Reviews - What do customers think about Partial Differential Equations in Action: From Modelling to Theory (Universitext)?
a valuable new addition for students and Professionals Jun 14, 2008
Sandro Salsa's book: "Partial Differential Equations in Action: From modelling to Theory" is true to it's title. It guides the reader from the modeling stage to the theory, i.e. it is written from the point of view of an applied mathematician who wishes to understand the phenomenon that gives rise the PDE but who also seeks to gain an analytical understanding of the PDE before proceeding to it's numerical implementation. The book is written at a level suitable for both an advanced undergraduate or first year graduate school class at most American Institutions. Salsa's light but incisive touch in writing about PDE's is reminiscent, for those familiar with Gilbert Strang's books, with Strang's way of entertaining while at the same time challenging the reader. The book is unique in many ways. For instance the use of Fourier series in treating the diffusion equation is, in of itself standard, but Salsa's use of the energy method to show that the Fourier series solution is the unique solution is a nice illustration of how the book alternates between the practical and the more qualitative or technical aspects of the subject. For students of mathematical finance and mathematical biology, as well as for students of mathematical physics the treatment of random walks and their relations to Brownian motion and to the diffusion equation is the best I've ever seen. For students of mathematical finance there is a nice section on the Black-Scholes equation and a use of the maximum principle to show that call option prices are increasing with increasing volatility. For student in applied physics the sections on the wave equation and on hyperbolic problems are some of the best I've found available.
In later Chapters more advanced material introducing the student to the use of Sobolev spaces in solving Elliptic equations and evolution equations is carried out in a highly efficient and very clear fashion.
In summary, I highly recommend this book. Indeed, I think it is destined to become a classic.