Differential Equations Methods And Applications
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Differential Equations: Methods and Applications
Mathematical equations which can be used to establish a relation between various functions and their derivatives are known as differential equations. They can be used for representing physical quantities, their rates of change, and a correlation between the two. Differential equations can be classified into ordinary differential equations, non-linear differential equations and partial differential equations. These can also be divided on the basis of their order. The order of a differential equation is determined by the term having the highest derivative. The various sub topics of this discipline are delay differential equations, integro-differential equations, stochastic differential equations, etc. The subject of differential equations finds extensive application in the fields of physics, engineering, chemistry, biology and economics. This book presents the complex subject of differential equations in the most comprehensible and easy to understand language. Different approaches, evaluations and methodologies on differential equations have been included herein. Those in search of information to further their knowledge will be greatly assisted by this book.
Differential Equations: Methods and Applications
This book presents a variety of techniques for solving ordinary differential equations analytically and features a wealth of examples. Focusing on the modeling of real-world phenomena, it begins with a basic introduction to differential equations, followed by linear and nonlinear first order equations and a detailed treatment of the second order linear equations. After presenting solution methods for the Laplace transform and power series, it lastly presents systems of equations and offers an introduction to the stability theory. To help readers practice the theory covered, two types of exercises are provided: those that illustrate the general theory, and others designed to expand on the text material. Detailed solutions to all the exercises are included. The book is excellently suited for use as a textbook for an undergraduate class (of all disciplines) in ordinary differential equations. .
Partial Differential Equations: Methods, Applications And Theories
Author: Harumi Hattori
language: en
Publisher: World Scientific Publishing Company
Release Date: 2013-01-28
This volume is an introductory level textbook for partial differential equations (PDE's) and suitable for a one-semester undergraduate level or two-semester graduate level course in PDE's or applied mathematics. Chapters One to Five are organized according to the equations and the basic PDE's are introduced in an easy to understand manner. They include the first-order equations and the three fundamental second-order equations, i.e. the heat, wave and Laplace equations. Through these equations we learn the types of problems, how we pose the problems, and the methods of solutions such as the separation of variables and the method of characteristics. The modeling aspects are explained as well. The methods introduced in earlier chapters are developed further in Chapters Six to Twelve. They include the Fourier series, the Fourier and the Laplace transforms, and the Green's functions. The equations in higher dimensions are also discussed in detail.This volume is application-oriented and rich in examples. Going through these examples, the reader is able to easily grasp the basics of PDE's.