Mathematik
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Lamotke, Klaus
Riemannsche Flächen
Die Theorie Riemannscher Flächen wird als ein Mikrokosmos der Reinen
Mathematik dargestellt, in dem Methoden der Topologie und Geometrie, der
komplexen und reellen Analysis sowie der Algebra zusammenwirken, um die
reichhaltige Struktur dieser Flächen aufzuklären. Viele Beispiele und Bilder, die
in der historischen Entwicklung eine Rolle spielten, ergänzen die Darstellung.
Das Buch beruht auf Vorlesungen und Seminaren im Anschluß an eine
Einführung in die komplexe Funktionentheorie. Wegen seiner Methodenvielfalt
enthält es gleichzeitig Einführungen in die Topologie (Fundamentalgruppe,
Überlagerungen, Flächen), in die algebraische Geometrie (Kurven und ihre
Singularitäten) und in die Potentialtheorie (harmonische Funktionen).
Die 2. Auflage wurde um eine genauere Betrachtung des Kleinschen 14-Ecks,
ein Kapitel über die de Rhamsche Cohomologie und einen Paragraphen über
die Lösung nicht-linearer Gleichungen der Mathematischen Physik mittels
Riemannscher Thetafunktionen ergänzt.
(Series: Springer-Lehrbuch)
2., erg. u. verb. Aufl., 2009, X, 341 S. 49 Abb., Softcover
ISBN: 978-3-642-01710-0
Aubin, Jean-Pierre
Viability Theory
This work examines viability theory and its applications to control theory and
differential games. The emphasis is on the construction of feedbacks and
dynamical systems by myopic optimization methods. Systems of first-order
partial differential inclusions, whose solutions are feedbacks, are constructed
and investigated. Basic results are then extended to the case of fuzzy control
problems, distributed control problems, and control systems with delays and
memory.
Aimed at graduate students and research mathematicians, both pure and
applied, this book offers specialists in control and nonlinear systems tools to
take into account general state constraints. Viability theory also allows
researchers in other disciplines—artificial intelligence, economics, game
theory, theoretical biology, population genetics, cognitive sciences—to go
beyond deterministic models by studying them in a dynamical or evolutionary
perspective in an uncertain environment.
The book is a compendium of the state of knowledge about
viability...Mathematically, the book should be accessible to anyone who has
had basic graduate courses in modern analysis and functional analysis…The
concepts are defined and many proofs of the requisite results are reproduced
here, making the present book essentially self-contained.
—Bulletin of the AMS
Because of the wide scope, the book is an ideal reference for people
encountering problems related to viability theory in their research…It gives a
very thorough mathematical presentation. Very useful for anybody confronted
with viability constraints.
—Mededelingen van het Wiskundig
(Series: Modern Birkhäuser Classics)
1st ed. 2001. 2nd printing, 2009, XXVIII, 544 p. 10 illus., Softcover
ISBN: 978-0-8176-4909-8
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Deza, Michel M.; Deza, Elena
Encyclopedia of Distances
Distance metrics and distances have become an essential tool in many areas
of pure and applied Mathematics, and this encyclopedia is the first one to treat
the subject in full.
The book appears just as research intensifies into metric spaces and
especially, distance design for applications. These distances are particularly
crucial, for example, in computational biology, image analysis, speech
recognition, and information retrieval.
Here, an assessment of the practical questions arising during selection of a
"good'' distance function has been left aside in favor of a comprehensive listing
of the main available distances, a useful tool for the distance design
community.
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This reader-friendly reference offers both independent introductions and
definitions, while at the same time making cross-referencing easy through
hyperlink-like boldfaced references to original definitions. This high-quality
publication is a mix of reference resource and coffee-table book.
2009, XIV, 530 p. With CD-ROM., Hardcover
ISBN: 978-3-642-00233-5
Gut, Allan
An Intermediate Course in Probability
The purpose of this book is to provide the reader with a solid background and
understanding of the basic results and methods in probability theory before
