Linear Algebra and Analytic Geometry for Physical Sciences

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 physic...

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Hlavný autor: Landi, Giovanni (Autor)
Médium: Elektronický zdroj E-kniha
Jazyk:English
Vydavateľské údaje: Cham : Springer International Publishing, 2018.
Vydanie:1st ed. 2018.
Edícia:Undergraduate Lecture Notes in Physics,
Predmet:
Physics.
Matrix theory.
Algebra.
Applied mathematics.
Engineering mathematics.
Geometry.
Computer science-Mathematics.
Mathematical physics.
ISBN:9783319783611
ISSN:2192-4791
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245 1 0 |a Linear Algebra and Analytic Geometry for Physical Sciences  |h [electronic resource] /  |c by Giovanni Landi, Alessandro Zampini. 
250 |a 1st ed. 2018. 
260 1 |a Cham :  |b Springer International Publishing,  |c 2018. 
300 |a XII, 345 p.  |b online resource. 
490 1 |a Undergraduate Lecture Notes in Physics,  |x 2192-4791 
500 |a Physics and Astronomy  
505 0 |a 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. 
516 |a text file PDF 
520 |a 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. 
650 0 |a Physics. 
650 0 |a Matrix theory. 
650 0 |a Algebra. 
650 0 |a Applied mathematics. 
650 0 |a Engineering mathematics. 
650 0 |a Geometry. 
650 0 |a Computer science-Mathematics. 
650 0 |a Mathematical physics. 
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