Scientists and technicians know very well that any physical process can be analyzed by mathematical models, which are very often based on partial differential equations. Celebrated and historical examples are
given by the Maxwell equations, which admirably describe the electro-magnetic field, or Einstein’s equations in Relativity, or Schr¨odinger’s equation in Quantum Mechanics. During the last two hundred years, the research on partial differential equations has never ended. This book introduces Finite-Difference Method (FDM) and Finite Element Method (FEM) for parabolic, hyperbolic and elliptic partial differential equations (PDE).