Differential calculus and equations

This volume presents a systematic and mathematically rigorous exposition of methods for studying linear partial differential equations.

A major step in differential games is determining an explicit form of the strategies of players who follow a certain optimality principle.

Hypersingular integrals arise as constructions inverse to potential-type operators and are realized by the methods of regularization and finite differences.

Linear nonautonomous equations arise as mathematical models in mechanics, chemistry, and biology.

The theory of distributions is most often presented as L.

Stability of Differential Equations with Aftereffect presents stability theory for differential equations concentrating on functional differential equations with delay, integro-differential equations, and related topics.

Line Integral Methods for Conservative Problems explains the numerical solution of differential equations within the framework of geometric integration, a branch of numerical analysis that devises numerical methods able to reproduce (in the discrete solution) relevant geometric properties of the continuous vector field.

Discover How Geometric Integrators Preserve the Main Qualitative Properties of Continuous Dynamical SystemsA Concise Introduction to Geometric Numerical Integration presents the main themes, techniques, and applications of geometric integrators for researchers in mathematics, physics, astronomy, and chemistry who are already familiar with numerical tools for solving differential equations.

This book contains about 3000 first-order partial differential equations with solutions.

Most books on linear operators are not easy to follow for students and researchers without an extensive background in mathematics.

The theory of linear Volterra integro-differential equations has been developing rapidly in the last three decades.

This monograph presents recent developments in spectral conditions for the existence of periodic and almost periodic solutions of inhomogenous equations in Banach Spaces.

Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations shows how four types of higher-order nonlinear evolution partial differential equations (PDEs) have many commonalities through their special quasilinear degenerate representations.

This second edition of The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance has been fully updated and revised to reflect recent developments in the theory and practical applications of wavelet transform methods.

Since publication of the first edition over a decade ago, Green's Functions with Applications has provided applied scientists and engineers with a systematic approach to the various methods available for deriving a Green's function.

Metasolutions of Parabolic Equations in Population Dynamics explores the dynamics of a generalized prototype of semilinear parabolic logistic problem.

Ten years after publication of the popular first edition of this volume, the index theorem continues to stand as a central result of modern mathematics-one of the most important foci for the interaction of topology, geometry, and analysis.

Mathematical Modelling with Case Studies: Using Maple and MATLAB, Third Edition provides students with hands-on modelling skills for a wide variety of problems involving differential equations that describe rates of change.

Differential equations play a vital role in the modeling of physical and engineering problems, such as those in solid and fluid mechanics, viscoelasticity, biology, physics, and many other areas.

The second edition of this book has a new title that more accurately reflects the table of contents.

Difference Equations: Theory, Applications and Advanced Topics, Third Edition provides a broad introduction to the mathematics of difference equations and some of their applications.

Several distinctive aspects make Dynamical Systems unique, including:treating the subject from a mathematical perspective with the proofs of most of the results included providing a careful review of background materials introducing ideas through examples and at a level accessible to a beginning graduate student<

Integral Transforms and Their Applications, Third Edition covers advanced mathematical methods for many applications in science and engineering.

This book is devoted to the study of non-linear evolution and difference equations of first or second order governed by maximal monotone operator.

Modeling and Inverse Problems in the Presence of Uncertainty collects recent research-including the authors' own substantial projects-on uncertainty propagation and quantification.

This book reflects a significant part of authors' research activity dur- ing the last ten years.

Stochastic Processes: General Theory starts with the fundamental existence theorem of Kolmogorov, together with several of its extensions to stochastic processes.

We come to know about the world in two distinctive ways: by direct perception and by application of rational reasoning which, in its highest form, is mathematical thinking.

This book covers the basic elements of difference equations and the tools of difference and sum calculus necessary for studying and solv- ing, primarily, ordinary linear difference equations.

The theory of functional equations has been developed in a rapid and productive way in the second half of the Twentieth Century.

Almost Automorphic and Almost Periodic Functions in Abstract Spaces introduces and develops the theory of almost automorphic vector-valued functions in Bochner's sense and the study of almost periodic functions in a locally convex space in a homogenous and unified manner.

This book originated from our interest in sea surface temperature variability.

Advances in Mechanics and Mathematics (AMMA) is intended to bridge the gap by providing multi-disciplinary publications.

The origins of the finite element method can be traced back to the 1950s when engineers started to solve numerically structural mechanics problems in aeronautics.

The years that have passed since the publication of the first edition of this book proved that the basic principles used to select and present the material made sense.

Goals and Emphasis of the Book Mathematicians have begun to find productive ways to incorporate computing power into the mathematics curriculum.

The use of the symmetries of a physical system in the study of its dynamics has a long history that goes back to the founders of c1assical mechanics.

For the past several years the Division of Applied Mathematics at Brown University has been teaching an extremely popular sophomore level differential equations course.

Analytic Extension is a mysteriously beautiful property of analytic functions.

This volume consists of papers presented in the special sessions on "e;Wave Phenomena and Related Topics"e;, and "e;Asymptotics and Homogenization"e; of the ISAAC'97 Congress held at the University of Delaware, during June 2-7, 1997.

In this book the theory of hyperbolic sets is developed, both for diffeomorphisms and flows, with an emphasis on shadowing.

There has been much recent progress in approximation algorithms for nonconvex continuous and discrete problems from both a theoretical and a practical perspective.

The First International Congress of the International Society for Analysis, its Applications and Computations (ISAAC'97) was held at the University of Delaware from 3 to 7 June 1997.

This book represents the first attempt at a unified picture for the pres- ence of the Gibbs (or Gibbs-Wilbraham) phenomenon in applications, its analysis and the different methods of filtering it out.

From a modelling point of view, it is more realistic to model a phenomenon by a dynamic system which incorporates both continuous and discrete times, namely, time as an arbitrary closed set of reals called time-scale or measure chain.