Linear algebra and analytic geometry for physical sciences /

Linear algebra and analytic geometry for physical sciences /

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Bibliographic Details
Author / Creator:	Landi, Giovanni, 1959- author.
Imprint:	Cham, Switzerland : Springer, 2018.
Description:	1 online resource (xii, 345 pages)
Language:	English
Series:	Undergraduate lecture notes in physics, 2192-4791 Undergraduate lecture notes in physics,
Subject:	Algebras, Linear. Geometry, Analytic. Algebras, Linear. Geometry, Analytic.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11654878

Hidden Bibliographic Details
Other authors / contributors:	Zampini, Alessandro, author.
ISBN:	9783319783611 3319783610 9783319783604 3319783602
Digital file characteristics:	text file PDF
Notes:	Includes index. Online resource; title from PDF title page (SpringerLink, viewed May 14, 2018).
Summary:	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.
Other form:	Print version: Landi, Giovanni, 1959- Linear algebra and analytic geometry for physical sciences. Cham, Switzerland : Springer, 2018 3319783602 9783319783604
Standard no.:	10.1007/978-3-319-78361-1

Table of Contents:

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.