Differential Equations Tags

# Differential Equations Tags

## Introductory concepts

- Verification of solutions
- Classifications of differential equations

## First order differential equations

- Linear
- Exact
- Separable
- Substitutions
- Equilibrium points and phase lines
- Direction fields
- Integrating factors
- Bifurcations
- Existence and uniqueness

## Higher order differential equations

- Reduction of order
- Linear, constant coefficients, homogeneous
- Euler equations
- Undetermined coefficients
- Variation of parameters
- Boundary value problems
- Linear independence
- Differential operators
- Existence and uniqueness

## Laplace transforms

- Basic transformations
- Inverse transformations
- Convolutions
- Impulse functions
- Step functions
- Shift functions
- Solving initial-value problems

## Systems of differential equations

- Matrix notation for systems
- Distinct real eigenvalues
- Complex eigenvalues
- Repeated eigenvalues
- Reduction to first order systems
- Nonhomogeneous systems
- Phase planes
- Nonlinear systems

## Numerical methods

- Euler
- Runge-Kutta
- Systems

## Series solutions

- Ordinary point
- Singular point
- Bessel functions

## Partial differential equations

- Classification
- Verification of solutions
- Heat equation
- Wave equation
- Laplace's equation
- Other separable equations
- Fourier series
- Inhomogenous equations