id: 05819422
dt: b
an: 2012a.00697
au: Suzuki, Takashi; Senba, Takasi
ti: Applied analysis. Mathematical methods in natural science. 2nd ed.
so: Hackensack, NJ: World Scientific (ISBN 978-1-84816-652-3/hbk). xiv, 515~p.
(2011).
py: 2011
pu: Hackensack, NJ: World Scientific
la: EN
cc: M15 I95 U25
ut: mathematical applications; nonlinear partial differential equations;
chemotaxis; fundamental solutions; layer potential; iteration scheme;
textbooks
ci: Zbl 1053.00001
li:
ab: This volume provides a general introduction to applied analysis. The
authors are mainly concerned with vector analysis and its physical
motivation, calculus of variations, Fourier analysis, eigenfunction
expansion, and distribution of eigenvalues. The main mathematical
fields present in this volume are topological spaces, complex function
theory, real analysis, and abstract analysis. Several tools in linear
and nonlinear partial differential equations theory, such as
fundamental solutions, Perron’s method, layer potentials, and
iteration schemes, are described, as well as systematic descriptions of
the recent study of the blowup of the solution. This book also uses
fundamental ideas of applied mathematics to discuss recent developments
in nonlinear science, such as mathematical modeling of reinforced
random motion of particles, the semiconductor device equation in
applied physics, and chemotaxis in biology. Other relevant applications
include forward and backward self-similar transformations;
Michaelis-Menten reduction; Smoluchowski-Poisson equation. The content
of the book is divided into eight main chapters, as follows: I. Field
Formation; II. Geometric Objects; III. Calculus of Variations; IV.
Infinite-Dimensional Analysis; V. Scattering; VI. Random Motion of
Particles; VII. Linear PDE; VIII. Nonlinear PDE. Additional material
may be found in the three appendices of this volume: A. Catalogue of
Mathematical Theories; B. An Elliptic-Parabolic System; C. Commentary.
This well-written volume contains a large amount of material. The clear
style of exposition is worth noting because of the necessarily
technical nature of the subject matter. The book under review is mainly
addressed to students in higher-level undergraduate courses and for
self-study for both graduate and higher-level undergraduate students.
rv: Vicenţiu D. Rădulescu (Craiova)