
EqWorld
The World of Mathematical Equations 

Mathematical Books >
Handbook of Mathematics for Engineers and Scientists > Contents > 12. Ordinary Differential Equations
12. Ordinary Differential Equations
 12.1. FirstOrder Differential Equations
 12.1.1. General Concepts. The Cauchy Problem. Uniqueness and Existence Theorems
 12.1.2. Equations Solved for the Derivative. Simplest Techniques of Integration
 12.1.3. Exact Differential Equations. Integrating Factor
 12.1.4. Riccati Equation
 12.1.5. Abel Equations of the First Kind
 12.1.6. Abel Equations of the Second Kind
 12.1.7. Equations Not Solved for the Derivative
 12.1.8. Contact Transformations
 12.1.9. Approximate Analytic Methods for Solution of Equations
 12.1.10. Numerical Integration of Differential Equations
 12.2. SecondOrder Linear Differential Equations
 12.2.1. Formulas for the General Solution. Some Transformations
 12.2.2. Representation of Solutions as a Series in the Independent Variable
 12.2.3. Asymptotic Solutions
 12.2.4. Boundary Value Problems
 12.2.5. Eigenvalue Problems
 12.2.6. Theorems on Estimates and Zeros of Solutions
 12.3. SecondOrder Nonlinear Differential Equations
 12.3.1. Form of the General Solution. Cauchy Problem
 12.3.2. Equations Admitting Reduction of Order
 12.3.3. Methods of Regular Series Expansions with Respect to the Independent Variable
 12.3.4. Movable Singularities of Solutions of Ordinary Differential Equations. Painleve Transcendents
 12.3.5. Perturbation Methods of Mechanics and Physics
 12.3.6. Galerkin Method and Its Modifications (Projection Methods)
 12.3.7. Iteration and Numerical Methods
 12.4. Linear Equations of Arbitrary Order
 12.4.1. Linear Equations with Constant Coefficients
 12.4.2. Linear Equations with Variable Coefficients
 12.4.3. Asymptotic Solutions of Linear Equations
 12.4.4. Collocation Method and Its Convergence
 12.5. Nonlinear Equations of Arbitrary Order
 12.5.1. Structure of the General Solution. Cauchy Problem
 12.5.2. Equations Admitting Reduction of Order
 12.6. Linear Systems of Ordinary Differential Equations
 12.6.1. Systems of Linear ConstantCoefficient Equations
 12.6.2. Systems of Linear VariableCoefficient Equations
 12.7. Nonlinear Systems of Ordinary Differential Equations
 12.7.1. Solutions and First Integrals. Uniqueness and Existence Theorems
 12.7.2. Integrable Combinations. Autonomous Systems of Equations
 12.7.3. Elements of Stability Theory
 References for Chapter 12
To book contents

The EqWorld website presents extensive information on solutions to
various classes of ordinary differential equations, partial differential
equations, integral equations, functional equations, and other mathematical
equations.
Copyright © 20042017 Andrei D. Polyanin
