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| Chapter | Topic | Trickiest Problem Type | |---------|----------------------------|--------------------------------------| | 3 | First-order linear PDEs | Method of characteristics with Cauchy data on a curve | | 6 | Separation of variables | Spherical coordinates with Legendre polynomials | | 8 | Wave equation | D’Alembert’s solution with non-zero initial velocity | | 11 | Non-homogeneous PDEs | Eigenfunction expansion with time-dependent forcing | | 12 | Fourier transforms | Solving the heat equation on an infinite rod with piecewise ICs | PDE homework help