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Linear algebra and analytic geometry for physical sciences

A self-contained introduction to finite dimensional vector spaces, matrices, systems of linear equations, spectral analysis on euclidean and hermitian spaces, affine euclidean geometry, quadratic forms and conic sections. The mathematical formalism is motivated and introduced by problems from physic...

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Detalles Bibliográficos
Autores principales: Landi, Giovanni, Zampini, Alessandro
Lenguaje:eng
Publicado: Springer 2018
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-319-78361-1
http://cds.cern.ch/record/2622127
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author Landi, Giovanni
Zampini, Alessandro
author_facet Landi, Giovanni
Zampini, Alessandro
author_sort Landi, Giovanni
collection CERN
description A self-contained introduction to finite dimensional vector spaces, matrices, systems of linear equations, spectral analysis on euclidean and hermitian spaces, affine euclidean geometry, quadratic forms and conic sections. The mathematical formalism is motivated and introduced by problems from physics, notably mechanics (including celestial) and electro-magnetism, with more than two hundreds examples and solved exercises. Topics include: The group of orthogonal transformations on euclidean spaces, in particular rotations, with Euler angles and angular velocity. The rigid body with its inertia matrix. The unitary group. Lie algebras and exponential map. The Dirac’s bra-ket formalism. Spectral theory for self-adjoint endomorphisms on euclidean and hermitian spaces. The Minkowski spacetime from special relativity and the Maxwell equations. Conic sections with the use of eccentricity and Keplerian motions. An appendix collects basic algebraic notions like group, ring and field; and complex numbers and integers modulo a prime number. The book will be useful to students taking a physics or engineer degree for a basic education as well as for students who wish to be competent in the subject and who may want to pursue a post-graduate qualification.
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spelling cern-26221272021-04-21T18:48:47Zdoi:10.1007/978-3-319-78361-1http://cds.cern.ch/record/2622127engLandi, GiovanniZampini, AlessandroLinear algebra and analytic geometry for physical sciencesMathematical Physics and MathematicsA self-contained introduction to finite dimensional vector spaces, matrices, systems of linear equations, spectral analysis on euclidean and hermitian spaces, affine euclidean geometry, quadratic forms and conic sections. The mathematical formalism is motivated and introduced by problems from physics, notably mechanics (including celestial) and electro-magnetism, with more than two hundreds examples and solved exercises. Topics include: The group of orthogonal transformations on euclidean spaces, in particular rotations, with Euler angles and angular velocity. The rigid body with its inertia matrix. The unitary group. Lie algebras and exponential map. The Dirac’s bra-ket formalism. Spectral theory for self-adjoint endomorphisms on euclidean and hermitian spaces. The Minkowski spacetime from special relativity and the Maxwell equations. Conic sections with the use of eccentricity and Keplerian motions. An appendix collects basic algebraic notions like group, ring and field; and complex numbers and integers modulo a prime number. The book will be useful to students taking a physics or engineer degree for a basic education as well as for students who wish to be competent in the subject and who may want to pursue a post-graduate qualification.Springeroai:cds.cern.ch:26221272018
spellingShingle Mathematical Physics and Mathematics
Landi, Giovanni
Zampini, Alessandro
Linear algebra and analytic geometry for physical sciences
title Linear algebra and analytic geometry for physical sciences
title_full Linear algebra and analytic geometry for physical sciences
title_fullStr Linear algebra and analytic geometry for physical sciences
title_full_unstemmed Linear algebra and analytic geometry for physical sciences
title_short Linear algebra and analytic geometry for physical sciences
title_sort linear algebra and analytic geometry for physical sciences
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-319-78361-1
http://cds.cern.ch/record/2622127
work_keys_str_mv AT landigiovanni linearalgebraandanalyticgeometryforphysicalsciences
AT zampinialessandro linearalgebraandanalyticgeometryforphysicalsciences