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Linear algebra and group theory for ...

Shapira, Yair.

Linear algebra and group theory for physicists and engineers

Record Type:	Electronic resources : Monograph/item
Title/Author:	Linear algebra and group theory for physicists and engineersby Yair Shapira.
Author:	Shapira, Yair.
Published:	Cham :Springer International Publishing :2019.
Description:	xxxi, 441 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Algebras, Linear.
Online resource:	https://doi.org/10.1007/978-3-030-17856-7
ISBN:	9783030178567$q(electronic bk.)

Linear algebra and group theory for physicists and engineers
Shapira, Yair.

Linear algebra and group theory for physicists and engineers[electronic resource] /by Yair Shapira. - Cham :Springer International Publishing :2019. - xxxi, 441 p. :ill., digital ;24 cm.

Part 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.

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.

ISBN: 9783030178567$q(electronic bk.)

Standard No.: 10.1007/978-3-030-17856-7doiSubjects--Topical Terms:

183087
Algebras, Linear.

LC Class. No.: QA184.2 / .S537 2019

Dewey Class. No.: 512.5

Linear algebra and group theory for physicists and engineers
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100 1 $a Shapira, Yair. $3 285976
245 1 0 $a Linear algebra and group theory for physicists and engineers $h [electronic resource] / $c by Yair Shapira.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhauser, $c 2019.
300 $a xxxi, 441 p. : $b ill., digital ; $c 24 cm.
505 0 $a Part 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 $a 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.
650 0 $a Algebras, Linear. $3 183087
650 0 $a Group theory. $3 189579
650 1 4 $a Linear and Multilinear Algebras, Matrix Theory. $3 274063
650 2 4 $a Mathematical Applications in Computer Science. $3 530811
650 2 4 $a Group Theory and Generalizations. $3 274819
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773 0 $t Springer eBooks
856 4 0 $u https://doi.org/10.1007/978-3-030-17856-7
950 $a Mathematics and Statistics (Springer-11649)