entering into more advanced courses. The first six chapters focus on some
central areas of what might be called pure probability theory: multivariate
random variables, conditioning, transforms, order variables, the multivariate
normal distribution, convergence. A final chapter is devoted to the Poisson
process as a means both to introduce stochastic processes and to apply many
of the techniques introduced earlier in the text.
Students are assumed to have taken a first course in probability, though no
knowledge of measure theory is assumed. Throughout, the presentation is
thorough and includes many examples that are discussed in detail. Thus,
students considering more advanced research in probability theory will benefit
from this wide-ranging survey of the subject that provides them with a foretaste
of the subject’s many treasures.
The present second edition offers updated content, one hundred additional
problems for solution, and a new chapter that provides an outlook on further
areas and topics, such as stable distributions and domains of attraction,
extreme value theory and records, and martingales. The main idea is that this
chapter may serve as an appetizer to the more advanced theory.
(Series: Springer Texts in Statistics)
2nd ed., 2009, XIV, 302 p., Hardcover
ISBN: 978-1-4419-0161-3
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Möller, Torsten; Hamann, Bernd; Russell, Robert
Mathematical Foundations of Scientific Visualization, Computer
Graphics, and Massive Data Exploration
Visualization is one of the most active and exciting areas of Mathematics and
Computing Science, and indeed one which is only beginning to mature.
Current visualization algorithms break down for very large data sets. While
present approaches use multi-resolution ideas, future data sizes will not be
handled that way. New algorithms based on sophisticated mathematical
modeling techniques must be devised which will permit the extraction of highlevel topological structures that can be visualized.
For these reasons a workshop was organized at the Banff International
Research Station, focused specifically on mathematical issues. A primary
objective of the workshop was to gather together a diverse set of researchers
in the mathematical areas relevant to the recent advances in order to discuss
the research challenges facing this field in the next several years. The
workshop was organized into five different thrusts: - Topology and Discrete
Methods; - Signal and Geometry Processing; - Partial Differential Equations; Data Approximation Techniques; - Massive Data Applications. This book
presents a summary of the research ideas presented at this workshop.
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(Series: Mathematics and Visualization)
2009, X, 360 p. 183 illus., 134 in color., Hardcover
ISBN: 978-3-540-25076-0
Helms, Lester L.
Potential Theory
This book presents a clear path from calculus to classical potential theory and
beyond with the aim of moving the reader into a fertile area of mathematical
research as quickly as possible. The first half of the book develops the subject
matter from first principles using only calculus. The second half comprises
more advanced material for those with a senior undergraduate or beginning
graduate course in real analysis. For specialized regions, solutions of
Laplace’s equation are constructed having prescribed normal derivatives on
the flat portion of the boundary and prescribed values on the remaining portion
of the boundary. By means of transformations known as diffeomorphisms,
these solutions are morphed into local solutions on regions with curved
boundaries. The Perron-Weiner-Brelot method is then used to construct global
solutions for elliptic PDEs involving a mixture of prescribed values of a
boundary differential operator on part of the boundary and prescribed values
on the remainder of the boundary.
(Series: Universitext)
2009, XI, 441 p. 2 illus., Softcover
ISBN: 978-1-84882-318-1
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Padberg, Friedhelm
Didaktik der Bruchrechnung
für Lehrerausbildung und Lehrerfortbildung
Die neuesten Lehrpläne und die nationalen Bildungsstandards im Fach
Mathematik haben zu substanziellen Veränderungen im Bruchrechenunterricht
geführt. Darauf bereiten wir in dieser stark überarbeiteten Neuauflage
gründlich vor durch u.a.:

