Alfio Quarteroni is Professor and Director of MATHICSE at EPFL, Lausanne (Switzerland), and Professor and Director of MOX at the Politecnico di Milano (Italy). Author of 20 books (mostly published with Springer) and of more than 200 papers, he is actually one of the strongest and reliable mathematicians in the world in the field of Modelling and SC. Fausto Saleri was Professor of Numerical Analysis at Politecnico di Milano (Italy) until 2007. Author of 11 books published with Springer, he worked on the approximation of partial differential equations, giving important contributions to the study of shallow water equations and to the development of scientific software libraries for finite elements. Paola Gervasio is Associate Professor of Numerical Analysis at University of Brescia (Italy) since 2005. Her research work focuses on the approximation of partial differential equations by spectral methods and domain decomposition techniques.

• 1. What can' t be ignored.- 2. Nonlinear equations.- 3. Approximation of functions and data.- 4. Numerical differentiation and integration.- 5. Linear systems.- 6. Eigenvalues and eigenvectors.- 7. Numerical optimization.- 8. Ordinary differential equations.- 9. Numerical approximation of boundary-value problems.- 10. Solutions of the exercises.- References.- Index.

Alfio Quarteroni is Professor and Director of MATHICSE at EPFL, Lausanne (Switzerland), and Professor and Director of MOX at the Politecnico di Milano (Italy). Author of 20 books (mostly published with Springer) and of more than 200 papers, he is actually one of the strongest and reliable mathematicians in the world in the field of Modelling and SC. Fausto Saleri was Professor of Numerical Analysis at Politecnico di Milano (Italy) until 2007. Author of 11 books published with Springer, he worked on the approximation of partial differential equations, giving important contributions to the study of shallow water equations and to the development of scientific software libraries for finite elements. Paola Gervasio is Associate Professor of Numerical Analysis at University of Brescia (Italy) since 2005. Her research work focuses on the approximation of partial differential equations by spectral methods and domain decomposition techniques.

• 1. What can' t be ignored.- 2. Nonlinear equations.- 3. Approximation of functions and data.- 4. Numerical differentiation and integration.- 5. Linear systems.- 6. Eigenvalues and eigenvectors.- 7. Numerical optimization.- 8. Ordinary differential equations.- 9. Numerical approximation of boundary-value problems.- 10. Solutions of the exercises.- References.- Index.