Ordinary Differential Equations


 * /Definition, reduction of explicit equations to first order/
 * /Existence and uniqueness of solutions/
 * /Differential inequalities/
 * Solutions to specific equations
 * /One-dimensional time-independent equations of first or second order/

OLD TOC
Ordinary Differential Equations

covering uses of and solutions to ordinary differential equations

This book aims to lead the reader through the topic of differential equations, a vital area of modern mathematics and science. This book provides information about the whole area of differential equations, concentrating first on the simpler equations.

Table of contents

 * /Introduction/
 * /Preliminaries from calculus/
 * Form and Solutions of Differential Equations
 * First-Order Differential Equations
 * Separation of Variables
 * Linear Differential Equations
 * Exact Differential Equations
 * Substitution Methods
 * 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
 * Frobenius Solution to the Hypergeometric Equation
 * Legendre Equation
 * Bessel Equation
 * Mathieu Equation
 * Continued Fraction Solutions
 * Applications of Second-Order Differential Equations
 * 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
 * /Sturm-Liouville theory/
 * Systems of linear differential equations
 * /Nonlinear Systems/
 * /Green's Functions/
 * Existence and Uniqueness of Solutions
 * /The Picard–Lindelöf theorem/
 * /Peano's theorem/
 * /Blow-ups and moving to boundary/
 * /Global uniqueness of solution over interval/
 * /Maximum domain of solution/
 * 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
 * /Glossary/
 * /List of Some Equations/
 * Help Needed
 * /Roadmap/