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

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
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