Calculus and mathematical analysis Books

Applied mathematics is a central connecting link between scientific observations and their theoretical interpretation. Nonlinear analysis has surely contributed major developments which nowadays shape the face of applied...

During the last decade enormous progress has been achieved in the field of computational fluid dynamics. This became possible by the development of robust and high-order accurate numerical algorithms as well as the construc­...

Many partial differential equations arising in practice are parameter-dependent problems that are of singularly perturbed type. Prominent examples include plate and shell models for small thickness in solid mechanics, ...

Nonholonomic systems are a widespread topic in several scientific and commercial domains, including robotics, locomotion and space exploration. This work sheds new light on this interdisciplinary character through the ...

This book is not a textbook, but rather a coherent collection of papers from the field of partial differential equations. Nevertheless we believe that it may very well serve as a good introduction into some topics of this...

Meshfree methods for the solution of partial differential equations gained much attention in recent years, not only in the engineering but also in the mathematics community. One of the reasons for this development is the fact...

The present volume offers a state-of-the-art report on the various recent sci­ entific developments in the Theory of Porous Media (TPM) comprehending the basic theoretical concepts in continuum mechanics on porous and mul­...

Many problems of stability in the theory of dynamical systems face the difficulty of small divisors. The most famous example is probably given by Kolmogorov-Arnold-Moser theory in the context of Hamiltonian systems, with many...

Numerische Mathematik ist ein zentrales Gebiet der Mathematik, das für vielfältige Anwendungen die Grundlage bildet und das alle Studierenden der Mathematik, Ingenieurwissenschaften, Informatik und Physik kennenlernen.Das...

Dieses Buch soll in erster Linie Studenten der Ingenieurwissenschaften und Physik, aber auch Informatik- und Mathematikstudenten (vor allem fürs Lehramt) helfen, das Grundstudium zu überstehen; es ist kein Geheimnis, dass für...

This text teaches finite element methods and basic finite difference methods from a computational point of view. It emphasizes developing flexible computer programs using the numerical library Diffpack, which is detailed for...

This book provides an approach to the study of perturbation and discretization effects on the long-time behavior of dynamical and control systems. It analyzes the impact of time and space discretizations on asymptotically...

The International conference on Multiscale problems in science and technol­ ogy; Challenges to mathematical analysis and applications brought together mathematicians working on multiscale techniques (homogenisation, singular...

This book is one of the first to provide a general overview of order and chaos in dynamical astronomy. The progress of the theory of chaos has a profound impact on galactic dynamics. It has even invaded celestial mechanics,...

Model reduction is an important engineering problem in which one aims to replace an elaborate model by a simpler model without undue loss of accuracy. The accuracy can be mathematically measured in several possible norms and...

This volume contains a collection of research papers dedicated to Hans Grauert on the occasion of his seventieth birthday. Hans Grauert is a pioneer in modern complex analysis, continuing the il­ lustrious German tradition in...

The aim of this book is to present a recently developed approach suitable for investigating a variety of qualitative aspects of order-preserving random dynamical systems and to give the background for further development of the...

This volume of proceedings is an offspring of the special semester Ergodic Theory, Geometric Rigidity and Number Theory which was held at the Isaac Newton Institute for Mathematical Sciences in Cambridge, UK, from Jan­ uary...

The second volume of the Geometry of Algebraic Curves is devoted to the foundations of the theory of moduli of algebraic curves. Its authors are research mathematicians who have actively participated in the development of the...

The notion of amenability has its origins in the beginnings of modern measure theory: Does a finitely additive set function exist which is invariant under a certain group action? Since the 1940s, amenability has become an...

stratified collectionsofdiffer- inamore intuitive are Expressed terminology, spaces in This characteristic tiable manifoldswhich are an glued together appropriate way. of manifolds" feature becomes in the name or original...

Since the dawn of computing, the quest for a better understanding of Nature has been a driving force for technological development. Groundbreaking achievements by great scientists have paved the way from the abacus to the...

Based on well-known lectures given at Scuola Normale Superiore in Pisa, this book introduces analysis in a separable Hilbert space of infinite dimension. It starts from the definition of Gaussian measures in Hilbert spaces,...

