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Linear Algebra and Analytic Geometry for Physical Sciences

  • Giovanni Landi
  • Alessandro Zampini

Part of the Undergraduate Lecture Notes in Physics book series (ULNP)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Giovanni Landi, Alessandro Zampini
    Pages 1-16
  3. Giovanni Landi, Alessandro Zampini
    Pages 17-34
  4. Giovanni Landi, Alessandro Zampini
    Pages 35-45
  5. Giovanni Landi, Alessandro Zampini
    Pages 47-67
  6. Giovanni Landi, Alessandro Zampini
    Pages 69-78
  7. Giovanni Landi, Alessandro Zampini
    Pages 79-95
  8. Giovanni Landi, Alessandro Zampini
    Pages 97-124
  9. Giovanni Landi, Alessandro Zampini
    Pages 125-130
  10. Giovanni Landi, Alessandro Zampini
    Pages 131-150
  11. Giovanni Landi, Alessandro Zampini
    Pages 151-172
  12. Giovanni Landi, Alessandro Zampini
    Pages 173-196
  13. Giovanni Landi, Alessandro Zampini
    Pages 197-211
  14. Giovanni Landi, Alessandro Zampini
    Pages 213-233
  15. Giovanni Landi, Alessandro Zampini
    Pages 235-267
  16. Giovanni Landi, Alessandro Zampini
    Pages 269-292
  17. Giovanni Landi, Alessandro Zampini
    Pages 293-327
  18. Back Matter
    Pages 329-345

About this book

Introduction

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.

Keywords

Euclidean vector spaces Diagonalisation of matrices linear algebra textbook analytic geometry textbook geometry textbook Self-adjoint endomorphims Affine linear geometry Orthonormal basis Conic sections Spectral theorems Riged body rotation Hermitian products Dual of a vector space Dirac's bra-ket Jordan normal form Quadratic forms

Authors and affiliations

  • Giovanni Landi
    • 1
  • Alessandro Zampini
    • 2
  1. 1.University of TriesteTriesteItaly
  2. 2.INFN Sezione di NapoliNapoliItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-78361-1
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-319-78360-4
  • Online ISBN 978-3-319-78361-1
  • Series Print ISSN 2192-4791
  • Series Online ISSN 2192-4805
  • Buy this book on publisher's site