Linear Algebra and Analytic Geometry for Physical Sciences, 1st ed. 2018 Undergraduate Lecture Notes in Physics Series
Langue : Anglais
Auteurs : Landi Giovanni, Zampini Alessandro
A self-contained introduction to finite dimensional vector spaces, matrices, systems of linear equations, spectral analysis on euclidean and hermitian spaces, affine euclidean geometry, quadratic forms and conic sections.
The mathematical formalism is motivated and introduced by problems from physics, notably mechanics (including celestial) and electro-magnetism, with more than two hundreds examples and solved exercises.
Topics include: The group of orthogonal transformations on euclidean spaces, in particular rotations, with Euler angles and angular velocity. The rigid body with its inertia matrix. The unitary group. Lie algebras and exponential map. The Dirac?s bra-ket formalism. Spectral theory for self-adjoint endomorphisms on euclidean and hermitian spaces. The Minkowski spacetime from special relativity and the Maxwell equations. Conic sections with the use of eccentricity and Keplerian motions.
An appendix collects basic algebraic notions like group, ring and field; and complex numbers and integers modulo a prime number.
The book will be useful to students taking a physics or engineer degree for a basic education as well as for students who wish to be competent in the subject and who may want to pursue a post-graduate qualification.
Introduction.- Vectors and coordinate systems.- Vector spaces.- Euclidean vector spaces.- Matrices.- The determinant.- Systems of linear equations.- Linear transformations.- Dual spaces.- Endomorphisms and diagonalization.- Spectral theorems on euclidean spaces.- Rotations.- Spectral theorems on hermitian spaces.- Quadratic forms.- Affine linear geometry.- Euclidean affine linear geometry.- Conic sections.- A Algebraic Structures.- A.1 A few notions of Set Theory.- A.2 Groups.- A.3 Rings and Fields.- A.4 Maps between algebraic structures.- A5 Complex numbers.- A.6 Integers modulo a prime number.
Giovanni Landi is Professor of Mathematical Physics at the University of Trieste. He is a leading expert of noncummutative geometry, and board member of several journals in the field. He has also written the monograph "An Introduction to Noncommutative Spaces and their Geometries" published by Springer (1997).
Alessandro Zampini works at the University of Luxemburg, where he gives a course on linear algebra and analytic geometry.
In-depth, self-contained textbook for students in physical sciences
With more than 200 examples and solved exercises
The mathematical formalism is motivated and introduced by problems from physics
Date de parution : 05-2018
Ouvrage de 345 p.
15.5x23.5 cm
Thèmes de Linear Algebra and Analytic Geometry for Physical Sciences :
Mots-clés :
Euclidean vector spaces; Diagonalisation of matrices; linear algebra textbook; analytic geometry textbook; geometry textbook; Self-adjoint endomorphims; Affine linear geometry; Orthonormal basis; Conic sections; Spectral theorems; Riged body rotation; Hermitian products; Dual of a vector space; Dirac's bra-ket; Jordan normal form; Quadratic forms; matrix theory
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