Ordinary Differential Equations
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Ordinary differential equations are equations involving derivatives in one direction, to be solved for a solution curve.
Table of contents[edit]
Existence of ODEs[edit]
- Preliminaries from calculus
- The Picard–Lindelöf theorem
- Peano's theorem
- Blow-ups and moving to boundary
- Dependence on parameters
First order equations[edit]
- One-dimensional first-order linear equations
- Separable equations
- Integrating factor
- Exact equations
- Linearize
- Autonomous equations
- Derived cases 1: Rational functions in the right hand side
- Derived cases 2: Bernoulli equations, Ricatti equations
- Derived cases 3: Euler factors
Second order equations[edit]
- Homogeneous second order equations
- Nonhomogeneous second order equations:Method of undetermined coefficients
- Nonhomogeneous second order equations: Variations of parameters
- Nonhomogeneous second order equations: Reduction of order
Higher order equations[edit]
- Homogeneous higher order equations
- Nonhomogeneous higher order equations
- Linear autonomous equations of higher order with constant coefficients
- Linear autonomous equations of higher order with varying coefficients
Systems of equations[edit]
- Homogeneous linear systems with constant coefficients
- Nonhomogeneous linear systems: Diagonalization method
- Nonhomogeneous linear systems: Method of undetermined coefficients
- Nonhomogeneous linear systems: Integrating factor
- Nonhomogeneous linear systems: Variation of parameters
Laplace Transform[edit]
Nonlinear systems of equations[edit]
Lyapunov's stability results[edit]
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.