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Linear algebra and group theory for physicists and engineers

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Linear algebra and group theory for physicists and engineers/ by Yair Shapira.
作者:	Shapira, Yair.
出版者:	Cham :Springer International Publishing : : 2019.,
面頁冊數:	xxxi, 441 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	Algebras, Linear. -
電子資源:	https://doi.org/10.1007/978-3-030-17856-7
ISBN:	9783030178567

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

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

528115
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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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.
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650 0 $a Group theory. $3 527791
650 1 4 $a Linear and Multilinear Algebras, Matrix Theory. $3 672090
650 2 4 $a Mathematical Applications in Computer Science. $3 815331
650 2 4 $a Group Theory and Generalizations. $3 672112
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856 4 0 $u https://doi.org/10.1007/978-3-030-17856-7
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