Overview
- 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
Part of the book series: Undergraduate Lecture Notes in Physics (ULNP)
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Table of contents (16 chapters)
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Front Matter
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Back Matter
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
- matrix theory
About this book
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.
Reviews
Authors and Affiliations
About the authors
Alessandro Zampini works at the University of Luxemburg, where he gives a course on linear algebra and analytic geometry.
Bibliographic Information
Book Title: Linear Algebra and Analytic Geometry for Physical Sciences
Authors: Giovanni Landi, Alessandro Zampini
Series Title: Undergraduate Lecture Notes in Physics
DOI: https://doi.org/10.1007/978-3-319-78361-1
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer International Publishing AG, part of Springer Nature 2018
Softcover ISBN: 978-3-319-78360-4Published: 22 May 2018
eBook ISBN: 978-3-319-78361-1Published: 12 May 2018
Series ISSN: 2192-4791
Series E-ISSN: 2192-4805
Edition Number: 1
Number of Pages: XII, 345
Topics: Mathematical Methods in Physics, Linear and Multilinear Algebras, Matrix Theory, Mathematical and Computational Engineering, Geometry, Math Applications in Computer Science, Mathematical Applications in the Physical Sciences