Realistische Bestandsaufnahmen anschaulicher Vorkenntnisse

Aufbau tragfähiger Grundvorstellungen / Thematisierung intuitivanschaulicher Zugangswege

Vielfältige Anregungen zum Argumentieren, Begründen, Reflektieren

Vorstellung und Bewertung verschiedener Zugangswege und
Konzeptionen zur systematischen Erarbeitung der Bruchrechnung

Bereitstellung diagnostischer Tests

Gründliche Analysen möglicher Problembereiche und verbreiteter
Fehlerstrategien

Vorstellung gut gelungener Beispiele aus neuesten Schulbüchern

Konkrete, gut umsetzbare Vorschläge zur deutlichen Verbesserung
des Bruchrechenunterrichts
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Jun-09
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Das Buch wendet sich an Studierende für das Lehramt der Primar- und
Sekundarstufen sowie an Lehramtsanwärterinnen und Lehramtsanwärter mit
Mathematik als Fach.
(Series: Mathematik Primar- und Sekundarstufe)
4., wesentl.überarb. Aufl., 2009, XV, 274 S. 89 Abb., Softcover
ISBN: 978-3-8274-1940-8
Pham, Huyên
Continuous-time Stochastic Control and Optimization with Financial
Applications
Stochastic optimization problems arise in decision-making problems under
uncertainty, and find various applications in economics and finance. On the
other hand, problems in finance have recently led to new developments in the
theory of stochastic control.
This volume provides a systematic treatment of stochastic optimization
problems applied to finance by presenting the different existing methods:
dynamic programming, viscosity solutions, backward stochastic differential
equations, and martingale duality methods. The theory is discussed in the
context of recent developments in this field, with complete and detailed proofs,
and is illustrated by means of concrete examples from the world of finance:
portfolio allocation, option hedging, real options, optimal investment, etc.
This book is directed towards graduate students and researchers in
mathematical finance, and will also benefit applied mathematicians interested
in financial applications and practitioners wishing to know more about the use
of stochastic optimization methods in finance.
(Series: Stochastic Modelling and Applied Probability)
2009, XVII, 232 p., Hardcover
ISBN: 978-3-540-89499-5
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Gohberg, Israel; Leiterer, Jürgen
Holomorphic Operator Functions of One Variable and Applications
Methods from Complex Analysis in Several Variables
This is a book on holomorphic operator functions of a single variable and
applications, which is focused on the relations between local and global
theories. It is based on methods and technics of complex analysis of several
variables.
The first part of the theory starts with a straightforward generalization of some
results from the basics of analysis of scalar functions of one complex variable.
In the second part, which is the main part of the theory, results are obtained by
methods and tools adapted from complex analysis of functions of several
variables. We have in mind the theory of holomorphic cocycles (fiber bundles)
with values in infinite-dimensional non-commutative groups. As a rule, these
results do not appear in traditional complex analysis of one variable, not even
for matrix valued cocycles. The third part consists of applications to operator
theory. Here applications are presented for holomorphic families of subspaces
and Plemelj-Muschelishvili factorization. The fourth part presents a
generalization of the theory of cocycles to cocycles with restrictions. This part
contains also applications to interpolation problems, to the problem of
holomorphic equivalence and diagonalization.
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(Series: Operator Theory: Advances and Applications)
2009, 444 p., Hardcover
ISBN: 978-3-0346-0125-2
Goodman, Roe; Wallach, Nolan R.
Symmetry, Representations, and Invariants
Symmetry is a key ingredient in many mathematical, physical, and biological
theories. Using representation theory and invariant theory to analyze the
symmetries that arise from group actions, and with strong emphasis on the
geometry and basic theory of Lie groups and Lie algebras, Symmetry,
Representations, and Invariants is a significant reworking of an earlier highlyacclaimed work by the authors. The result is a comprehensive introduction to
Lie theory, representation theory, invariant theory, and algebraic groups, in a
new presentation that is more accessible to students and includes a broader
range of applications.
The philosophy of the earlier book is retained, i.e., presenting the principal
theorems of representation theory for the classical matrix groups as motivation
for the general theory of reductive groups. The wealth of examples and
discussion prepares the reader for the complete arguments now given in the
general case.
Key Features of Symmetry, Representations, and Invariants: (1) Early chapters
suitable for honors undergraduate or beginning graduate courses, requiring
only linear algebra, basic abstract algebra, and advanced calculus; (2)
Applications to geometry (curvature tensors), topology (Jones polynomial via
symmetry), and combinatorics (symmetric group and Young tableaux); (3) Selfcontained chapters, appendices, comprehensive bibliography; (4) More than
350 exercises (most with detailed hints for solutions) further explore main
concepts; (5) Serves as an excellent main text for a one-year course in Lie
group theory; (6) Benefits physicists as well as mathematicians as a reference
