عنوان

Linear algebra and analytic geometry for physical sciences

(Number (ISBN

9783319783611

Number

E2895

.Language of Text, Soundtrack etc

انگلیسی

Title Proper

Linear algebra and analytic geometry for physical sciences

General Material Designation

[Electronic book]

First Statement of Responsibility

/ Giovanni Landi, Alessandro Zampini.

Place of Publication, Distribution, etc.

Cham, Switzerland

Name of Publisher, Distributor, etc.

: Springer

Date of Publication, Distribution, etc.

, 2018.

Specific Material Designation and Extent of Item

xii, 345 p.

Series Title

(Undergraduate lecture notes in physics)

Text of Note

Includes index.

Text of Note

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

0

Text of Note

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

Entry Element

Algebras, Linear

Entry Element

Geometry, Analytic

a04

a06

Class number

Book number

Landi, Giovanni, 1959-

Zampini, Alessandro.

Country

ایران

Agency

University of Tehran. Library of College of Science

Date and Hour of Consultation and Access

UT_SCI_BL_DB_1003125_0001.pdf

e

BL

278840

1

a

Y