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Title
Linear algebra and analytic geometry for physical sciences / Giovanni Landi, Alessandro Zampini.
ISBN
9783319783611 (electronic book)
3319783610 (electronic book)
9783319783604
3319783602
Published
Cham, Switzerland : Springer, 2018.
Language
English
Description
1 online resource (xii, 345 pages).
Item Number
10.1007/978-3-319-78361-1 doi
Call Number
QA184.2
Dewey Decimal Classification
512/.5
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.
Note
Includes index.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed May 14, 2018).
Series
Undergraduate lecture notes in physics.
Available in Other Form
Print version: 9783319783604
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.
