Lectures on selected topics in mathematical physics :introduction to lie theory with applications /

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"Version: 20170401"--Title page verso."A Morgan & Claypool publication as part of IOP Concise Physics"--Title page verso.Includes bibliographical references.Preface -- Introduction -- 1. Groups -- 1.1. Permutations and symmetries -- 1.2. Subgroups and classes -- 1.3. Representations -- 1.4. Orthogonality2. 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 group3. 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. Symmetries in terms of A -- 3.4. Note on evaluating commutators -- 3.5. Symmetries of first-order DEs -- 3.6. Tabulating DEs according to groups they admit -- 3.7. Lie's integrating factor -- 3.8. Finding symmetries of a second order -- 3.9. Using a symmetry to reduce the order -- 3.10. Classical mechanics: N?other's theorem.This book provides an introduction to Lie theory for first-year graduate students and professional physicists who may not have come across the theory in their studies. It is an 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. Interested readers should acquire a tool that is complete and that actually works to simplify or solve differential equations as well as moving them on to other topics.First and second year graduate students, and researchers needing an introduction to the subject.Also available in print.Mode of access: World Wide Web.System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.Professor William A Schwalm received his PhD from Montana State University in 1978 in condensed matter theory. He held a postdoctoral position at the University of Utah before coming to UND in 1980. Dr. Schwalm belongs to the American Physical Society. He has received awards for teaching from both UND and the University of Utah.Title from PDF title page (viewed on May 5, 2017).

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: .,

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1 online resource (various pagings) :illustrations.

Language

English

ISBN/ISSN

9781681744490

Classification

530.15/255

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Subject(s)

SCIENCE / Physics / Mathematical & Computational.
Mathematical physics.
Lie groups.
Lie algebras.

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William A. Schwalm.

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