Linear Algebra And Analytic Geometry For Physical Sciences Paperback

Switzerland

Giovanni Landi

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

3319783602

9783319783604

English

Springer International Publishing AG

5th Jun 2018

345

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

Alessandro Zampini

There are over 230 exercises integrated into the text, most with several parts and explained in detail. These exercises also serve as examples. The book contains about 20 figures and several additional examples. This text will interest both beginning and advanced undergraduates studying physics. ... Summing Up: Recommended. Undergraduates through faculty and professionals.