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About this book :-
Applications of Lie Groups to Differential Equations written by Peter J. Olver .
Symmetry methods have long been recognized to be of great importance for the study of the differential equations arising in mathematics, physics, engineering, and many other disciplines. The purpose of this book is to provide a solid introduction to those applications of Lie groups to differential equations which have proved to be useful in practice, including determination of symmetry groups, integration of orginary differential equations, construction of group-invariant solutions to partial differential equations, symmetries and conservation laws, generalized symmetries, and symmetry methods in Hamiltonian systems. The computational methods are presented so that grauate students and researchers in other fields can readily learn to use them. Following an exposition of the applications, the book develops the underlying theory. Many of the topics are presented in a novel way, with an emphasis on explicit examples and computations. Further examples, as well as new theoretical developments, appear in the exercises at the end of each chapter. This second edition contains a new section on formal symmetries and the calculus of pseudo-differential operators, simpler proofs of some theorems, new exercises, and a substantially updated bibiography.
Book Detail :-
Title: Applications of Lie Groups to Differential Equations
Author(s): Peter J. Olver
Publisher: Springer US
Series: Graduate Texts in Mathematics 107
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About Author :-
The author Peter J. Olver is an American mathematician whose primary research interests involve the applications of symmetry and Lie groups to differential equations. He has been a full professor at the University of Minnesota since 1985 and is currently head of their mathematics department. In 2003, Olver was one of the top 234 most cited mathematicians in the world.
In 2014, Olver became a fellow of the Society for Industrial and Applied Mathematics for "developing new geometric methods for differential equations leading to applications in fluid mechanics, elasticity, quantum mechanics, and image processing.". In addition, Olver is an elected fellow of the Institute of Physics and a fellow of the American Mathematical Society.
Olver is a prolific author, having written over 200 academic papers as of 2015. Of these, 137 have appeared or will appear in major refereed journals, 46 have appeared in conference proceedings and seven have appeared as appendices and chapters in books.
All Famous Books of this Author :-
Here is list all books, text books, editions, versions or solution manuals avaliable of this author, We recomended you to download all.
• Download PDF Applied Linear Algebra by Peter J. Olver, Chehrzad Shakiban
• Download PDF Applied Linear Algebra (Solution Manual) by Peter J. Olver, Chehrzad Shakiban
• Download PDF Applications of Lie Groups to Differential Equations by Peter J. Olver
• Download PDF Introduction to Partial Differential Equations by Peter J. Olver
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Book Contents :-
Applications of Lie Groups to Differential Equations written by Peter J. Olver cover the following topics. '
1. Introduction to Lie Groups
2. Symmetry Groups of Differential Equations
3. Group Invariant Solutions
4. Symmetry Groups and Conservation Laws
5. Generalized Symmetries
6. Finite Dimensional Hamiltonian Sysems
7. Hamiltonian Methods for Evolution Equations
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