Elements of Advanced Mathematical Analysis for Physics and Engineering - Filippo Gazzola

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Deep comprehension of applied sciences requires a solid knowledge of
Mathematical Analysis. For most of high level scientific research, the
good understanding of Functional Analysis and weak solutions to
differential equations is essential. This book aims to deal with the
main topics that are necessary to achieve such a knowledge. Still, this
is the goal of many other texts in advanced analysis; and then, what
would be a good reason to read or to consult this book? In order to
answer this question, let us introduce the three Authors. Alberto
Ferrero got his degree in Mathematics in 2000 and presently he is
researcher in Mathematical Analysis at the Università del Piemonte
Orientale. Filippo Gazzola got his degree in Mathematics in 1987 and he
is now full professor in Mathematical Analysis at the Politecnico di
Milano. Maurizio Zanotti got his degree in Mechanical Engineering in
2004 and presently he is structural and machine designer and lecturer
professor in Mathematical Analysis at the Politecnico di Milano.

The
three Authors, for the variety of their skills, decided to join their
expertises to write this book. One of the reasons that should encourage
its reading is that the presentation turns out to be a reasonable
compromise among the essential mathematical rigor, the importance of the
applications and the clearness, which is necessary to make the
reference work pleasant to the readers, even to the inexperienced ones.
The range of treated topics is quite wide and covers the main basic
notions of the scientific research which is based upon mathematical
models. We start from vector spaces and Lebesgue integral to reach the
frontier of theoretical research such as the study of critical exponents
for semilinear elliptic equations and recent problems in fluid
dynamics. This long route passes through the theory of Banach and
Hilbert spaces, Sobolev spaces, differential equations, Fourier and
Laplace transforms, before which we recall some appropriate tools of
Complex Analysis. We give all the proofs that have some didactic or
applicative interest, while we omit the ones which are too technical or
require too high level knowledge. This book has the ambitious purpose to
be useful to a broad variety of readers. The first possible
beneficiaries are of course the second or third year students of a
scientific course of degree: in what follows they will find the topics
that are necessary to approach more advanced studies in Mathematics and
in other fields, especially Physics and Engineering. This text could be
also useful to graduate students who want to start a Ph.D. course:
indeed it contains the matter of a multidisciplinary Ph.D. course given
by Filippo Gazzola for several years at Politecnico di Milano. Finally,
this book could be addressed also to the ones who have already left
education far-back but occasionally need to use mathematical tools: we
refer both to university professors and their research, and to
professionals and designers who want to model a certain phenomenon, but
also to the nostalgics of the good old days when they were students. It
is precisely for this last type of reader that we have also reported
some elementary topics, such as the properties of numerical sets and of
the integrals; moreover, every chapter is provided with examples and
specific exercises aimed at the involvement of the reader.


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ISBN :  9788874888955

Language : English

Formats : epub ,
mobi , PDF

 

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