Ordinary Differential Equations
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- Definition, reduction of explicit equations to first order
- Existence and uniqueness of solutions
- Differential inequalities
- Solutions to specific equations
OLD TOC
[edit | edit source]Ordinary Differential Equations
covering uses of and solutions to ordinary differential equations
![](http://upload.wikimedia.org/wikipedia/commons/thumb/7/75/Roessler_attractor.png/400px-Roessler_attractor.png)
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 | edit source]- 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
[edit | edit source]Differential 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.