work.
(Series: Graduate Texts in Mathematics)
2009, XX, 716 p. 10 illus., Hardcover
ISBN: 978-0-387-79851-6
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Tabuada, Paulo
Verification and Control of Hybrid Systems
A Symbolic Approach
Hybrid systems describe the interaction of software, described by finite models
such as finite-state machines, with the physical world, described by infinite
models such as differential equations. This book addresses problems of
verification and controller synthesis for hybrid systems. Although these
problems are very difficult to solve for general hybrid systems, several authors
have identified classes of hybrid systems that admit symbolic or finite models.
The novelty of the book lies on the systematic presentation of these classes of
hybrid systems along with the relationships between the hybrid systems and
the corresponding symbolic models. To show how the existence of symbolic
models can be used for verification and controller synthesis, the book also
outlines several key results for the verification and controller design of finite
systems. Several examples illustrate the different methods and techniques
discussed in the book.
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2009, XV, 202 p. 200 illus., Hardcover
ISBN: 978-1-4419-0223-8
Papadopoulos, Chrissoleon T.; O'Kelly, Michael E.J.; Vidalis, Michael J.;
Spinellis, Diomidis
Analysis and Design of Discrete Part Production Lines
Analysis and Design of Discrete Part Production Lines provides a complete
overview of production systems, investigating several production line
problems, and describing the best approaches to the analysis of production
line performance. Written by experts in the field of production and
manufacturing research, this book also presents numerous techniques that can
be used to describe and model various types of production lines.
Special Features:
* Includes access to a supplementary web-based software package, providing
algorithms and examples, developed by distinguished experts of the field.
* Describes new results for evaluative techniques and design algorithms as
well as several open problems in production line optimization.
* Presents in detail the theory and techniques that underlie production system
management, design, and analysis, allowing the book to serve as an excellent
introduction to newcomers in the field.
* Has potential for use in a graduate level course in industrial or manufacturing
engineering, or in a business course with a manufacturing focus.
* Contains appendices providing an overview of several mathematical
techniques employed to design and evaluate production line models.
(Series: Springer Optimization and Its Applications)
2009, XVIII, 269 p. 113 illus., 18 in color., Hardcover
ISBN: 978-0-387-89493-5
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Schechter, Martin
Minimax Systems and Critical Point Theory
Many problems in science and engineering involve the solution of differential
equations or systems. One of most successful methods of solving nonlinear
equations is the determination of critical points of corresponding functionals.
The study of critical points has grown rapidly in recent years and has led to
new applications in other scientific disciplines. This monograph continues this
theme and studies new results discovered since the author's preceding book
entitled Linking Methods in Critical Point Theory.
Written in a clear, sequential exposition, topics include semilinear problems,
Fucik spectrum, multidimensional nonlinear wave equations, elliptic systems,
and sandwich pairs, among others. With numerous examples and applications,
this book explains the fundamental importance of minimax systems and
describes how linking methods fit into the framework.
Minimax Systems and Critical Point Theory is accessible to graduate students
with some background in functional analysis, and the new material makes this
book a useful reference for researchers and mathematicians.
Review of the author's previous Birkhäuser work, Linking Methods in Critical
Point Theory:
The applications of the abstract theory are to the existence of (nontrivial) weak
solutions of semilinear elliptic boundary value problems for partial differential
equations, written in the form Au = f(x, u). . . . The author essentially shows
how his methods can be applied whenever the nonlinearity has sublinear
growth, and the associated functional may increase at a certain rate in every
direction of the underlying space. This provides an elementary approach to
such problems. . . . A clear overview of the contents of the book is presented in
the first chapter, while bibliographical comments and variant results are
described in the last one. -MathSciNet
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2009, XIV, 242 p., Hardcover
ISBN: 978-0-8176-4805-3
Dieudonné, Jean
A History of Algebraic and Differential Topology, 1900 - 1960
(Series: Modern Birkhäuser Classics)
1st ed. 1989. 2nd printing, 2009, XXIV, 648 p., Softcover
ISBN: 978-0-8176-4906-7
Sala, Massimiliano ; Mora, Teo; Perret, Ludovic; Sakata, Shojjiro;
Traverso, Carlo
Gröbner Bases, Coding, and Cryptography
Coding theory and cryptography allow secure and reliable data transmission,
which is at the heart of modern communication. Nowadays, it is hard to find an
electronic device without some code inside. Gröbner bases have emerged as
the main tool in computational algebra, permitting numerous applications, both
