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