Differential Equations: Theory and Applications

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