User:Dnessett/Print Version of Differential Equations

Table of Contents

 * Introduction


 * Form and Solutions of Differential Equations


 * Formation of Differential Equations


 * First-Order Differential Equations


 * Exact Differential Equations
 * Separable Variables
 * Substitution Methods
 * Linear Differential Equations
 * Bernoulli Equations
 * Ricatti Equations
 * Orthogonal and Oblique Trajectories
 * Equations of higher degrees
 * Equations without x or y
 * Equations that are homogeneous in x and y
 * d'Alembert's Equation
 * Clairaut Equations
 * Legendre Transformations
 * Graphing Differential Equations


 * Second-Order Differential Equations
 * Constant Coefficients
 * Series Solutions
 * Hypergeometric Equation
 * Legendre Equation
 * Bessel Equation
 * Mathieu Equation
 * Continued Fraction Solutions


 * Higher Order Differential Equations
 * Linear equations
 * General Linear Equations
 * Infinite Series Solutions to Linear Equations
 * Integration methods
 * Laplace Transform
 * Bessel Function
 * Euler Transform
 * Mellin Transform
 * Hypergeometric Series
 * Double Integration


 * Applications of Second-Order Differential Equations


 * Sturm-Liouville theory


 * Systems of linear differential equations


 * Nonlinear systems


 * Green's Functions


 * Existence of solutions to ODEs
 * The Successive Approximations Method of Proof
 * Applications to Linear Equations
 * The Cauchy-Lipschitz Method of Proof
 * Existence Theorems for Complex Numbers


 * Continuous Transformation Groups
 * Infinitesimal Transformations
 * Invariant Functions

Roadmap
= 1. Introduction =

= 2. Structure of Differential Equations =

= 3. Formation of Differential Equations =

= 4. First Order Differential Equations =

= 5. Second Order Differential Equations =

= 6. Higher Order Differential Equations =

= 7. Applications of Second Order Differential Equations =

= 8. Sturm-Liouville theory =

= 9. System of Linear Differential Equations =

= 10. Non-Linear Systems =

= 11. Green's Functions =

= 12. Existence of Solutions to ODEs =

= 13. Continuous Transformation Groups =

= GNU Free Documentation License =