# Search Results for "an-introduction-to-differential-equations-and-their-applications"

## An Introduction to Differential Equations and Their Applications

**Author**: Stanley J. Farlow**Publisher:**Courier Corporation**ISBN:**0486135136**Category:**Mathematics**Page:**640**View:**9874

This introductory text explores 1st- and 2nd-order differential equations, series solutions, the Laplace transform, difference equations, much more. Numerous figures, problems with solutions, notes. 1994 edition. Includes 268 figures and 23 tables.

## 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:**7203

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.

## Differential Equations and Their Applications

*An Introduction to Applied Mathematics*

**Author**: M. Braun**Publisher:**Springer Science & Business Media**ISBN:**1468401645**Category:**Mathematics**Page:**546**View:**4795

There are three major changes in the Third Edition of Differential Equations and Their Applications. First, we have completely rewritten the section on singular solutions of differential equations. A new section, 2.8.1, dealing with Euler equations has been added, and this section is used to motivate a greatly expanded treatment of singular equations in sections 2.8.2 and 2.8.3. Our second major change is the addition of a new section, 4.9, dealing with bifurcation theory, a subject of much current interest. We felt it desirable to give the reader a brief but nontrivial introduction to this important topic. Our third major change is in Section 2.6, where we have switched to the metric system of units. This change was requested by many of our readers. In addition to the above changes, we have updated the material on population models, and have revised the exercises in this section. Minor editorial changes have also been made throughout the text. New York City November. 1982 Martin Braun Preface to the First Edition This textbook is a unique blend of the theory of differential equations and their exciting application to "real world" problems. First, and foremost, it is a rigorous study of ordinary differential equations and can be fully understood by anyone who has completed one year of calculus. However, in addition to the traditional applications, it also contains many exciting "real life" problems. These applications are completely self contained.

## Differentialgleichungen und ihre Anwendungen

**Author**: Martin Braun**Publisher:**Springer-Verlag**ISBN:**3642973418**Category:**Mathematics**Page:**596**View:**4758

Dieses richtungsweisende Lehrbuch für die Anwendung der Mathematik in anderen Wissenschaftszweigen gibt eine Einführung in die Theorie der gewöhnlichen Differentialgleichungen. Fortran und APL-Programme geben den Studenten die Möglichkeit, verschiedene numerische Näherungsverfahren an ihrem PC selbst durchzurechnen. Aus den Besprechungen: "Die Darstellung ist überall mathematisch streng und zudem ungemein anregend. Abgesehen von manchen historischen Bemerkungen ... tragen dazu die vielen mit ausführlichem Hintergrund sehr eingehend entwickelten praktischen Anwendungen bei. ... Besondere Aufmerksamkeit wird der physikalisch und technisch so wichtigen Frage nach Stabilität von Lösungen eines Systems von Differentialgleichungen gewidmet. Das Buch ist wegen seiner geringen Voraussetzungen und vorzüglichen Didaktik schon für alle Studenten des 3. Semesters geeignet; seine eminent praktische Haltung empfiehlt es aber auch für alle Physiker, die mit Differentialgleichungen und ihren Anwendungen umzugehen haben." #Physikalische Blätter#

## An introduction to differential equations and their applications

**Author**: Stephen La Vern Campbell**Publisher:**Brooks/Cole**ISBN:**9780534094683**Category:**Mathematics**Page:**596**View:**1824

## An Introduction to Minimax Theorems and Their Applications to Differential Equations

**Author**: Maria do Rosário Grossinho,Stepan Agop Tersian**Publisher:**Springer Science & Business Media**ISBN:**1475733089**Category:**Mathematics**Page:**274**View:**6582

The book is intended to be an introduction to critical point theory and its applications to differential equations. Although the related material can be found in other books, the authors of this volume have had the following goals in mind: To present a survey of existing minimax theorems, To give applications to elliptic differential equations in bounded domains, To consider the dual variational method for problems with continuous and discontinuous nonlinearities, To present some elements of critical point theory for locally Lipschitz functionals and give applications to fourth-order differential equations with discontinuous nonlinearities, To study homoclinic solutions of differential equations via the variational methods. The contents of the book consist of seven chapters, each one divided into several sections. Audience: Graduate and post-graduate students as well as specialists in the fields of differential equations, variational methods and optimization.

## 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:**6352

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

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

**Author**: V. Kolmanovskii,A. Myshkis**Publisher:**Springer Science & Business Media**ISBN:**9780792355045**Category:**Mathematics**Page:**648**View:**5772

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.

## Differential Equations

*An Introduction to Basic Concepts, Results, and Applications*

**Author**: Ioan I. Vrabie**Publisher:**World Scientific**ISBN:**9814335622**Category:**Mathematics**Page:**460**View:**9906

This book presents, in a unitary frame and from a new perspective, the main concepts and results of one of the most fascinating branches of modern mathematics, namely differential equations, and offers the reader another point of view concerning a possible way to approach the problems of existence, uniqueness, approximation, and continuation of the solutions to a Cauchy problem. In addition, it contains simple introductions to some topics which are not usually included in classical textbooks: the exponential formula, conservation laws, generalized solutions, Caratheodory solutions, differential inclusions, variational inequalities, viability, invariance, gradient systems. In this new edition we have corrected several small errors and added the following new topics: Volterra Integral Equations and Elements of Calculus of Variations. Some problems and exercises, referring to these two new topics are also included. The bibliography has been updated and expanded.

