Customer Reviews

Inverse Problems for Partial Differential Equations (Applied Mathematical Sciences)

5 star:		(0)
4 star:		(1)
3 star:		(0)
2 star:		(1)
1 star:		(0)

 

 

Isakov describes various ways to solve the inverse problem. In simplest form, one might have, say, Poisson's equation. But whereas the conventional problem is to find the potential, given the source, the inverse problem involves knowing the potential, or its gradient, and having to find the source.

The book draws together many results which thus far have mostly resided in maths journals. Isakov explains common themes to these research papers. Plus, and more importantly to some readers, he also gives the practical contexts in which the problems might arise. Such include determining the inside of a portion of a person's body, given various external measurements. Or finding structural data of a machine from external probes. The basic situation is that we are often outside something, and cannot physically go inside that object in a non-destructive manner.

The level of maths is broadly accessible to a reader with an undergrad major in maths or physics.

One would think that Springer-Verlag would be able to afford an editor
for the second edition of a book they charge $80 for. Apparently not.
This book is so full of typos, misspellings, and bad grammar that it is
essentially unreadable. The completely stochastic sprinkling of "the"'s
and "a"'s throughout the text (a particular grammar difficulty of native
Russian speakers) suggests that no editor has ever read this manuscript.

On the positive side, the mathematical expertise of the author in PDE
theory is not in question, and the book does contain useful technical
information on inverse problems once you strip away the typos and
decipher the grammar.