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OverviewThis book provides an introduction to Lie Theory for first year graduate students and professional physicists who may not have across the theory in their studies. In particular, it is a summary overview of the theory of finite groups, a brief description of a manifold, and then an informal development of the theory of one-parameter Lie groups, especially as they apply to ordinary differential equations. The treatment is informal, but systematic and reasonably self-contained, as it assumes a familiarity with basic physics and applied calculus, but it does not assume additional mathematical training. Interested readers should have a fair chance of finding symmetries of a second order differential equation and should be able to use it to reduce the order of the differential equation. Full Product DetailsAuthor: William A. SchwalmPublisher: Morgan & Claypool Publishers Imprint: Morgan & Claypool Publishers Dimensions: Width: 17.80cm , Height: 0.50cm , Length: 25.40cm Weight: 0.525kg ISBN: 9781681744483ISBN 10: 1681744481 Pages: 85 Publication Date: 30 May 2017 Audience: College/higher education , Undergraduate Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of Contents1 Groups - 1.1 Permutations and symmetries 1.2 Subgroups and classes 1.3 Representations, 1.4 Orthogonality 2 Lie Groups - 2.1 Lie groups as manifolds 2.2 Lie groups as groups of transformations or substitutions 2.3 Infinitesimal generators 2.4 Generator example: Lorentz boost 2.5 Transformations acting in three or more dimensions 2.6 Changing coordinates 2.7 Changing variables in the generator 2.8 Invariant functions, invariant curves, and groups that permute curves in a family 2.9 Canonical coordinates for a one-parameter group 3 Ordinary Differential Equations - 3.1 Prolongation of the group generator and a symmetry criterion 3.2 Reformulation of symmetry in terms of partial differential operators 3.3 Note on evaluating commutators 3.4 Tabulating DEs according to groups they admit 3.5 Lie's integrating factor 3.6 Finding symmetries of a second order DE 3.7 Classical mechanics: Nother's theoremReviewsThis book, written for graduate student physicists, contains all the necessary basics one needs to know about Lie theory. In particular, it provides a summary overview of the theory of finite groups, a brief description of a manifold, and an informal development of the theory of one-parameter Lie groups, especially as they apply to ordinary differential equations. The treatment is informal, although systematic and reasonably self-contained, as it assumes a familiarity with basic physics and applied calculus but does not assume additional mathematical training. The presentation is concise, although there are some points on which it is more expansive ... I would recommend this book to professors who want to introduce their students to Lie groups, symmetries, and their applications in theoretical physics. - Leonardo Colombo in Mathematical Reviews """This book, written for graduate student physicists, contains all the necessary basics one needs to know about Lie theory. In particular, it provides a summary overview of the theory of finite groups, a brief description of a manifold, and an informal development of the theory of one-parameter Lie groups, especially as they apply to ordinary differential equations. The treatment is informal, although systematic and reasonably self-contained, as it assumes a familiarity with basic physics and applied calculus but does not assume additional mathematical training. The presentation is concise, although there are some points on which it is more expansive ... I would recommend this book to professors who want to introduce their students to Lie groups, symmetries, and their applications in theoretical physics."" - Leonardo Colombo in Mathematical Reviews" Author InformationDr William A. Schwalm has been in the Department of Physics and Astrophysics at the University of North Dakota since 1980. His research is in condensed matter theory and application of mathematical methods to physical problems. He has taught lots of different physics courses at all levels. Current research involves application of Lie groups to finding generating functions for the stationary states of quantum systems, and also applying them to decoupling discrete dynamical systems. Another area of active interest is in finding Green functions for certain classes of lattice problems involving electron transport, vibrations and other collective excitations. Dr Schwalm has received two outstanding teaching awards, the University of Utah Physics Outstanding Undergraduate Instructor (1979) and the McDermott award for Excellence in Teaching, UND (1995). Tab Content 6Author Website:Countries AvailableAll regions |
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