Linear Algebra and Analytic Geometry for Physical Sciences

Nonfiction, Science & Nature, Science, Physics, Mathematical Physics, Mathematics, Algebra
Cover of the book Linear Algebra and Analytic Geometry for Physical Sciences by Giovanni Landi, Alessandro Zampini, Springer International Publishing
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Author: Giovanni Landi, Alessandro Zampini ISBN: 9783319783611
Publisher: Springer International Publishing Publication: May 12, 2018
Imprint: Springer Language: English
Author: Giovanni Landi, Alessandro Zampini
ISBN: 9783319783611
Publisher: Springer International Publishing
Publication: May 12, 2018
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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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