# Search Results for "introduction-to-the-theory-and-applications-of-functional-differential-equations-mathematics-and-its-applications"

## Introduction to the Theory and Applications of Functional Differential Equations

**Author**: V. Kolmanovskii,A. Myshkis**Publisher:**Springer Science & Business Media**ISBN:**9401719659**Category:**Mathematics**Page:**648**View:**6991

This book covers the most important issues in the theory of functional differential equations and their applications for both deterministic and stochastic cases. Among the subjects treated are qualitative theory, stability, periodic solutions, optimal control and estimation, the theory of linear equations, and basic principles of mathematical modelling. The work, which treats many concrete problems in detail, gives a good overview of the entire field and will serve as a stimulating guide to further research. Audience: This volume will be of interest to researchers and (post)graduate students working in analysis, and in functional analysis in particular. It will also appeal to mathematical engineers, industrial mathematicians, mathematical system theoreticians and mathematical modellers.

## Applied Theory of Functional Differential Equations

**Author**: V. Kolmanovskii,A. Myshkis**Publisher:**Springer Science & Business Media**ISBN:**9401580847**Category:**Mathematics**Page:**234**View:**9189

This volume provides an introduction to the properties of functional differential equations and their applications in diverse fields such as immunology, nuclear power generation, heat transfer, signal processing, medicine and economics. In particular, it deals with problems and methods relating to systems having a memory (hereditary systems). The book contains eight chapters. Chapter 1 explains where functional differential equations come from and what sort of problems arise in applications. Chapter 2 gives a broad introduction to the basic principle involved and deals with systems having discrete and distributed delay. Chapters 3-5 are devoted to stability problems for retarded, neutral and stochastic functional differential equations. Problems of optimal control and estimation are considered in Chapters 6-8. For applied mathematicians, engineers, and physicists whose work involves mathematical modeling of hereditary systems. This volume can also be recommended as a supplementary text for graduate students who wish to become better acquainted with the properties and applications of functional differential equations.

## Theory and Applications of Partial Functional Differential Equations

**Author**: Jianhong Wu**Publisher:**Springer Science & Business Media**ISBN:**9780387947716**Category:**Mathematics**Page:**432**View:**3334

Abstract semilinear functional differential equations arise from many biological, chemical, and physical systems which are characterized by both spatial and temporal variables and exhibit various spatio-temporal patterns. The aim of this book is to provide an introduction of the qualitative theory and applications of these equations from the dynamical systems point of view. The required prerequisites for that book are at a level of a graduate student. The style of presentation will be appealing to people trained and interested in qualitative theory of ordinary and functional differential equations.

## Ordinary Differential Equations with Applications

**Author**: Carmen Chicone**Publisher:**Springer Science & Business Media**ISBN:**9780387985350**Category:**Mathematics**Page:**561**View:**4911

This graduate-level textbook offers students a rapid introduction to the language of ordinary differential equations followed by a careful treatment of the central topics of the qualitative theory. In addition, special attention is given to the origins and applications of differential equations in physical science and engineering.

## Applications of Lie's Theory of Ordinary and Partial Differential Equations

**Author**: L Dresner**Publisher:**CRC Press**ISBN:**9781420050783**Category:**Science**Page:**225**View:**1527

Lie's group theory of differential equations unifies the many ad hoc methods known for solving differential equations and provides powerful new ways to find solutions. The theory has applications to both ordinary and partial differential equations and is not restricted to linear equations. Applications of Lie's Theory of Ordinary and Partial Differential Equations provides a concise, simple introduction to the application of Lie's theory to the solution of differential equations. The author emphasizes clarity and immediacy of understanding rather than encyclopedic completeness, rigor, and generality. This enables readers to quickly grasp the essentials and start applying the methods to find solutions. The book includes worked examples and problems from a wide range of scientific and engineering fields.

## Volterra Integral Equations

*An Introduction to Theory and Applications*

**Author**: Hermann Brunner**Publisher:**Cambridge University Press**ISBN:**1107098726**Category:**Mathematics**Page:**410**View:**9852

This book offers a comprehensive introduction to the theory of linear and nonlinear Volterra integral equations. It includes applications and an extensive bibliography.

## Applications of Lie Groups to Differential Equations

**Author**: Peter J. Olver**Publisher:**Springer Science & Business Media**ISBN:**9780387950006**Category:**Language Arts & Disciplines**Page:**513**View:**404

A solid introduction to applications of Lie groups to differential equations which have proved to be useful in practice. The computational methods are presented such that graduates and researchers can readily learn to use them. Following an exposition of the applications, the book develops the underlying theory, with many of the topics presented in a novel way, emphasising explicit examples and computations. Further examples, as well as new theoretical developments, appear in the exercises at the end of each chapter.

## Nonlinear Functional Analysis and Its Applications

*II/ A: Linear Monotone Operators*

**Author**: E. Zeidler**Publisher:**Springer Science & Business Media**ISBN:**9780387968025**Category:**Mathematics**Page:**467**View:**9883

This is the second of a five-volume exposition of the main principles of nonlinear functional analysis and its applications to the natural sciences, economics, and numerical analysis. The presentation is self -contained and accessible to the nonspecialist. Part II concerns the theory of monotone operators. It is divided into two subvolumes, II/A and II/B, which form a unit. The present Part II/A is devoted to linear monotone operators. It serves as an elementary introduction to the modern functional analytic treatment of variational problems, integral equations, and partial differential equations of elliptic, parabolic and hyperbolic type. This book also represents an introduction to numerical functional analysis with applications to the Ritz method along with the method of finite elements, the Galerkin methods, and the difference method. Many exercises complement the text. The theory of monotone operators is closely related to Hilbert's rigorous justification of the Dirichlet principle, and to the 19th and 20th problems of Hilbert which he formulated in his famous Paris lecture in 1900, and which strongly influenced the development of analysis in the twentieth century.

## Introduction to the Theory of Functional Differential Equations

*Methods and Applications*

**Author**: N. V. Azbelev,Lina F. Rakhmatullina**Publisher:**Hindawi Publishing Corporation**ISBN:**9775945496**Category:**Electronic books**Page:**314**View:**1774

## Applied Functional Analysis

*Applications to Mathematical Physics*

**Author**: Eberhard Zeidler**Publisher:**Springer Science & Business Media**ISBN:**9780387944425**Category:**Mathematics**Page:**481**View:**5915

The first part of a self-contained, elementary textbook, combining linear functional analysis, nonlinear functional analysis, numerical functional analysis, and their substantial applications with each other. As such, the book addresses undergraduate students and beginning graduate students of mathematics, physics, and engineering who want to learn how functional analysis elegantly solves mathematical problems which relate to our real world. Applications concern ordinary and partial differential equations, the method of finite elements, integral equations, special functions, both the Schroedinger approach and the Feynman approach to quantum physics, and quantum statistics. As a prerequisite, readers should be familiar with some basic facts of calculus. The second part has been published under the title, Applied Functional Analysis: Main Principles and Their Applications.