000 | 03760nam a22004815i 4500 | ||
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001 | 978-3-030-17856-7 | ||
003 | DE-He213 | ||
005 | 20200812132241.0 | ||
007 | cr nn 008mamaa | ||
008 | 190511s2019 gw | s |||| 0|eng d | ||
020 |
_a9783030178567 _9978-3-030-17856-7 |
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024 | 7 |
_a10.1007/978-3-030-17856-7 _2doi |
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040 | _cCUS | ||
050 | 4 | _aQA184-205 | |
072 | 7 |
_aPBF _2bicssc |
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072 | 7 |
_aMAT002050 _2bisacsh |
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072 | 7 |
_aPBF _2thema |
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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. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
||
338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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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 |