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partial-differential-equations

Solving linear first-order PDEs by characteristics

taught

Reduce a linear first-order PDE to an ordinary differential equation along each characteristic curve, and integrate it.

Taught in

Requires

Required by

Local knowledge map

Local knowledge map

Characteristics for quasilinear PDEs Domain of dependence, range of influence, and finite propagatio… Duhamel's principle for the wave equation Representing a solution as a convolution Riemann invariants The Green's function for the wave equation Characteristics for a system Characteristics with variable coefficients D'Alembert's formula for the wave equation Reducing a 2nd-order PDE to canonical form via characteristics Solving linear first-order PDEs by characteristics Boundary-value problems, contrasted with IVPs Classifying second-order PDEs: the discriminant test Deriving the heat equation Deriving the wave equation Diagonalizing to canonical form Indefinite integral notation and the Net Change Theorem The superposition principle for linear PDEs Writing a first-order system in matrix form Initial value problems and particular antiderivatives Order, linearity, and homogeneity of a PDE Basic antiderivative rules -- power, constant multiple,… Linear vs. nonlinear differential equations

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