This volume introduces some basic mathematical models for cell cycle, proliferation, cancer, and cancer therapy. Chapter 1 gives an overview of the modeling of the cell division cycle. Chapter 2 describes how tumor secretes...

ECMI has a brand name in Industrial Mathematics and organises successful biannual conferences. This time, the conference on Industrial Mathematics held in Eindhoven in June 2004 Mathematics focused on Aerospace, Electronic...

The study of idempotent elements in group algebras (or, more generally, the study of classes in the K-theory of such algebras) originates from geometric and analytic considerations. For example, C.T.C. Wall [72] has shown that...

Comprehensive and state-of-the art study of the basic concepts and principles of variational analysis and generalized differentiation in both finite-dimensional and infinite-dimensional spaces Presents numerous applications to...

Comprehensive and state-of-the art study of the basic concepts and principles of variational analysis and generalized differentiation in both finite-dimensional and infinite-dimensional spaces Presents numerous applications to...

Systèmes multi-échelles est une introduction à la problématique des systémes multi-échelles du point de vue du mathématicien appliqué. Il se compose d'une mosaique d'exemples de problèmes issus de la physique au sens large qui...

Stochastic numerical methods play an important role in large scale computations in the applied sciences. The first goal of this book is to give a mathematical description of classical direct simulation Monte Carlo (DSMC)...

Whatdoasupernovaexplosioninouterspace,?owaroundanairfoil and knocking in combustion engines have in common? The physical and chemical mechanisms as well as the sizes of these processes are quite di?erent. So are the motivations...

The fundamental question of characterizing continuity and boundedness of Gaussian processes goes back to Kolmogorov. After contributions by R. Dudley and X. Fernique, it was solved by the author. This book provides an overview...

There has recently been a renewal of interest in Fokker-Planck operators, motivated by problems in statistical physics, in kinetic equations, and differential geometry. Compared to more standard problems in the spectral theory...

This book offers a systematic presentation of up-to-date material scattered throughout the literature from the methodology point of view. It reviews the basic theories and methods, with many interesting problems in partial and...

Complexity science has been a source of new insight in physical and social systems and has demonstrated that unpredictability and surprise are fundamental aspects of the world around us. This book is the outcome of a discussion...

Ergodic theory is hard to study because it is based on measure theory, which is a technically difficult subject to master for ordinary students, especially for physics majors. Many of the examples are introduced from a...

Over the past years meshfree methods for the solution of partial di?erential equations have signi?cantly matured and are used in various ?elds of appli- tions. One of the reasons for this development is the fact that meshfree...

The Israeli GAFA seminar (on Geometric Aspect of Functional Analysis) during the years 2002-2003 follows the long tradition of the previous volumes. It reflects the general trends of the theory. Most of the papers deal with...

The Summer School has been dedicated to one of the proponents and ?rst Chairman of the Strategy Board of MACSI-net, the late Jacques Louis Lions (see the dedication by Roland Glowinski). MACSI-net is a European Network of...

In the aftermath of the discoveries in foundations of mathematiC's there was surprisingly little effect on mathematics as a whole. If one looks at stan­ dard textbooks in different mathematical disciplines, especially those...

Proof of the "Fundamental Theorem of Asset Pricing" in its general form by Delbaen and Schachermayer was a milestone in the history of modern mathematical finance and now forms the cornerstone of this book.Puts into book format a series of major results...

This monograph combines the knowledge of both the field of nonlinear dynamics and non-smooth mechanics, presenting a framework for a class of non-smooth mechanical systems using techniques from both fields. The book reviews...

This is the third Selecta of publications of Elliott Lieb, the first two being Stabil­ ity of Matter: From Atoms to Stars, edited by Walter Thirring, and Inequalities, edited by Michael Loss and Mary Beth Ruskai. A companion...

Tauberian theory compares summability methods for series and integrals, helps to decide when there is convergence, and provides asymptotic and remainder estimates. The author shows the development of the theory from the...

Differential equations are often used in mathematical models for technological processes or devices. However, the design of a differential mathematical model is crucial and difficult in engineering. As a hands-on...

Vladimir Arnold is one of the most outstanding mathematicians of our time Many of these problems are at the front line of current research