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MATH4540J – Boundary Value Problems for Partial Differential Equations


Instructors (Faculty):


Pre-requisites: Vv255 and Vv256; or Vv285 and Vv286; or permission of instructor


Conservation laws and the derivation of PDEs from physical models; quasilinear first-order PDEs and
the method of characteristics; Burgers’s equation and weak solutions; shock waves; the eikonal equation and other
nonlinear first-order PDEs; classification of quasilinear second-order PDEs and their transformation into normal
form; boundary value problems of various kinds; the wave equation on an infinite string and d’Alembert’s method;
the heat equation in a finite bar and its solution through separation of variables; Fourier-Euler series and their
convergence; spaces of weighted square-integrable functions and the problem of best approximation; Sturm-
Liouville boundary value problems; separation of variables for nonhomogeneous one-dimensional evolution
equations; problems on infinite and semi-infinite bars and the Fourier transform; dispersive solutions; analysis of
the telegraph equation; separation of variables in higher dimensions; Bessel functions and Legendre polynomials;
multipole expansions in electromagnetics; the Poisson equation and properties of harmonic functions.

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