft
University of Technology
Series:
Princeton Series in Applied Mathematics
Ingrid Daubechies, Weinan E, Jan Karel Lenstra, and Endre Suli,
Editors