Partial Differential Equations

Introductory notions for Partial Differential Equations (PDE’s) (definition of a PDE, initial and boundary conditions, important examples of linear and nonlinear PDE’s and motivation from physical sciences).  First-order equations: the method of characteristics and illustration of the method for linear and nonlinear examples. Second-order linear equations: classification of second order PDE’s. The one-dimensional wave equation: the Cauchy problem and d’ Alembert’s formula, domain of dependence and region of influence. The method of separation of variables, for the heat, wave and Laplace’s equation. The method of separation of variables for problems in higher dimensional domains. The maximum principle and applications. An introduction to Green’s functions and integral representations. An introduction to the main ideas of the calculus of variations for PDE’s.

• Strauss W. A., Partial Differential Equations: An introduction, 2^nd ed., John Wiley & Sons, Inc., 2008.
• Pinchover Y., Rubinstein J., An Introduction to Partial Differential Equations, Cambridge University Press, 2005.
• Haberman R., Applied Partial Differential Equations: with Fourier Series and Boundary Value Problems, 5^th ed., Pearson, 2013.