in theoretical contexts and in practical situations.
This book is the first book ever giving a comprehensive overview on the
application of commutative algebra to coding theory and cryptography. For
example, all important properties of algebraic/geometric coding systems
(including encoding, construction, decoding, list decoding) are individually
analysed, reporting all significant approaches appeared in the literature. Also,
stream ciphers, PK cryptography, symmetric cryptography and Polly Cracker
systems deserve each a separate chapter, where all the relevant literature is
reported and compared. While many short notes hint at new exciting
directions, the reader will find that all chapters fit nicely within a unified
notation.
2009, XVI, 430 p., Hardcover
ISBN: 978-3-540-93805-7
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Anastassiou, George A.
Fractional Differentiation Inequalities
In this book the author presents the Opial, Poincaré, Sobolev, Hilbert, and
Ostrowski fractional differentiation inequalities. Results for the above are
derived using three different types of fractional derivatives, namely by
Canavati, Riemann-Liouville and Caputo. The univariate and multivariate
cases are both examined. Each chapter is self-contained. The theory is
presented systematically along with the applications. The application to
information theory is also examined.
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This monograph is suitable for researchers and graduate students in pure
mathematics. Applied mathematicians, engineers, and other applied scientists
will also find this book useful.
2009, XIV, 686 p., Hardcover
ISBN: 978-0-387-98127-7
Bartocci, Claudio; Bruzzo, Ugo; Hernández Ruipérez, Daniel
Fourier–Mukai and Nahm Transforms in Geometry and Mathematical
Physics
Integral transforms, such as the Laplace and Fourier transforms, have been
major tools in mathematics for at least two centuries. In the last three decades
the development of a number of novel ideas in algebraic geometry, category
theory, gauge theory, and string theory has been closely related to
generalizations of integral transforms of a more geometric character.
"Fourier–Mukai and Nahm Transforms in Geometry and Mathematical Physics"
examines the algebro-geometric approach (Fourier–Mukai functors) as well as
the differential-geometric constructions (Nahm). Also included is a
considerable amount of material from existing literature which has not been
systematically organized into a monograph.
Key features: Basic constructions and definitions are presented in preliminary
background chapters - Presentation explores applications and suggests
several open questions - Extensive bibliography and index.
This self-contained monograph provides an introduction to current research in
geometry and mathematical physics and is intended for graduate students and
researchers just entering this field.
(Series: Progress in Mathematics)
2009, XVI, 418 p. 83 illus., Hardcover
ISBN: 978-0-8176-3246-5
Dontchev, Asen L.; Rockafellar, R. Tyrrell
Implicit Functions and Solution Mappings
A View from Variational Analysis
The implicit function theorem is one of the most important theorems in analysis
and its many variants are basic tools in partial differential equations and
numerical analysis. This book treats the implicit function paradigm in the
classical framework and beyond, focusing largely on properties of solution
mappings of variational problems.
The purpose of this self-contained work is to provide a reference on the topic
and to provide a unified collection of a number of results which are currently
scattered throughout the literature. The first chapter of the book treats the
classical implicit function theorem in a way that will be useful for students and
teachers of undergraduate calculus. The remaining part becomes gradually
more advanced, and considers implicit mappings defined by relations other
than equations, e.g., variational problems. Applications to numerical analysis
and optimization are also provided.
This valuable book is a major achievement and is sure to become a standard
reference on the topic.
(Series: Springer Monographs in Mathematics)
2009, XII, 376 p. 12 illus., Hardcover
ISBN: 978-0-387-87820-1
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Atkinson, Kendall; Han, Weimin
Theoretical Numerical Analysis
A Functional Analysis Framework
This textbook prepares graduate students for research in numerical
analysis/computational mathematics by giving to them a mathematical
framework embedded in functional analysis and focused on numerical
analysis. This helps the student to move rapidly into a research program. The
text covers basic results of functional analysis, approximation theory, Fourier
analysis and wavelets, iteration methods for nonlinear equations, finite
difference methods, Sobolev spaces and weak formulations of boundary value
problems, finite element methods, elliptic variational inequalities and their
numerical solution, numerical methods for solving integral equations of the
second kind, and boundary integral equations for planar regions. The
presentation of each topic is meant to be an introduction with certain degree of
depth. Comprehensive references on a particular topic are listed at the end of
each chapter for further reading and study.
Because of the relevance in solving real world problems, multivariable
polynomials are playing an ever more important role in research and
