Section
Differential equations
Ordinary differential equations, evolution, stability and parameter dependence.
Core idea
Differential equations specify relations between unknown functions and their derivatives. The entries below begin with initial-value problems and develop quantitative tools for constructing and comparing solutions.
Ordinary differential equations
- Ordinary differential equation
- Initial-value problem for an ODE
- Linear ordinary differential system
- Picard iteration
- Picard–Lindelöf local existence and uniqueness theorem
- Gronwall inequality
- Integrating factor for a scalar linear ODE
- Fundamental matrix and principal propagator
- Duhamel formula for a linear ODE
- Peano–Baker series
- Smooth dependence of ODE solutions on parameters
- Continuous-dependence estimate for ODEs
- Continuation criterion for a finite-dimensional ODE
- Scalar comparison barriers for an ODE
- Regular singular point of a second-order linear ODE
- Regular inverse of Y d2/dY2 plus nu d/dY
Analytic dependence and coefficient estimates
Partial differential equations
The PDE subject introduces equations for functions of several variables. The fluid-dynamics subject develops incompressible transport and momentum equations.