# Ordinary Differential Equations

## OLD TOC

edit**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

edit- 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
- Higher Order Differential Equations
- Linear equations
- Integration methods

- 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
- Glossary
- List of Some Equations
- Help Needed
- Roadmap

## Sources

editDifferential Equations and Boundary Value Problems- C.H. Edwards Jr and David E. Penny

MIT Open Courseware- http://ocw.mit.edu/index.html

- Kong, Qingkai (0000).
*A Short Course in Ordinary Differential Equations*. Universe: Publisher. - Walter, Wolfgang (1998).
*Ordinary Differential Equations*. New York: Springer.