Partial Differential Equations

An Introduction

Nita H. Shah, Mrudul Y. Jani

• Publisher: CRC Press
• Year: 2020
• Print ISBN: 9780367613228
• eBook ISBN: 9781000337280
• Topic: Business
• Subtopic: Operations
• Index: Business

Differential equations play a noticeable role in engineering, physics, economics, and other disciplines. They permit us to model changing forms in both mathematical and physical problems. These equations are precisely used when a deterministic relation containing some continuously varying quantities and their rates of change in space and/or time is recognized or postulated.

This book is intended to provide a straightforward introduction to the concept of partial differential equations. It provides a diversity of numerical examples framed to nurture the intellectual level of scholars. It includes enough examples to provide students with a clear concept and also offers short questions for comprehension. Construction of real-life problems is considered in the last chapter along with applications.

Research scholars and students working in the fields of engineering, physics, and different branches of mathematics need to learn the concepts of partial differential equations to solve their problems. This book will serve their needs instead of having to use more complex books that contain more concepts than needed.

1 Introduction of Partial Differential Equations

Partial differential equations arise quite often in numerous engineering and physical problems when the functions contain two or more independent variables. Several problems in fluid mechanics and solid mechanics, electromagnetic theory, heat transfer, vibrations, and many other thrust areas of engineering lead to the study of partial differential equations.

While solving the problems of an ordinary differential equation, one should find the general solution first and then determine the arbitrary constants using the initial conditions and finally evaluate the particular solution. But, the same method cannot be applicable in the case of partial differential equations. Instead, in most of the problems of partial differential equations in a region, initial conditions are used to get the particular solution; and boundary conditions are used to evaluate the arbitrary constants or arb...

Table of contents

• Cover
• Half Title
• Series Page
• Title Page
• Copyright Page
• Contents
• Acknowledgments
• Preface
• Authors
• Chapter 1 Introduction of Partial Differential Equations
• Chapter 2 First-Order Partial Differential Equations
• Chapter 3 Second- and Higher-Order Linear Partial Differential Equations
• Chapter 4 Applications of Partial Differential Equations
• Multiple-Choice Questions and Fill in the Blanks
• Bibliography
• Index