Differential calculus and equations

A monotone iterative technique is used to obtain monotone approximate solutions that converge to the solution of nonlinear problems of partial differential equations of elliptic, parabolic and hyperbolic type.

Aims to construct the inverse problem theory for ordinary non-self-adjoint differential operators of arbitary order on the half-line and on a finite interval.

This volume comprises selected papers presented at the Volterra Centennial Symposium and is dedicated to Volterra and the contribution of his work to the study of systems - an important concept in modern engineering.

This collection of 24 papers, which encompasses the construction and the qualitative as well as quantitative properties of solutions of Volterra, Fredholm, delay, impulse integral and integro-differential equations in various spaces on bounded as well as unbounded intervals, will conduce and spur further research in this direction.

Quantitative approximation methods apply in many diverse fields of research-neural networks, wavelets, partial differential equations, probability and statistics, functional analysis, and classical analysis to name just a few.

Although the study of classical thermoelasticity has provided information on linear systems, only recently have results on the asymptotic behavior completed our basic understanding of the generic behavior of solutions.

This Research Note explores existence and multiplicity questions for periodic solutions of first order, non-convex Hamiltonian systems.

Multivariate calculus, as traditionally presented, can overwhelm students who approach it directly from a one-variable calculus background.

This collection of carefully refereed and edited papers were originally presented at the Fourth International Conference on Difference Equations held in Poznan, Poland.

The book presents a more comprehensive treatment of transmutation operators associated with the Bessel operator, and explores many of their properties.

This volume presents a particular aspect of control theory-stabilization of programmed motion.

Combining mathematical theory, physical principles, and engineering problems, Generalized Calculus with Applications to Matter and Forces examines generalized functions, including the Heaviside unit jump and the Dirac unit impulse and its derivatives of all orders, in one and several dimensions.

Extremality results proved in this Monograph for an abstract operator equation provide the theoretical framework for developing new methods that allow the treatment of a variety of discontinuous initial and boundary value problems for both ordinary and partial differential equations, in explicit and implicit forms.

Although twistor theory originated as an approach to the unification of quantum theory and general relativity, twistor correspondences and their generalizations have provided powerful mathematical tools for studying problems in differential geometry, nonlinear equations, and representation theory.

Of considerable importance to numerical analysts, this text contains the proceedings of the 18th Dundee Biennial Conference on Numerical Analysis, featuring eminent analysts and current topics.

Based on the Working Conference on Boundary Control and Boundary Variation held in Sophia-Antipolis, France, this work provides important examinations of shape optimization and boundary control of hyperbolic systems, including free boundary problems and stabilization.

This useful reference provides recent results as well as entirely new material on control problems for partial differential equations.

This important new book sets forth a comprehensive description of various mathematical aspects of problems originating in numerical solution of hyperbolic systems of partial differential equations.

Celebrating the work of renowned mathematician Jerome A.

"e;Contains over 2500 equations and exhaustively covers not only nonparametrics but also parametric, semiparametric, frequentist, Bayesian, bootstrap, adaptive, univariate, and multivariate statistical methods, as well as practical uses of Markov chain models.

This series on the International Conference on Difference Equations and Applications has established a tradition within the mathematical community.

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.