Linear Algebra and Group Theory for Physicists and Engineers

Yair Shapira (Autor)

Buch | Hardcover

XXVII, 574 Seiten

2023 | 2. Second Edition 2023
Springer International Publishing (Verlag)
978-3-031-22421-8 (ISBN)

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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.

Yair Shapira, PhD, Department of Computer Science, Technion, Israeli Institute of Technology

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.

Erscheinungsdatum	18.01.2023
Zusatzinfo	XXVII, 574 p. 100 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	1157 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Themenwelt	Naturwissenschaften ► Physik / Astronomie
Schlagworte	Fourier matrices • group theory • High dimensional vectors • jordan decomposition • Jordan form • linear algebra • Markov Chain • matrix theory • Mesh Generation • quantum mechanics
ISBN-10	3-031-22421-3 / 3031224213
ISBN-13	978-3-031-22421-8 / 9783031224218
Zustand	Neuware