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Linear Algebra and Analytic Geometry for Physical Sciences

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Publisher:

Springer

Pages: 345
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Recommend to library

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Paperback - 9783319783604

13 May 2018

€49.99

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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...

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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.

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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

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.
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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.

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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.

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