applications. In this third editon, a new chapter on this topic has been included
and some major changes are made on two chapters from the previous edition.
In addition, there are numerous minor changes throughout the entire text and
new exercises are added.
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Review of earlier edition:
"...the book is clearly written, quite pleasant to read, and contains a lot of
important material; and the authors have done an excellent job at balancing
theoretical developments, interesting examples and exercises, numerical
experiments, and bibliographical references."
R. Glowinski, SIAM Review, 2003
(Series: Texts in Applied Mathematics)
3rd ed., 2009, X, 590 p., Hardcover
ISBN: 978-1-4419-0457-7
Ibrahimbegovic, Adnan
Nonlinear Solid Mechanics
Theoretical Formulations and Finite Element Solution Methods
The main purpose of this book is to present all the ingredients for constructing
the numerical models for representing the complex nonlinear behavior of
structures and their components, which are represented as deformable solid
bodies. Nonetheless, the book will also prove useful for those mostly interested
in linear problems of mechanics, since the sure way to obtain a sound
theoretical formulation of a linear problem goes through the consistent
linearization of the more general nonlinear problem.
The original French edition published by Hermes Science - Lavoisier Paris in
2006 was nominated for the Roberval Award for University Textbooks in
French.
(Series: Solid Mechanics and Its Applications)
2009, XX, 576 p., Hardcover
ISBN: 978-90-481-2330-8
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Radulescu, Teodora-Liliana; Radulescu, Vincentiu D.; Andreescu, Titu
Problems in Real Analysis
Advanced Calculus on the Real Axis
Problems in Real Analysis: Advanced Calculus on the Real Axis features a
comprehensive collection of challenging problems in mathematical analysis
that aim to promote creative, non-standard techniques for solving problems.
This self-contained text offers a host of new mathematical tools and strategies
which develop a connection between analysis and other mathematical
disciplines, such as physics and engineering. A broad view of mathematics is
presented throughout; the text is excellent for the classroom or self-study. It is
intended for undergraduate and graduate students in mathematics, as well as
for researchers engaged in the interplay between applied analysis,
mathematical physics, and numerical analysis.
Key features:
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*Uses competition-inspired problems as a platform for training typical inventive
skills;
*Develops basic valuable techniques for solving problems in mathematical
analysis on the real axis and provides solid preparation for deeper study of real
analysis;
*Includes numerous examples and interesting, valuable historical accounts of
ideas and methods in analysis;
*Offers a systematic path to organizing a natural transition that bridges
elementary problem-solving activity to independent exploration of new results
and properties.
2009, XX, 452 p. 10 illus., Softcover
ISBN: 978-0-387-77378-0
Silverman, Joseph H.
The Arithmetic of Elliptic Curves
The theory of elliptic curves is distinguished by its long history and by the
diversity of the methods that have been used in its study. This book treats the
arithmetic theory of elliptic curves in its modern formulation, through the use of
basic algebraic number theory and algebraic geometry. The book begins with a
brief discussion of the necessary algebro-geometric results, and proceeds with
an exposition of the geometry of elliptic curves, the formal group of an elliptic
curve, and elliptic curves over finite fields, the complex numbers, local fields,
and global fields. Included are proofs of the Mordell–Weil theorem giving finite
generation of the group of rational points and Siegel’s theorem on finiteness of
integral points.
For this second edition of The Arithmetic of Elliptic Curves, there is a new
chapter entitled Algorithmic Aspects of Elliptic Curves, with an emphasis on
algorithms over finite fields which have cryptographic applications. These
include Lenstra’s factorization algorithm, Schoof’s point counting algorithm,
Miller’s algorithm to compute the Tate and Weil pairings, and a description of
aspects of elliptic curve cryptography. There is also a new section on Szpiro’s
conjecture and ABC, as well as expanded and updated accounts of recent
developments and numerous new exercises.
The book contains three appendices: Elliptic Curves in Characteristics 2 and 3,
Group Cohomology, and a third appendix giving an overview of more
advanced topics.
(Series: Graduate Texts in Mathematics)
2nd ed., 2009, XVIII, 514 p. 14 illus., Hardcover
ISBN: 978-0-387-09493-9
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Plaue, Matthias; Scherfner, Mike
Mathematik für das Bachelorstudium I
Grundlagen, lineare Algebra und Analysis
Dies ist ein Buch über die Mathematik, welches insbesondere die neuen
Anforderungen des Bachelorstudiums sinnvoll bedient. Es behandelt die
Grundlagen und danach den Stoff der linearen Algebra und eindimensionalen
Analysis. Damit deckt es den Stoff ab, der an Universitäten wesentlich im
ersten Semester behandelt wird. Dabei wenden wir uns an Physiker,
Mathematiker sowie ambitionierte Lehramtskandidaten und Ingenieure.
Das Buch fördert sowohl das Verständnis als auch das konzentrierte Lernen
für Klausuren und mündliche Prüfungen.
Auf einen Blick:

