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MTH-201.4 Introductory PDE

First order PDE - solutions by characteristics.

Classification of 2nd order PDEs, fundamental solutions and Green functions for Laplace, heat and wave equations, explicit solution formulas, harmonic functions, mean value property, maximum principles, uniqueness of solutions.

Solutions by other methods: separation of variables, similarity methods, transform methods, power series method, Cauchy- Kowalewsky theorem, Holmgren's uniqueness theorem.