M-425, Partial Differential Equations

Classification and formation of PDE, First order equation, solution of the quasillinear equation by Lagrange Method, Cauchy problem, Second order linear equation, classification, solution factorization of operator and by separation of variables, Cauchy problem, Laplace’s equation, harmonic functions; Dirichlet, Neumann, and Mixed conditions; examples in Cartesian, polar, cylindrical, and spherical coordinates, Wave equation in one and two dimensions, solution by Fourier series , Heat equation in bounded and unbounded one-dimensional domain, solution by Fourier series and transform