Klarer Stil, klare Sprache, klare Struktur.

Zahlreiche Erläuterungen.

Zu jedem Thema wird gesondert ein informativer Ein- und Ausblick
geliefert.

Grafiken und viele Beispiele helfen beim Verstehen.

Fragen zum Selbsttest unterstützen zusätzlich beim Lernen.

Aufgaben mit vollständigen Lösungen dienen der Vertiefung und
Vorbereitung auf Prüfungen jeglicher Art.
Jun-09
€(D) 22,95
€(A) 23,60
*sFr 36,00
Jun-09
*€(D) 96,25
*€(A) 98,95
*sFr 149,50
2009, XIV, 306 S. 60 Abb. in Farbe., Softcover
ISBN: 978-3-8274-2067-1
Agarwal, Ravi P.; O'Regan, Donal; Sahu, D.R.
Fixed Point Theory for Lipschitzian-type Mappings with Applications
In recent years, the fixed point theory of Lipschitzian-type mappings has
rapidly grown into an important field of study in both pure and applied
mathematics. It has become one of the most essential tools in nonlinear
functional analysis.
This self-contained book provides the first systematic presentation of
Lipschitzian-type mappings in metric and Banach spaces. The first chapter
covers some basic properties of metric and Banach spaces. Geometric
considerations of underlying spaces play a prominent role in developing and
understanding the theory. The next two chapters provide background in terms
of convexity, smoothness and geometric coefficients of Banach spaces
including duality mappings and metric projection mappings. This is followed by
results on existence of fixed points, approximation of fixed points by iterative
methods and strong convergence theorems. The final chapter explores several
applicable problems arising in related fields.
This book can be used as a textbook and as a reference for graduate students,
researchers and applied mathematicians working in nonlinear functional
analysis, operator theory, approximations by iteration theory, convexity and
related geometric topics, and best approximation theory.
(Series: Topological Fixed Point Theory and Its Applications)
2009, XIV, 366 p., Hardcover
ISBN: 978-0-387-75817-6
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Bruns, Winfried; Gubeladze, Joseph
Polytopes, Rings, and K-Theory
This book examines interactions of polyhedral discrete geometry and algebra.
What makes this book different from others is the presentation of several
central results in all three areas of the exposition - from discrete geometry, to
commutative algebra, and K-theory. The only prerequisite for the reader is a
background in algebra. The basics of polyhedral geometry have been included
as background material in Chapter 1.
Jun-09
*€(D) 96,25
*€(A) 98,95
*sFr 149,50
Jun-09
*€(D) 50,24
*€(A) 51,65
*sFr 78,00
The text will be of interest to graduate students and mathematicians. Included
are numerous exercises, historical background, and notes throughout the
chapters.
(Series: Springer Monographs in Mathematics)
2009, XIV, 460 p. 52 illus., Hardcover
ISBN: 978-0-387-76355-2
Lasserre, Jean Bernard
Linear and Integer Programming vs Linear Integration and Counting
A Duality Viewpoint
This book analyzes and compares four closely related problems, namely linear
programming, integer programming, linear integration, and linear summation
(or counting). The focus is on duality and the novel approach puts integer
programming in perspective with three associated problems, and permits one
to define discrete analogues of well-known continuous duality concepts, and
the rationale behind them. Also, the approach highlights the difference
between the discrete and continuous cases. Central in the analysis are the
continuous and discrete Brion and Vergne’s formulae for linear integration and
counting which are not very well-known in the optimization community. This
approach provides some new insights on duality concepts for integer
programs, and also permits to retrieve and shed new light on some well-known
results. For instance, Gomory relaxations and the abstract superadditive dual
of integer programs are re-interpreted in this algebraic approach.
This book will serve graduate students and researchers in applied
mathematics, optimization, operations research and computer science. Due to
the substantial practical importance of some presented problems, researchers
in other areas will also find this book useful.
(Series: Springer Series in Operations Research and Financial Engineering)
2009, XIV, 168 p. 2 illus., Hardcover
ISBN: 978-0-387-09413-7
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Micunovic, Milan V.
Thermomechanics of Viscoplasticity
Fundamentals and Applications
This comprehensive monograph is the first to treat an important and
challenging subject in mechanics, namely, the thermomechanics of
viscoplasticity. This entails an examination of the geometrical and
thermodynamical properties of mechanical behavior of metals and many
polymeric and paste-like materials which are indispensable for developing a
rational theory of viscoplasticity.
Key features and topics include:

