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partial-differential-equations

Order, linearity, and homogeneity of a PDE

taught

Classify a PDE by its highest derivative, whether it's linear in the unknown function, and whether it's homogeneous.

Taught in

Requires

Required by

Local knowledge map

Local knowledge map

Boundary condition types: Dirichlet, Neumann, Robin Characteristics for a system Characteristics with variable coefficients Constructing the heat kernel by self-similarity D'Alembert's formula for the wave equation Hyperbolicity: real, distinct eigenvalues Laplace's equation as a steady state Reducing a 2nd-order PDE to canonical form via characteristics Superposing four one-sided rectangle problems Classifying second-order PDEs: the discriminant test Deriving the heat equation Deriving the wave equation Solving linear first-order PDEs by characteristics The superposition principle for linear PDEs Writing a first-order system in matrix form Order, linearity, and homogeneity of a PDE Initial value problems and particular antiderivatives Second-order linear equations, standard form The superposition principle Linear vs. nonlinear differential equations What a differential equation is (order, solutions, general vs…

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