id: 06110075
dt: b
an: 2015b.00800
au: Henner, Victor; Belozerova, Tatyana; Khenner, Mikhail
ti: Ordinary and partial differential equations. With CD-ROM.
so: Boca Raton, FL: CRC Press (ISBN 978-1-4665-1500-0/hbk). xiv, 629~p. (2013).
py: 2013
pu: Boca Raton, FL: CRC Press
la: EN
cc: I75
ut: ordinary differential equations; solution techniques; partial differential
equations; Fourier method
ci:
li:
ab: As the authors point in the preface, “the primary motivation for writing
this textbook is that, to our knowledge, there has not been published a
comprehensive textbook that covers both ODE and PDE. A professor who
teaches ODE using this book can use the PDE sections to complement the
main ODE course. Professors teaching PDE very often face the situations
with students, despite having an ODE as prerequisite, do not remember
the techniques for solving ODE and thus can’t do well in the PDE
course." The book is divided into two parts dealing with ordinary and
partial differential equations. Material that can be found in most
standard books on ODEs is presented in Chapters 1‒6. Chapters 1‒3
present solution techniques for first and second order differential
equations, along with fundamental methods for linear equations and
systems. Chapter 4 deals with boundary value problems and
Sturm-Liouville problems, whereas an introduction to qualitative
methods of analysis and stability theory is provided in Chapter 5. A
brief account of Laplace transform can be found in Chapter 6. The first
part concludes with material on two topics which are not so popular in
modern textbooks but have widely been discussed in classical older
texts on ODEs: basic facts on integral equations and on series
solutions of ODEs, Bessel and Lagrange equations are collected in
Chapters 7 and 8. Part II is dedicated to PDEs. It starts with the
discussion of one- and two-dimensional hyperbolic equations in Chapters
10 and 11, proceeds with fundamental methods for one- and
two-dimensional parabolic equations in Chapters 12 and 13 and concludes
with the analysis of elliptic equations in Chapter 14. In this part,
the authors stress applications of the Fourier method for solving PDEs
and do not discuss other important techniques like the method of
characteristics, similarity methods, Green’s functions, Laplace
transforms, perturbation methods, etc. The text uses software developed
by the authors and provided on a CD which accompanies the book. For
ODEs, the program plots the graph of the analytical solution obtained
by the readers against the numerical solution suggested by the program
itself. More options are available for PDEs ‒ one can analyze the
dependence of the solutions on parameters, the accuracy of the
solution, the speed of the convergence of a series, etc. The text may
suit goals of instructors looking for a combination of fundamentals of
ODEs and PDEs in one course and can be also used as supplementary
reading.
rv: Svitlana P. Rogovchenko (Kristiansand)