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Lectures on the theory of group properties of differential equations / L. V. Ovsyannikov; N. Kh Ibragimov, E. D. Avdonina (editor)
Beijing : World Scientific, 2013
xi, 141 pages. ; 25 cm.
Ký hiệu phân loại (DDC): 515.3
These lecturers provide a clear introduction to Lie group methods for determining and using symmetries of differential equations, a variety of their applications in gas dynamics and other nonlinear models as well as the author's remarkable contribution to this classical subject. It contains material that is useful for students and teachers but cannot be found in modern texts. For example, the theory of partially invariant solutions developed by Ovsyannikov provides a powerful tool for solving systems of nonlinear differential equations and investigating complicated mathematical models
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Lie groups and Lie algebras for physicists / Ashok Das, Susumu Okubo
New Jersey : World Scientific, 2014
xi, 345 pages. ; 24 cm.
Ký hiệu phân loại (DDC): 512.57
The book is intended for graduate students of theoretical physics (with a background in quantum mechanics) as well as researchers interested in applications of Lie group theory and Lie algebras in physics. The emphasis is on the inter-relations of representation theories of Lie groups and the corresponding Lie algebras
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3
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Physics from symmetry / Jakob Schwichtenberg
Cham, Switzerland : Springer, 2018.
294 pages. : illustrations
Ký hiệu phân loại (DDC): 539.725
This is a textbook that derives the fundamental theories of physics from symmetry. It starts by introducing, in a completely self-contained way, all mathematical tools needed to use symmetry ideas in physics. Thereafter, these tools are put into action and by using symmetry constraints, the fundamental equations of Quantum Mechanics, Quantum Field Theory, Electromagnetism, and Classical Mechanics are derived. As a result, the reader is able to understand the basic assumptions behind, and the connections between the modern theories of physics. The book concludes with first applications of the previously derived equations. Thanks to the input of readers from around the world, this second edition has been purged of typographical errors and also contains several revised sections with improved explanations.#xE000.
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