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In this program

Sturm–Liouville theory
Eigenfunction expansions
Separation of variables for canonical PDEs
Fourier and Laplace transform methods for PDEs
Distribution theory for PDEs (introduction)
Well-posedness for initial-boundary value problems

Spectral and transform methods

Distribution theory for PDEs (introduction)

Advanced differential equations · STEM / applied

Topic

Distribution theory for PDEs (introduction)

Practice by unit: Spectral and transform methods

Graduate Advanced Differential Equations — scope drawn from open advanced DE / dynamical systems notes and typical US graduate advanced DE syllabi.

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