LEADER 04671nam 22007335 450 001 9910644262603321 005 20240130130311.0 010 $a9783031224225$b(electronic bk.) 010 $z9783031224218 024 7 $a10.1007/978-3-031-22422-5 035 $a(MiAaPQ)EBC7179181 035 $a(Au-PeEL)EBL7179181 035 $a(CKB)26020963400041 035 $a(DE-He213)978-3-031-22422-5 035 $a(PPN)267812604 035 $a(EXLCZ)9926020963400041 100 $a20230116d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aLinear Algebra and Group Theory for Physicists and Engineers /$fby Yair Shapira 205 $a2nd ed. 2023. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2023. 215 $a1 online resource (583 pages) 311 08$aPrint version: Shapira, Yair Linear Algebra and Group Theory for Physicists and Engineers Cham : Springer International Publishing AG,c2023 9783031224218 320 $aIncludes bibliographical references and index. 327 $aPart I: Introduction to Linear Algebra -- Vectors and Matrices -- Determinant and Vector Product in Physics -- Markov Matrix and its Spectrum: Towards Search Engines -- Special Relativity: Algebraic Point of View -- Part II: Introduction to Group Theory -- Groups 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 3D -- Part IV: Finite Elements in 3-D. - Automatic Mesh Generation -- Mesh Regularity -- Numerical Integration -- Spline: Variational Model in 3D -- Part V: Permuation Group in Quantum Chemistry -- Determinant and Electronic Structure -- Part VI: The Jordan Form -- The Jordan Form -- Jordan Decomposition -- Algebras and their Derivation -- Part VII: Linearization in Numerical Relativity -- Einstein Equations and their Linearization. 330 $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. The second edition has been revised and updated throughout and includes new material on the Jordan form, the Hermitian matrix and its eigenbasis, and applications in numerical relativity and electromagnetics. . 606 $aAlgebras, Linear 606 $aMathematical physics 606 $aGroup theory 606 $aNumerical analysis 606 $aComputer science?Mathematics 606 $aLinear Algebra 606 $aMathematical Physics 606 $aGroup Theory and Generalizations 606 $aNumerical Analysis 606 $aMathematical Applications in Computer Science 606 $aÀlgebra lineal$2thub 606 $aTeoria de grups$2thub 608 $aLlibres electrònics$2thub 615 0$aAlgebras, Linear. 615 0$aMathematical physics. 615 0$aGroup theory. 615 0$aNumerical analysis. 615 0$aComputer science?Mathematics. 615 14$aLinear Algebra. 615 24$aMathematical Physics. 615 24$aGroup Theory and Generalizations. 615 24$aNumerical Analysis. 615 24$aMathematical Applications in Computer Science. 615 7$aÀlgebra lineal 615 7$aTeoria de grups 676 $a512.2 676 $a512 700 $aShapira$b Yair$f1960-$01354443 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910644262603321 996 $aLinear Algebra and Group Theory for Physicists and Engineers$93329670 997 $aUNINA