Linear Algebra and Group Theory for Physicists and Engineers

• Main Author: Shapira, Yair (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2019.
• Edition: 1st ed. 2019.
• Subjects: Matrix theory.; Algebra.; Computer science-Mathematics.; Computer mathematics.; Group theory.; Linear and Multilinear Algebras, Matrix Theory.; Mathematical Applications in Computer Science.; Group Theory and Generalizations.

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 at...

Table of Contents:

• 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.