Linear Algebra and Group Theory for Physic...

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Beschreibung

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.

Über den Autor

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

Zusammenfassung

Introduces linear algebra and group theory together for a more intuitive understanding of applied mathematics

Utilizes an interdisciplinary approach to appeal to a broad scientific audience

Provides an array of examples throughout, perfect for practicing what is taught

Inhaltsverzeichnis

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.

Erscheinungsjahr:	2023
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	xxvii 574 S. 100 s/w Illustr. 574 p. 100 illus.
ISBN-13:	9783031224218
ISBN-10:	3031224213
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Shapira, Yair
Auflage:	Second Edition 2023
Hersteller:	Springer International Publishing
Maße:	241 x 160 x 36 mm
Von/Mit:	Yair Shapira
Erscheinungsdatum:	17.01.2023
Gewicht:	1,172 kg

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