Partial Differential Equations of the first order. Characteristics, first integrals, Lagrange multipliers. Cauchy problem. Classification of 2nd order PDE's and reduction to canonical form. Hyperbolic, parabolic and elliptic equations of mathematical physics. Initial and boundary conditions. Travelling waves, characteristics, D'Alembert's solution. Separation of variables, eigenvalues and eigenfunctions. Source functions. Forced oscillations, resonance. Extreme value principles. Uniqueness and stability with respect to boundary and initial conditions.