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001 978-3-030-17856-7
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020 _a9783030178567
_9978-3-030-17856-7
024 7 _a10.1007/978-3-030-17856-7
_2doi
040 _cCUS
050 4 _aQA184-205
072 7 _aPBF
_2bicssc
072 7 _aMAT002050
_2bisacsh
072 7 _aPBF
_2thema
082 0 4 _a512.5
_223
100 1 _aShapira, Yair.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aLinear Algebra and Group Theory for Physicists and Engineers
_h[electronic resource] /
_cby Yair Shapira.
250 _a1st ed. 2019.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Birkhäuser,
_c2019.
300 _aXXI, 441 p. 93 illus., 1 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aPart I Introduction to Linear Algebra -- Vectors and Matrices -- Vector Product in Geometrical Mechanics -- Markov Chain in a Graph -- Special Relativity - Algebraic Point of View -- Part II Introduction to Group Theory -- Group Representation and Isomorphism Theorems -- Projective Geometry in Computer Graphics -- Quantum Mechanics - Algebraic Point of View -- Part III Polynomials and Basis Functions -- Polynomials and their Gradient -- Basis Functions: Barycentric Coordinates in 3-D -- Part IV Finite Elements in 3-D -- Automatic Mesh Generation -- Mesh Regularity -- Numerical Integration -- Spline: Variational Model -- Part V Advanced Applications in Physics and Chemistry -- Quantum Chemistry: Electronic Structure -- General Relativity: Einstein Equations -- References.
520 _aThis textbook demonstrates the strong interconnections between linear algebra and group theory by presenting them simultaneously, a pedagogical strategy ideal for an interdisciplinary audience. Being approached together at the same time, these two topics complete one another, allowing students to attain a deeper understanding of both subjects. The opening chapters introduce linear algebra with applications to mechanics and statistics, followed by group theory with applications to projective geometry. Then, high-order finite elements are presented to design a regular mesh and assemble the stiffness and mass matrices in advanced applications in quantum chemistry and general relativity. This text is ideal for undergraduates majoring in engineering, physics, chemistry, computer science, or applied mathematics. It is mostly self-contained—readers should only be familiar with elementary calculus. There are numerous exercises, with hints or full solutions provided. A series of roadmaps are also provided to help instructors choose the optimal teaching approach for their discipline.
650 0 _aMatrix theory.
650 0 _aAlgebra.
650 0 _aComputer science—Mathematics.
650 0 _aComputer mathematics.
650 0 _aGroup theory.
650 1 4 _aLinear and Multilinear Algebras, Matrix Theory.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M11094
650 2 4 _aMathematical Applications in Computer Science.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M13110
650 2 4 _aGroup Theory and Generalizations.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M11078
856 4 0 _uhttps://doi.org/10.1007/978-3-030-17856-7
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
942 _cEBK
999 _c206366
_d206366