Linear Algebra and Analytic Geometry for Physical Sciences

Giovanni Landi, Alessandro Zampini (Autoren)

Buch | Softcover

XII, 345 Seiten

2018 | 1st ed. 2018
Springer International Publishing (Verlag)
978-3-319-78360-4 (ISBN)

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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.

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.

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.

"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." (D. P. Turner, Choice, Vol. 56 (04), December, 2018)

“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.” (D. P. Turner, Choice, Vol. 56 (04), December, 2018)

Erscheinungsdatum	03.06.2018
Reihe/Serie	Undergraduate Lecture Notes in Physics
Zusatzinfo	XII, 345 p.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	551 g
Themenwelt	Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika
Themenwelt	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	Affine linear geometry • analytic geometry textbook • conic sections • Diagonalisation of matrices • Dirac's bra-ket • Dual of a vector space • Euclidean vector spaces • geometry textbook • Hermitian products • Jordan normal form • linear algebra textbook • matrix theory • Orthonormal basis • quadratic forms • Riged body rotation • Self-adjoint endomorphims • Spectral theorems
ISBN-10	3-319-78360-2 / 3319783602
ISBN-13	978-3-319-78360-4 / 9783319783604
Zustand	Neuware