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Symmetriemethoden für Differentialgleichungen: Ein Leitfaden für Anfänger (Cambridge-Mathematik)

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Artikelzustand
Neuwertig: Buch, das wie neu aussieht, aber bereits gelesen wurde. Der Einband weist keine ...
EAN
9780521497862
ISBN
9780521497862
UPC
9780521497862
MPN
N/A
Level
Beginner

Über dieses Produkt

Product Identifiers

Publisher
Cambridge University Press
ISBN-10
0521497868
ISBN-13
9780521497862
eBay Product ID (ePID)
1653159

Product Key Features

Number of Pages
228 Pages
Language
English
Publication Name
Symmetry Methods for Differential Equations : a Beginner's Guide
Subject
Differential Equations / General, General
Publication Year
2000
Type
Textbook
Subject Area
Mathematics
Author
Peter E. Hydon
Series
Cambridge Texts in Applied Mathematics Ser.
Format
Trade Paperback

Dimensions

Item Height
1 in
Item Weight
12 Oz
Item Length
9.1 in
Item Width
6 in

Additional Product Features

Intended Audience
Scholarly & Professional
LCCN
99-031354
Dewey Edition
21
Reviews
'This new book by Peter Hydon ... is eminently suitable for advanced undergraduates and beginning postgraduate students ... Overall I thoroughly recommend this book and believe that it will be a useful textbook for introducing students to symmetry methods for differential equations.' Journal of Nonlinear Mathematical Physics, 'I really enjoyed reading this book and I am planning on using some parts for one of my next courses.' Monatshefte f r Mathematik, ‘Hydon’s book stands out as perhaps the best introductory level text currently available … Hydon’s book is extremely well-written, and a welcome addition to the literature on Lie’s methods. The author has clearly devoted a lot of effort to pedagogical details, and the exposition is designed to effortlessly bring the beginning student up to speed in basic applications of the method.’Peter Olver, ZAMM, 'I really enjoyed reading this book and I am planning on using some parts for one of my next courses.'Monatshefte für Mathematik, 'I really enjoyed reading this book and I am planning on using some parts for one of my next courses.' Monatshefte für Mathematik, 'This new book by Peter Hydon … is eminently suitable for advanced undergraduates and beginning postgraduate students … Overall I thoroughly recommend this book and believe that it will be a useful textbook for introducing students to symmetry methods for differential equations.' Journal of Nonlinear Mathematical Physics, '… a nice introduction to symmetry methods for ordinary and partial differential equations written with passion by a specialist … after a few pages it becomes clear that the book is written in a lucid and precise manner.'Zentralblatt MATH, 'Hydon's book stands out as perhaps the best introductory level text currently available ... Hydon's book is extremely well-written, and a welcome addition to the literature on Lie's methods. The author has clearly devoted a lot of effort to pedagogical details, and the exposition is designed to effortlessly bring the beginning student up to speed in basic applications of the method.' Peter Olver, ZAMM, "Throughout the text numerous examples are worked out in detail and the exercises have been well chosen. This is the most readable text on this material I have seen and I would recommend the book for self-study." Mathematical Reviews, 'Hydon's book stands out as perhaps the best introductory level text currently available ... Hydon's book is extremely well-written, and a welcome addition to the literature on Lie's methods. The author has clearly devoted a lot of effort to pedagogical details, and the exposition is designed to effortlessly bring the beginning student up to speed in basic applications of the method.'Peter Olver, ZAMM, 'This new book by Peter Hydon … is eminently suitable for advanced undergraduates and beginning postgraduate students … Overall I thoroughly recommend this book and believe that it will be a useful textbook for introducing students to symmetry methods for differential equations.'Journal of Nonlinear Mathematical Physics, 'It is very suitable for, and is specifically aimed at, postgraduate courses in the field. it is the more enjoyable for being written with infectious enthusiasm and there is a good selection of examples.' Mathematical Gazette, '... a nice introduction to symmetry methods for ordinary and partial differential equations written with passion by a specialist ... after a few pages it becomes clear that the book is written in a lucid and precise manner.' Zentralblatt MATH, 'Throughout the text numerous examples are worked out in detail and the exercises have been well chosen. this is the most readable text on this material I have seen and I would recommend the book for self-study (as an introduction).' MathSciNet, 'I really enjoyed reading this book and I am planning on using some parts for one of my next courses.' Monatshefte fr Mathematik, '… a nice introduction to symmetry methods for ordinary and partial differential equations written with passion by a specialist … after a few pages it becomes clear that the book is written in a lucid and precise manner.' Zentralblatt MATH, 'Hydon's book stands out as perhaps the best introductory level text currently available … Hydon's book is extremely well-written, and a welcome addition to the literature on Lie's methods. The author has clearly devoted a lot of effort to pedagogical details, and the exposition is designed to effortlessly bring the beginning student up to speed in basic applications of the method.' Peter Olver, ZAMM, ‘I really enjoyed reading this book and I am planning on using some parts for one of my next courses.’Monatshefte für Mathematik, "[A] valuable addition to the bookshelf for both the beginner and research worker in the field." Mathematical Geology