## Introduction to random differential equations and their applications

**Author**: S. Kidambi Srinivasan,Ramabhadra Vasudevan**Publisher:**Elsevier Publishing Company**ISBN:**N.A**Category:**Mathematics**Page:**166**View:**9616

## Differential Equations

*An Introduction to Modern Methods and Applications*

**Author**: William E. Boyce**Publisher:**John Wiley & Sons**ISBN:**0470458240**Category:**Mathematics**Page:**704**View:**6029

Unlike other books in the market, this second edition presents differential equations consistent with the way scientists and engineers use modern methods in their work. Technology is used freely, with more emphasis on modeling, graphical representation, qualitative concepts, and geometric intuition than on theoretical issues. It also refers to larger-scale computations that computer algebra systems and DE solvers make possible. And more exercises and examples involving working with data and devising the model provide scientists and engineers with the tools needed to model complex real-world situations.

## Nonlinear Partial Differential Equations and Their Applications

*College de France Seminar*

**Author**: Doina Cioranescu,Jaques-Louis Lions**Publisher:**Elsevier**ISBN:**9780080537672**Category:**Mathematics**Page:**664**View:**3967

This book contains the written versions of lectures delivered since 1997 in the well-known weekly seminar on Applied Mathematics at the Collège de France in Paris, directed by Jacques-Louis Lions. It is the 14th and last of the series, due to the recent and untimely death of Professor Lions. The texts in this volume deal mostly with various aspects of the theory of nonlinear partial differential equations. They present both theoretical and applied results in many fields of growing importance such as Calculus of variations and optimal control, optimization, system theory and control, operations research, fluids and continuum mechanics, nonlinear dynamics, meteorology and climate, homogenization and material science, numerical analysis and scientific computations The book is of interest to everyone from postgraduate, who wishes to follow the most recent progress in these fields.

## Introduction to Differential Equations with Dynamical Systems

**Author**: Stephen L. Campbell,Richard Haberman**Publisher:**Princeton University Press**ISBN:**1400841321**Category:**Mathematics**Page:**472**View:**2875

Many textbooks on differential equations are written to be interesting to the teacher rather than the student. Introduction to Differential Equations with Dynamical Systems is directed toward students. This concise and up-to-date textbook addresses the challenges that undergraduate mathematics, engineering, and science students experience during a first course on differential equations. And, while covering all the standard parts of the subject, the book emphasizes linear constant coefficient equations and applications, including the topics essential to engineering students. Stephen Campbell and Richard Haberman--using carefully worded derivations, elementary explanations, and examples, exercises, and figures rather than theorems and proofs--have written a book that makes learning and teaching differential equations easier and more relevant. The book also presents elementary dynamical systems in a unique and flexible way that is suitable for all courses, regardless of length.

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

**Author**: L Dresner**Publisher:**CRC Press**ISBN:**9781420050783**Category:**Science**Page:**225**View:**4023

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.

## An Introduction to Variational Inequalities and Their Applications

**Author**: David Kinderlehrer,Guido Stampacchia**Publisher:**SIAM**ISBN:**0898714664**Category:**Mathematics**Page:**313**View:**6485

Unabridged republication is a resource for topics in elliptic equations and systems and free boundary problems.

## Solutions manual to accompany an introduction to differential equations and their applications

**Author**: Stephen La Vern Campbell**Publisher:**N.A**ISBN:**N.A**Category:**Differential equations**Page:**116**View:**8827

## Differential Equations

*An Introduction with Mathematica®*

**Author**: Clay C. Ross**Publisher:**Springer Science & Business Media**ISBN:**1475739494**Category:**Mathematics**Page:**434**View:**5920

The first edition (94301-3) was published in 1995 in TIMS and had 2264 regular US sales, 928 IC, and 679 bulk. This new edition updates the text to Mathematica 5.0 and offers a more extensive treatment of linear algebra. It has been thoroughly revised and corrected throughout.

## An Introduction to Neural Network Methods for Differential Equations

**Author**: Neha Yadav,Anupam Yadav,Manoj Kumar**Publisher:**Springer**ISBN:**9401798168**Category:**Mathematics**Page:**114**View:**1532

This book introduces a variety of neural network methods for solving differential equations arising in science and engineering. The emphasis is placed on a deep understanding of the neural network techniques, which has been presented in a mostly heuristic and intuitive manner. This approach will enable the reader to understand the working, efficiency and shortcomings of each neural network technique for solving differential equations. The objective of this book is to provide the reader with a sound understanding of the foundations of neural networks and a comprehensive introduction to neural network methods for solving differential equations together with recent developments in the techniques and their applications. The book comprises four major sections. Section I consists of a brief overview of differential equations and the relevant physical problems arising in science and engineering. Section II illustrates the history of neural networks starting from their beginnings in the 1940s through to the renewed interest of the 1980s. A general introduction to neural networks and learning technologies is presented in Section III. This section also includes the description of the multilayer perceptron and its learning methods. In Section IV, the different neural network methods for solving differential equations are introduced, including discussion of the most recent developments in the field. Advanced students and researchers in mathematics, computer science and various disciplines in science and engineering will find this book a valuable reference source.

## Ordinary Differential Equations

*An Introduction to Nonlinear Analysis*

**Author**: Herbert Amann**Publisher:**Walter de Gruyter**ISBN:**3110853698**Category:**Mathematics**Page:**467**View:**6713

The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.

## Laplace Transforms and Their Applications to Differential Equations

**Author**: N.W. McLachlan**Publisher:**Courier Corporation**ISBN:**0486798232**Category:**Mathematics**Page:**240**View:**7083

Classic graduate-level exposition covers theory and applications to ordinary and partial differential equations. Includes derivation of Laplace transforms of various functions, Laplace transform for a finite interval, and more. 1948 edition.