a comparative review of various models of thermodynamics including
classical, rational, statistical, and endochronic, with a special
approach to inelastic high speed histories;

a tensor representation approach to thermo-inelastic coupled fields
connected to a generalized associativity of flow rule; includes a
comparison with the J2 approach;

discussion of Drucker, Iliushin, and Hill postulates; special attention
devoted to the slight disorder of polycrystal grains;

quasi-rate independence and its application to plastic waves,
ratcheting and diffuse localization;

micromechanics based on the micro grain approach leading to a
reduced number of material constants;

especially useful to the emergent field of biomechanics.
Jun-09
*€(D) 80,20
*€(A) 82,45
*sFr 124,50
Jun-09
*€(D) 42,75
*€(A) 43,95
*sFr 62,00
This book is intended for researchers as well as Ph.D. students in the fields of
material science and continuum mechanics. Designers and engineers in the
field of metal forming, car body calculations, airplane designers, and anyone
involved in the design of large scale industrial parts, will also find this book
highly useful. Additionally, the concepts and results illustrated in
Thermomechanics of Viscoplasticity are readily applicable to the rapidly
developing field of biomechanics.
(Series: Advances in Mechanics and Mathematics)
2009, XXII, 250 p. 47 illus., Hardcover
ISBN: 978-0-387-89489-8
Soifer, Alexander
Mathematics as Problem Solving
Various elementary techniques for solving problems in algebra, geometry, and
combinatorics are explored in this new second edition, "Mathematics as
Problem Solving". Each new chapter builds off the previous one, enhancing
the reader to reach new levels of using logic to solve problems.
Topics are presented in self-contained chapters, with classical solutions as
well as Soifer's own discoveries that he found through his problem-solving
experiences. With roughly 200 different problems and multiple proofs for each,
the reader is challenged to approach problems from different angles, and in
this way can experience the beauty of mathematics.
Review from the first edition:
"Retelling the best solutions and sharing the secrets of discovery are part of
the process of teaching problem solving. Ideally, this process is characterized
by mathematical skill, good taste, and wit. It is a characteristically personal
process and the best such teachers have surely left their personal marks on
students and readers. Alexander Soifer is a teacher of problem solving and his
book, "Mathematics as Problem Solving", is designed to introduce problem
solving to the next generation". The American Mathematical Monthly
Originally self-published by Alexander Soifer, 1987 at the Center for
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Excellence in Mathematical Education, Colorado Springs, CO.
2nd ed., 2009, XVIII, 106 p. 62 illus., Softcover
ISBN: 978-0-387-74646-3
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