Series Volume Number
Series Number 22
Illustrated
Yes
Dewey Decimal
530.15/535
Table Of Content
1. Introduction to symmetries; 1.1. Symmetries of planar objects; 1.2. Symmetries of the simplest ODE; 1.3. The symmetry condition for first-order ODEs; 1.4. Lie symmetries solve first-order ODEs; 2. Lie symmetries of first order ODEs; 2.1. The action of Lie symmetries on the plane; 2.2. Canonical coordinates; 2.3. How to solve ODEs with Lie symmetries; 2.4. The linearized symmetry condition; 2.5. Symmetries and standard methods; 2.6. The infinitesimal generator; 3. How to find Lie point symmetries of ODEs; 3.1 The symmetry condition. 3.2. The determining equations for Lie point symmetries; 3.3. Linear ODEs; 3.4. Justification of the symmetry condition; 4. How to use a one-parameter Lie group; 4.1. Reduction of order using canonical coordinates; 4.2. Variational symmetries; 4.3. Invariant solutions; 5. Lie symmetries with several parameters; 5.1. Differential invariants and reduction of order; 5.2. The Lie algebra of point symmetry generators; 5.3. Stepwise integration of ODEs; 6. Solution of ODEs with multi-parameter Lie groups; 6.1 The basic method: exploiting solvability; 6.2. New symmetries obtained during reduction; 6.3. Integration of third-order ODEs with sl(2); 7. Techniques based on first integrals; 7.1. First integrals derived from symmetries; 7.2. Contact symmetries and dynamical symmetries; 7.3. Integrating factors; 7.4. Systems of ODEs; 8. How to obtain Lie point symmetries of PDEs; 8.1. Scalar PDEs with two dependent variables; 8.2. The linearized symmetry condition for general PDEs; 8.3. Finding symmetries by computer algebra; 9. Methods for obtaining exact solutions of PDEs; 9.1. Group-invariant solutions; 9.2. New solutions from known ones; 9.3. Nonclassical symmetries; 10. Classification of invariant solutions; 10.1. Equivalence of invariant solutions; 10.2. How to classify symmetry generators; 10.3. Optimal systems of invariant solutions; 11. Discrete symmetries; 11.1. Some uses of discrete symmetries; 11.2. How to obtain discrete symmetries from Lie symmetries; 11.3. Classification of discrete symmetries; 11.4. Examples.
Synopsis
Symmetry is the key to solving differential equations. There are many well-known techniques for obtaining exact solutions, but most of them are special cases of a few powerful symmetry methods. Furthermore, these methods can be applied to differential equations of an unfamiliar type; they do not rely on special 'tricks'. Instead, a given differential equation is forced to reveal its symmetries, which are then used to construct exact solutions. This book is a straightforward introduction to the subject, and is aimed at applied mathematicians, physicists, and engineers. The presentation is informal, using many worked examples to illustrate the main symmetry methods. It is written at a level suitable for postgraduates and advanced undergraduates, and is designed to enable the reader to master the main techniques quickly and easily. The book contains methods that have not previously appeared in a text. These include methods for obtaining discrete symmetries and integrating factors., An introduction to symmetry methods, informally written and aimed at applied mathematicians, physicists, and engineers., A good working knowledge of symmetry methods is very valuable for those working with mathematical models. This book is a straightforward introduction to the subject for applied mathematicians, physicists, and engineers. The informal presentation uses many worked examples to illustrate the major symmetry methods. Written at a level suitable for postgraduates and advanced undergraduates, the text will enable readers to master the main techniques quickly and easily. The book contains some methods not previously published in a text, including those methods for obtaining discrete symmetries and integrating factors., This book is a straightforward introduction to symmetry methods, and is aimed at applied mathematicians, physicists, and engineers. The presentation is informal, using many worked examples to illustrate the main symmetry methods. It is designed to enable postgraduates and advanced undergraduates to master the main techniques quickly and easily.
LC Classification Number
QC20.7.D5 H93 2000

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