Partial Differential Equations

Table of contents

1. Cover
2. Half Title
3. Series Page
4. Title Page
5. Copyright Page
6. Contents
7. Acknowledgments
8. Preface
9. Authors
10. Chapter 1 Introduction of Partial Differential Equations
    1. 1.1 Partial Differential Equations
    2. 1.2 Formation of Partial Differential Equations
    3. 1.3 Solution of Partial Differential Equations
       1. 1.3.1 Direct Integration Method to Solve Partial Differential Equations
    4. Exercises
    5. Answers
11. Chapter 2 First-Order Partial Differential Equations
    1. 2.1 Linear First-Order Partial Differential Equations
       1. 2.1.1 Lagrange’s Linear Equation of the First Order
    2. 2.2 Non-Linear First-Order Partial Differential Equations
       1. 2.2.1 Charpit Method
       2. 2.2.2 Special Types of First-Order Partial Differential Equations
    3. Exercises
    4. Answers
12. Chapter 3 Second- and Higher-Order Linear Partial Differential Equations
    1. 3.1 Homogeneous Linear Partial Differential Equations with Constant Coefficients
    2. 3.2 Classification of Second-Order Linear Partial Differential Equations
    3. 3.3 Method of Separation of Variables
    4. Exercises
    5. Answers
13. Chapter 4 Applications of Partial Differential Equations
    1. 4.1 One-Dimensional Wave Equation
       1. 4.1.1 The Solution of the Wave Equation by Separation of Variables
       2. 4.1.2 D’Alemberts’ Solution of the Wave Equation
       3. 4.1.3 Duhamel’s Principle for the One-Dimensional Wave Equation
    2. 4.2 One-Dimensional Heat Equation
    3. 4.3 Laplace’s Equation
       1. 4.3.1 Laplacian in Cylindrical Coordinates
       2. 4.3.2 Laplacian in Spherical Coordinates
    4. Exercises
    5. Answers
14. Multiple-Choice Questions and Fill in the Blanks
15. Bibliography
16. Index