Partial differential equations : an introduction / Nita H. Shah and Mrudul Y. Jani.

Format:

Book

Author/Creator:

Shah, Nita H., author.

Jani, Mrudul Y., author.

Series:

Mathematical engineering, manufacturing, and management sciences.

Mathematical engineering, manufacturing, and management sciences

Language:

English

Subjects (All):

Differential equations, Partial.

Physical Description:

1 online resource (97 pages)

Edition:

First edition.

Place of Publication:

London ; New York, New York : Routledge, [2021]

Summary:

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.

Contents:

Intro

Half Title

Series Page

Title Page

Copyright Page

Contents

Acknowledgements

Preface

Authors

1. Introduction of Partial Differential Equations

1.1. Partial Differential Equations

1.2. Formation of Partial Differential Equations

1.3. Solution of Partial Differential Equations

1.3.1. Direct Integration Method to Solve Partial Differential Equations

Exercises

Answers

2. First-Order Partial Differential Equations

2.1. Linear First-Order Partial Differential Equations

2.1.1. Lagrange's Linear Equation of the First Order

2.2. Non-Linear First-Order Partial Differential Equations

2.2.1. Charpit Method

2.2.2. Special Types of First-Order Partial Differential Equations

3. Second- and Higher-Order Linear Partial Differential Equations

3.1. Homogeneous Linear Partial Differential Equations with Constant Coefficients

3.2. Classification of Second-Order Linear Partial Differential Equations

3.3. Method of Separation of Variables

4. Applications of Partial Differential Equations

4.1. One-Dimensional Wave Equation

4.1.1. The Solution of the Wave Equation by Separation of Variables

4.1.2. D'Alemberts' Solution of the Wave Equation

4.1.3. Duhamel's Principle for the One-Dimensional Wave Equation

4.2. One-Dimensional Heat Equation

4.3. Laplace's Equation

4.3.1. Laplacian in Cylindrical Coordinates

4.3.2. Laplacian in Spherical Coordinates

Multiple-Choice Questions

Fill in the Blanks

Bibliography

Index.

Notes:

Description based on print version record.

ISBN:

9781003105183

1003105181

9781000337167

1000337162

9781000337280

1000337286

OCLC:

1225287952