Differential Equations

From Wikibooks, the open-content textbooks collection

The Rössler Attractor. This chaotic system is generated by a set of ordinary differential equations.

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] 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
  • Frobenius Solution to the 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
• Glossary
• List of Some Equations
• Help Needed
• 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