Elementary Lie Group Analysis and Ordinary Differential Equations 1st Edition by Ibragimov (PDF)

Description

Lie group analysis, based on symmetry and invariance principles, is the only systematic method for solving nonlinear differential equations analytically. One of Lie’s striking achievements was the discovery that the majority of classical devices for integration of special types of ordinary differential equations could be explained and deduced by his theory. Moreover, this theory provides a universal tool for tackling considerable numbers of differential equations when other means of integration fail. * This is the first modern text on ordinary differential equations where the basic integration methods are derived from Lie group theory * Includes a concise and self contained introduction to differential equations * Easy to follow and comprehensive introduction to Lie group analysis * The methods described in this book have many applications The author provides students and their teachers with a flexible text for undergraduate and postgraduate courses, spanning a variety of topics from the basic theory through to its many applications. The philosophy of Lie groups has become an essential part of the mathematical culture for anyone investigating mathematical models of physical, engineering and natural problems.

User’s Reviews

Editorial Reviews: Review “…this is the first self-contained university text on ordinary differential equations…” (Zentralblatt Math, Vol.1047, No.22, 2004) From the Inside Flap Lie group analysis, based on symmetry and invariance principles, is the only systematic method for solving nonlinear differential equations analytically. One of Lie’s striking achievements was the discovery that the majority of classical devices for integration of special types of ordinary differential equations could be explained and deduced by his theory. Moreover, this theory provides a universal tool for tackling considerable numbers of differential equations when other means of integration fail. * This is the first modern text on ordinary differential equations where the basic integration methods are derived from Lie group theory * Includes a concise and self contained introduction to differential equations * Easy to follow and comprehensive introduction to Lie group analysis * The methods described in this book have many applications The author provides students and their teachers with a flexible text for undergraduate and postgraduate courses, spanning a variety of topics from the basic theory through to its many applications. The philosophy of Lie groups has become an essential part of the mathematical culture for anyone investigating mathematical models of physical, engineering and natural problems. From the Back Cover Lie group analysis, based on symmetry and invariance principles, is the only systematic method for solving nonlinear differential equations analytically. One of Lie’s striking achievements was the discovery that the majority of classical devices for integration of special types of ordinary differential equations could be explained and deduced by his theory. Moreover, this theory provides a universal tool for tackling considerable numbers of differential equations when other means of integration fail. * This is the first modern text on ordinary differential equations where the basic integration methods are derived from Lie group theory * Includes a concise and self contained introduction to differential equations * Easy to follow and comprehensive introduction to Lie group analysis * The methods described in this book have many applications The author provides students and their teachers with a flexible text for undergraduate and postgraduate courses, spanning a variety of topics from the basic theory through to its many applications. The philosophy of Lie groups has become an essential part of the mathematical culture for anyone investigating mathematical models of physical, engineering and natural problems. About the Author N. H. Ibragimov is the author of Elementary Lie Group Analysis and Ordinary Differential Equations, published by Wiley. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I wonder why this book is not one of the most famous mathematical textson differential equations.It’s excellent coverage of the subject doesn’tmatch the (small,I believe) amount of acknowledgment and citations it has received.I think that this book presents mathematics in the way it should be presented: first describe the problems,then emphasize the weakness of the existing theory to solve them,and then procceed to the development of a new theory,which provides solutions in a more systematic and powerful way than the old one.I wonder…(maby because we’re taught to judge math books by the “accessibility axiom”:the less accessible a math book is,the better it should be considered)

⭐It is wonderfull to find in this book that the need for the theory flows directly from ordinary problems in diferential equations, in one or more variables. The text is adorned with good physical examples and many otherwise mysterious things fit in place.

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