Differential Equations

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Welcome to the Wikibook of

Differential Equations

covering uses of and solutions to ordinary differential equations

[edit] Aim of this Book

This book aims to lead the reader through the topic of differential equations, a vital area of modern mathematics and science. It is hoped that this book will provide information about the whole area of differential equations, but for the moment it will concentrate on the simpler equations.

[edit] Print Versions

In the future, I hope to be able to post a printable version of this Wikibook, but at the moment, the focus lies on writing it.

[edit] 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

[edit] Glossary

[edit] List of Some Equations

[edit] Help Needed

[edit] Roadmap

[edit] Sources

Differential Equations and Boundary Value Problems- C.H. Edwards Jr and David E. Penny
MIT Open Courseware- http://ocw.mit.edu/index.html

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