Differential calculus and equations

Considering Poisson random measures as the driving sources for stochastic (partial) differential equations allows us to incorporate jumps and to model sudden, unexpected phenomena.

The purpose of this book is to give a quick and elementary, yet rigorous, presentation of the rudiments of the so-called theory of Viscosity Solutions which applies to fully nonlinear 1st and 2nd order Partial Differential Equations (PDE).

The purpose of the volume is to provide a support for a first course in Mathematics.

The purpose of the volume is to provide a support textbook for a second lecture course on Mathematical Analysis.

This book is an interdisciplinary introduction to optical collapse of laser beams, which is modelled by singular (blow-up) solutions of the nonlinear Schrodinger equation.

This book is a collection of papers from the 9th International ISAAC Congress held in 2013 in Krakow, Poland.

The international workshop on which this proceedings volume is based on brought together leading researchers in the field of elliptic and parabolic equations.

In this second volume, a general approach is developed to provide approximate parameterizations of the "e;small"e; scales by the "e;large"e; ones for a broad class of stochastic partial differential equations (SPDEs).

This first volume is concerned with the analytic derivation of explicit formulas for the leading-order Taylor approximations of (local) stochastic invariant manifolds associated with a broad class of nonlinear stochastic partial differential equations.

This textbook is for the standard, one-semester, junior-senior course that often goes by the title "e;Elementary Partial Differential Equations"e; or "e;Boundary Value Problems"e;.

In the field of Dynamical Systems, nonlinear iterative processes play an important role.

This book provides an introduction to dynamical systems with multiple time scales.

The book includes lectures given by the plenary and key speakers at the 9th International ISAAC Congress held 2013 in Krakow, Poland.

Many results, both from semi group theory itself and from the applied sciences, are phrased in discipline-specific languages and hence are hardly known to a broader community.

The techniques presented here are useful for solving mathematical contest problems in algebra and analysis.

This engaging text describes the development of singular perturbations, including its history, accumulating literature, and its current status.

This third edition is addressed to the mathematician or graduate student of mathematics - or even the well-prepared undergraduate - who would like, with a minimum of background and preparation, to understand some of the beautiful results at the heart of nonlinear analysis.

Topics covered in this volume (large deviations, differential geometry, asymptotic expansions, central limit theorems) give a full picture of the current advances in the application of asymptotic methods in mathematical finance, and thereby provide rigorous solutions to important mathematical and financial issues, such as implied volatility asymptotics, local volatility extrapolation, systemic risk and volatility estimation.

Investigating the correspondence between systems of partial differential equations and their analytic solutions using a formal approach, this monograph presents algorithms to determine the set of analytic solutions of such a system and conversely to find differential equations whose set of solutions coincides with a given parametrized set of analytic functions.

This book, based on a selection of talks given at a dedicated meeting in Cortona, Italy, in June 2013, shows the high degree of interaction between a number of fields related to applied sciences.

With the unifying theme of abstract evolutionary equations, both linear and nonlinear, in a complex environment, the book presents a multidisciplinary blend of topics, spanning the fields of theoretical and applied functional analysis, partial differential equations, probability theory and numerical analysis applied to various models coming from theoretical physics, biology, engineering and complexity theory.

Articles from many of the main contributors to recent progress in stochastic analysis are included in this volume, which provides a snapshot of the current state of the area and its ongoing developments.

This text is a rigorous treatment of the basic qualitative theory of ordinary differential equations, at the beginning graduate level.

This book gives a concise introduction to the basic techniques needed for the theoretical analysis of the Maxwell Equations, and filters in an elegant way the essential parts, e.

The present volume comprises survey articles on various fields of Differential-Algebraic Equations (DAEs), which have widespread applications in controlled dynamical systems, especially in mechanical and electrical engineering and a strong relation to (ordinary) differential equations.

By introducing a new stabilization methodology, this book characterizes the stability of a certain class of systems.

Targeted at mathematicians having at least a basic familiarity with classical bifurcation theory, this monograph provides a systematic classification and analysis of bifurcations without parameters in dynamical systems.

This volume of papers presented at the conference in honor of Calixto P.

These lecture notes provide a fresh approach to investigating singularly perturbed systems using asymptotic and geometrical techniques.

Paul Butzer, who is considered the academic father and grandfather of many prominent mathematicians, has established one of the best schools in approximation and sampling theory in the world.

This book collects the proceedings of the 2012 Abel Symposium, held at the Norwegian Academy of Science and Letters, Oslo.

This edited volume provides insights into and tools for the modeling, analysis, optimization, and control of large-scale networks in the life sciences and in engineering.

Lyons' rough path analysis has provided new insights in the analysis of stochastic differential equations and stochastic partial differential equations, such as the KPZ equation.

The book is a collection of contributions devoted to analytical, numerical and experimental techniques of dynamical systems, presented at the International Conference on Dynamical Systems: Theory and Applications, held in Lodz, Poland on December 2-5, 2013.

Delay differential and difference equations serve as models for a range of processes in biology, physics, engineering and control theory.

In April 2007, the Deutsche Forschungsgemeinschaft (DFG) approved the Priority Program 1324 "e;Mathematical Methods for Extracting Quantifiable Information from Complex Systems.

This book applies a step-by-step treatment of the current state-of-the-art of ordinary differential equations used in modeling of engineering systems/processes and beyond.

The book contains a selection of contributions given at the 23th Congress on Differential Equations and Applications (CEDYA) / 13th Congress of Applied Mathematics (CMA) that took place at Castellon, Spain, in 2013.

The book analyzes the existence of solitons, namely of finite energy solutions of field equations which exhibit stability properties.

This textbook, now in its second edition, provides a broad introduction to both continuous and discrete dynamical systems, the theory of which is motivated by examples from a wide range of disciplines.

This book presents mathematical models and numerical simulations of crowd dynamics.

This work introduces readers to the topic of maximal regularity for difference equations.

These proceedings were prepared in connection with the 14th International Conference on Approximation Theory, which was held April 7-10, 2013 in San Antonio, Texas.

The methods considered in the 7th conference on "e;Finite Volumes for Complex Applications"e; (Berlin, June 2014) have properties which offer distinct advantages for a number of applications.

This book collects papers presented during the European Workshop on High Order Nonlinear Numerical Methods for Evolutionary PDEs (HONOM 2013) that was held at INRIA Bordeaux Sud-Ouest, Talence, France in March, 2013.

This research monograph presents results to researchers in stochastic calculus, forward and backward stochastic differential equations, connections between diffusion processes and second order partial differential equations (PDEs), and financial mathematics.

The first volume of the proceedings of the 7th conference on "e;Finite Volumes for Complex Applications"e; (Berlin, June 2014) covers topics that include convergence and stability analysis, as well as investigations of these methods from the point of view of compatibility with physical principles.

This monograph presents the basic concepts of hyperbolic Lobachevsky geometry and their possible applications to modern nonlinear applied problems in mathematics and physics, summarizing the findings of roughly the last hundred years.

This book focuses on the constructive and practical aspects of spectral methods.

This book contains the proceedings of the 17th European Conference on Mathematics for Industry, ECMI2012, held in Lund, Sweden, July 2012, at which ECMI celebrated its 25th anniversary.