6675
a760c35b-12e0-494d-85a0-ff699731357f
Solution of Ordinary Differential Equations by Continuous Groups
Emanuel, George
calibre (7.6.0) [https://calibre-ebook.com]
2000-11-29T18:03:11+00:00
<div><div>ch. 3 is on method of characteristics</div><div>cited on <a href="http://eqworld.ipmnet.ru/">EqWorld</a><hr><div class="review"> The book deals with the theory <span class="searchHighlight">of</span> Lie <span class="searchHighlight">groups</span> applied to solve <span class="searchHighlight">ordinary</span>
<span class="searchHighlight">differential</span> <span class="searchHighlight">equations</span>. The emphasis is much more on the practical
rather than the theoretical aspects <span class="searchHighlight">of</span> the subject. Accordingly, no
excessive weight is given to mathematical proofs and derivations, which
are nevertheless provided when necessary. Background material is
required only up to a minimum level, and necessary tools (some group
theory, the method <span class="searchHighlight">of</span> characteristics, etc.) are developed in the
course <span class="searchHighlight">of</span> the text. The mathematical apparatus usually required in
other books dedicated to <span class="searchHighlight">continuous</span> <span class="searchHighlight">groups</span> and <span class="searchHighlight">differential</span> <span class="searchHighlight">equations</span>
is not required in this work. This mathematical apparatus is a
consequence <span class="searchHighlight">of</span> the link between Lie algebra theory, one <span class="searchHighlight">of</span> the major
research areas <span class="searchHighlight">of</span> mathematics, and Lie <span class="searchHighlight">groups</span>. This is certainly one
<span class="searchHighlight">of</span> the main reasons why Lie <span class="searchHighlight">groups</span> for <span class="searchHighlight">differential</span> <span class="searchHighlight">equations</span> have not
even more widespread use. However, not much abstraction is needed as
long as one is interested only in solving <span class="searchHighlight">differential</span> <span class="searchHighlight">equations</span> <span class="searchHighlight">by</span>
Lie group techniques. This work comes to present, in a self-contained
way and in a clear style, the Lie <span class="searchHighlight">groups</span> symmetry approach for solving
<span class="searchHighlight">ordinary</span> <span class="searchHighlight">differential</span> <span class="searchHighlight">equations</span>. No exhaustive material is
presented. The topics covered include some theory <span class="searchHighlight">of</span> <span class="searchHighlight">groups</span> <span class="searchHighlight">of</span> <span class="searchHighlight">continuous</span>
transformations, the method <span class="searchHighlight">of</span> characteristics, invariance concepts,
the theory <span class="searchHighlight">of</span> extended <span class="searchHighlight">groups</span>, canonical coordinates for a Lie group,
application <span class="searchHighlight">of</span> Lie <span class="searchHighlight">groups</span> to first- and second-order <span class="searchHighlight">ordinary</span>
<span class="searchHighlight">differential</span> <span class="searchHighlight">equations</span> and to systems <span class="searchHighlight">of</span> first-order <span class="searchHighlight">ordinary</span>
<span class="searchHighlight">differential</span> <span class="searchHighlight">equations</span>. Some new techniques are shown here for the
first time, including the enlargement procedure created <span class="searchHighlight">by</span> the
author. Also, the work includes tables <span class="searchHighlight">of</span> <span class="searchHighlight">ordinary</span> <span class="searchHighlight">differential</span>
<span class="searchHighlight">equations</span> invariant under specified <span class="searchHighlight">groups</span>. Worked out examples
and exercises for the reader are provided throughout the book.
</div>
<span class="ReviewedBy">Reviewed by <a href="https://mathscinet.ams.org/mathscinet/search/author.html?mrauthid=357238">Fernando Haas</a></span><br><hr><p class="description">Written by an engineer and sharply focused on practical matters, this text explores the application of Lie groups to solving ordinary differential equations (ODEs). Although the mathematical proofs and derivations in are de-emphasized in favor of problem solving, the author retains the conceptual basis of continuous groups and relates the theory to problems in engineering and the sciences.The author has developed a number of new techniques that are published here for the first time, including the important and useful enlargement procedure. The author also introduces a new way of organizing tables reminiscent of that used for integral tables. These new methods and the unique organizational scheme allow a significant increase in the number of ODEs amenable to group-theory solution.Solution of Ordinary Differential Equations by Continuous Groups offers a self-contained treatment that presumes only a rudimentary exposure to ordinary differential equations. Replete with fully worked examples, it is the ideal self-study vehicle for upper division and graduate students and professionals in applied mathematics, engineering, and the sciences.</p></div></div>
CRC Press
9781584882435
uXS3ATa5WXAC
QA372 .E43 2000
928243627
eng
Differential equations
Numerical solutions
Continuous groups