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 edit
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.