Linear Algebra and Group Theory for Physicists and Engineers

1. Auflage 2019
ISBN: 978-3-030-17855-0
Verlag: Birkhäuser

Buch, Englisch, 441 Seiten, Book, Format (B × H): 155 mm x 235 mm, Gewicht: 875 g

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.

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

Shapira, Yair

Fachgebiete

• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie

Inhaltsverzeichnis

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.

Über Autor(innen)

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