This book offers students a solid introduction to numerical methods, such as finite differences and finite elements. Each chapter ends with a brief introduction to numerical approximation techniques for the specific problem at hand.

This book is designed as an advanced undergraduate or a first-year graduate course for students from various disciplines like applied mathematics, physics, engineering. It has evolved while teaching courses on partial differential equations during the last decade at the Politecnico of Milan. The main purpose of these courses was twofold: on the one hand, to train the students to appreciate the interplay between theory and modelling in problems arising in the applied sciences and on the other hand to give them a solid background for numerical methods, such as finite differences and finite elements.

This minimal knowledge on numerical approximation schemes represents an useful tool for training on model applications Numerical simulations help to put into action and visualize the theoretical properties of the models that will be analysed Each chapter ends with a brief introduction to numerical approximation techniques for the specific problem at hand Includes supplementary material: sn.pub/extras

Inhalt
Introduction.- Scalar Conservation Laws.- Diffusion.- The Laplace Equation.- Reaction-diffusion models.- Waves and vibrations.- Elements of Functional Analysis.- Variational formulation of elliptic problems.- Weak formulation of evolution problems.- Solutions.- Fourier Series.- Notes on ordinary differential equations.- Finite difference approximation of time dependent problems.- Identities and Formulas.