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"This book stems from the long standing teaching experience of the authors in the courses on Numerical methods in engineering and numerical methods for partial differential equations given to undergraduate and graduate students of Politecnico di Milano (Italy), EPFL Lausanne (Switzerland), University of Bergamo (Italy) and Emory University (Atlanta, USA). It aims at introducing students to the numerical approximation of partial differential equations (PDEs). One of the difficulties of this subject is to identify the right trade-off between theoretical concepts and their actual use in practice. With this collection of examples and exercises we try to address this issue by illustrating "academic" examples which focus on basic concepts of numerical analysis as well as problems derived from practical application which the student is encouraged to formalize in terms of PDEs, analyze and solve. The latter examples are derived from the experience of the authors in research project developed in collaboration with scientists of different fields (biology, medicine, etc.) and industry. "

"Aimed at students and researchers entering the field, this pedagogical introduction to numerical relativity will also interest scientists seeking a broad survey of its challenges and achievements. --Assuming only a basic knowledge of classical general relativity, this textbook develops the mathematical formalism from first principles, then highlights some of the pioneering simulations involving black holes and neutron stars, gravitational collapse and gravitational waves. --Applications include calculations of coalescing binary black holes and binary neutron stars, rotating stars, colliding star clusters, gravitational and magnetorotational collapse, critical phenomena, the generation of gravitational waves, and many more. --"...an excellent introduction...covering both mathematical aspects and numerical techniques... The authors are world leaders in numerical relativity...This book will soon become the standard advanced text for younger researchers entering the field and will also serve as the authoritative reference for senior researchers..." Abhay Ashtekhar, Director, Institute for Gravitation and the Cosmos, The Pennsylvania State University --"Numerical relativity has come of age...Two leading experts give a lucid as well as richly detailed account building a bridge from the basics to current research-highly recommended." Bernd Brugmann, Friedrich-Schiller-Universitot --"...what a book this is!...a genuine learning manual...exceedingly well written...covers virtually all aspects of numerical relativity...replete with beautiful and helpful diagrams...a useful reference to the researcher and a source of enlightenment to many a student...." Eric Poisson, University of Guelph --"Baumgarte and Shapiro are established leaders in this subject. Their book is a timely contribution to the literature, and the ideal primer for researchers newly attracted to the burgeoning field of computational relativity." Martin Rees, Astronomer Royal and Master of Trinity College, Cambridge --Book Jacket."

"This comprehensive book not only introduces the C and C++ programming languages but also shows how to use them in the numerical solution of partial differential equations (PDEs). It leads the reader through the entire solution process, from the original PDE, through the discretization stage, to the numerical solution of the resulting algebraic system. The well-debugged and tested code segments implement the numerical methods efficiently and transparently. Basic and advanced numerical methods are introduced and implemented easily and efficiently in a unified object-oriented approach."