# 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:**9660

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.

## Theory and Applications of Partial Functional Differential Equations

**Author**: Jianhong Wu**Publisher:**Springer Science & Business Media**ISBN:**9780387947716**Category:**Mathematics**Page:**432**View:**5438

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.

## 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:**4179

## Differential Equations and Their Applications

*An Introduction to Applied Mathematics*

**Author**: Martin Braun**Publisher:**Springer Science & Business Media**ISBN:**9780387978949**Category:**Mathematics**Page:**578**View:**569

Used in undergraduate classrooms across the USA, this is a clearly written, rigorous introduction to differential equations and their applications. Fully understandable to students who have had one year of calculus, this book distinguishes itself from other differential equations texts through its engaging application of the subject matter to interesting scenarios. This fourth edition incorporates earlier introductory material on bifurcation theory and adds a new chapter on Sturm-Liouville boundary value problems. Computer programs in C, Pascal, and Fortran are presented throughout the text to show readers how to apply differential equations towards quantitative problems.

## Fractional Differential Equations

*An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications*

**Author**: Igor Podlubny**Publisher:**Elsevier**ISBN:**9780080531984**Category:**Mathematics**Page:**340**View:**1485

This book is a landmark title in the continuous move from integer to non-integer in mathematics: from integer numbers to real numbers, from factorials to the gamma function, from integer-order models to models of an arbitrary order. For historical reasons, the word 'fractional' is used instead of the word 'arbitrary'. This book is written for readers who are new to the fields of fractional derivatives and fractional-order mathematical models, and feel that they need them for developing more adequate mathematical models. In this book, not only applied scientists, but also pure mathematicians will find fresh motivation for developing new methods and approaches in their fields of research. A reader will find in this book everything necessary for the initial study and immediate application of fractional derivatives fractional differential equations, including several necessary special functions, basic theory of fractional differentiation, uniqueness and existence theorems, analytical numerical methods of solution of fractional differential equations, and many inspiring examples of applications. A unique survey of many applications of fractional calculus Presents basic theory Includes a unified presentation of selected classical results, which are important for applications Provides many examples Contains a separate chapter of fractional order control systems, which opens new perspectives in control theory The first systematic consideration of Caputo's fractional derivative in comparison with other selected approaches Includes tables of fractional derivatives, which can be used for evaluation of all considered types of fractional derivatives

## Volterra Integral Equations

*An Introduction to Theory and Applications*

**Author**: Hermann Brunner**Publisher:**Cambridge University Press**ISBN:**1107098726**Category:**Mathematics**Page:**410**View:**8372

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

## An Introduction to the Theory of the Boltzmann Equation

**Author**: Stewart Harris**Publisher:**Courier Corporation**ISBN:**9780486438313**Category:**Science**Page:**221**View:**4018

This introductory graduate-level course for students of physics and engineering features detailed presentations of Boltzmann's equation, including applications using both Boltzmann's equation and the model Boltzmann equations developed within the text. It emphasizes physical aspects of the theory and offers a practical resource for researchers and other professionals. 1971 edition.

## Stability of Linear Delay Differential Equations

*A Numerical Approach with MATLAB*

**Author**: Dimitri Breda,Stefano Maset,Rossana Vermiglio**Publisher:**Springer**ISBN:**149392107X**Category:**Science**Page:**158**View:**8569

This book presents the authors' recent work on the numerical methods for the stability analysis of linear autonomous and periodic delay differential equations, which consist in applying pseudospectral techniques to discretize either the solution operator or the infinitesimal generator and in using the eigenvalues of the resulting matrices to approximate the exact spectra. The purpose of the book is to provide a complete and self-contained treatment, which includes the basic underlying mathematics and numerics, examples from population dynamics and engineering applications, and Matlab programs implementing the proposed numerical methods. A number of proofs is given to furnish a solid foundation, but the emphasis is on the (unifying) idea of the pseudospectral technique for the stability analysis of DDEs. It is aimed at advanced students and researchers in applied mathematics, in dynamical systems and in various fields of science and engineering, concerned with delay systems. A relevant feature of the book is that it also provides the Matlab codes to encourage the readers to experience the practical aspects. They could use the codes to test the theory and to analyze the performances of the methods on the given examples. Moreover, they could easily modify them to tackle the numerical stability analysis of their own delay models.

## Introduction to Partial Differential Equations with Applications

**Author**: E. C. Zachmanoglou,Dale W. Thoe**Publisher:**Courier Corporation**ISBN:**048613217X**Category:**Mathematics**Page:**432**View:**2859

This text explores the essentials of partial differential equations as applied to engineering and the physical sciences. Discusses ordinary differential equations, integral curves and surfaces of vector fields, the Cauchy-Kovalevsky theory, more. Problems and answers.

## 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:**3724

This is a solid introduction to applications of Lie groups to differential equations which have proved to be useful in practice. Following an exposition of the applications, the book develops the underlying theory, with many of the topics presented in a novel way, emphasizing explicit examples and computations. Further examples and new theoretical developments appear in the exercises at the end of each chapter.