04671nam 22007335 450 991064426260332120240130130311.09783031224225(electronic bk.)978303122421810.1007/978-3-031-22422-5(MiAaPQ)EBC7179181(Au-PeEL)EBL7179181(CKB)26020963400041(DE-He213)978-3-031-22422-5(PPN)267812604(EXLCZ)992602096340004120230116d2023 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierLinear Algebra and Group Theory for Physicists and Engineers /by Yair Shapira2nd ed. 2023.Cham :Springer International Publishing :Imprint: Birkhäuser,2023.1 online resource (583 pages)Print version: Shapira, Yair Linear Algebra and Group Theory for Physicists and Engineers Cham : Springer International Publishing AG,c2023 9783031224218 Includes bibliographical references and index.Part 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.This 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. .Algebras, LinearMathematical physicsGroup theoryNumerical analysisComputer science—MathematicsLinear AlgebraMathematical PhysicsGroup Theory and GeneralizationsNumerical AnalysisMathematical Applications in Computer ScienceÀlgebra linealthubTeoria de grupsthubLlibres electrònicsthubAlgebras, Linear.Mathematical physics.Group theory.Numerical analysis.Computer science—Mathematics.Linear Algebra.Mathematical Physics.Group Theory and Generalizations.Numerical Analysis.Mathematical Applications in Computer Science.Àlgebra linealTeoria de grups512.2512Shapira Yair1960-1354443MiAaPQMiAaPQMiAaPQ9910644262603321Linear Algebra and Group Theory for Physicists and Engineers3329670UNINA