O'Reilly logo

Advanced Mathematics for Applications by Andrea Prosperetti

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

1

The Classical Field Equations

It is a remarkable aspect of the “unreasonable effectiveness of mathematics in the natural sciences” (Wigner 1960) that a handful of equations are sufficient to describe mathematically a vast number of physically disparate phenomena, at least at some level of approximation. Key reasons are the isotropy and uniformity of space-time (at least locally), the attendant conservation laws,1 and the useful range of applicability of linear approximations to constitutive relations.

After a very much abbreviated survey of the principal properties of vector fields, we present a summary of these fundamental equations and associated boundary conditions, and then describe several physical contexts in which they arise. ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required