Differential Equations: Theory and Applications

Differential Equations: Theory and Applications examines several aspects of differential equation including an extensive explanation of higher order differential equation. It includes applications of differential equations in mechanics and different types of differential equations. Provides the reader with clear understanding of theory and application of differential equations. Cover Half Title Page Title Page Copyright Page About the Author Table of Contents Preface Chapter 1 Basic Concepts of Differential Equations 1.1. Introduction 1.2. The Bernoulli Equation 1.3. Differential Equations of Higher Order 1.4. The Wronskian Chapter 2 Fundamental Concepts of Partial Differential Equations 2.1. Introduction 2.2. Classification of Second Order PDE 2.3. Summary and Discussion 2.4. Classification of Second Order PDE Chapter 3 Application of Differential Equations In Mechanics 3.1. Introduction 3.2. Projectile Motion 3.3. Summary and Discussion Chapter 4 Elliptic Differential Equation 4.1. Introduction 4.2. Boundary Value Problem (BVPs) 4.3. Some Important Mathematical Tools 4.4. Properties Of Harmonic Functions 4.5. Separation Of Variables 4.6. Dirichlet Problem For A Rectangle 4.7. The Neumann Problem For A Rectangle 4.8. Interior Dirichlet Problem For A Circle 4.9. Exterior Dirichlet Problem For A Circle 4.10. Interior Neumann Problem For A Circle 4.11. Solution Of Laplace Equation In Cylindrical Coordinates 4.12. Solution Of Laplace Equation In Spherical Coordinates 4.13. Miscellaneous Example 4.14. Summary And Discussions Chapter 5 Hyperbolic Differential Equation 5.1 Introduction 5.2. Solution Of One-Dimensional Wave Equation by Canonical Reduction 5.3. The Initial Value Problem; D’alembert’s Solution 5.4. Summary And Discussion Chapter 6 Parabolic Differential Equations 6.1. Introduction 6.2. Boundary Conditions 6.3. Elementary Solutions Of The Diffusion Equation 6.4. Dirac Delta Function 6.5. Separation Of Variables Method 6.6. Maximum-Minimum Principle and Consequences 6.7. Miscellaneous Example 6.8. Boundary Conditions Chapter 7 Laplace Transform Methods 7.1. Introduction 7.2. Transform Of Some Elementary Functions 7.3. Properties Of Laplace Transform 7.4. Transform Of A Periodic Function 7.5. Transform Of Error Function 7.6. Transform Of Bessel’s Function 7.7. Transform Of Dirac Delta Function 7.8. Convolution Theorem (Faltung Theorem) Chapter 8 Green’s Function 8.1. Introduction 8.2. The Eigenfunction Method 8.3. Summary and Discussion References Index