Geometric Multiplication of Vectors

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Sprache: Englisch

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Beschreibung

This book enables the reader to discover elementary concepts of geometric algebra and its applications with lucid and direct explanations. Why would one want to explore geometric algebra? What if there existed a universal mathematical language that allowed one: to make rotations in any dimension with simple formulas, to see spinors or the Pauli matrices and their products, to solve problems of the special theory of relativity in three-dimensional Euclidean space, to formulate quantum mechanics without the imaginary unit, to easily solve difficult problems of electromagnetism, to treat the Kepler problem with the formulas for a harmonic oscillator, to eliminate unintuitive matrices and tensors, to unite many branches of mathematical physics? What if it were possible to use that same framework to generalize the complex numbers or fractals to any dimension, to play with geometry on a computer, as well as to make calculations in robotics, ray-tracing and brain science? In addition, what if such a language provided a clear, geometric interpretation of mathematical objects, even for the imaginary unit in quantum mechanics? Such a mathematical language exists and it is called geometric algebra. High school students have the potential to explore it, and undergraduate students can master it. The universality, the clear geometric interpretation, the power of generalizations to any dimension, the new insights into known theories, and the possibility of computer implementations make geometric algebra a thrilling field to unearth.

Über den Autor

Miroslav Josipovi¿ is a Croatian physicist and musician with special interest in revising the language of mathematical physics and in creating new ways of teaching physics.

Zusammenfassung

An excellent starting point for beginners in the field

An advanced high school student can learn basic concepts from the book

Gradual introduction of concepts with many figures and solved examples

Inhaltsverzeichnis

Basic Concepts.- Euclidean 3D Geometric Algebra.- Applications.- Geometric Algebra and Matrices.- Appendix.- Solutions for Some Problems.- Problems.- Why Geometric Algebra?.- Formulae.- Literature.- References.

Details

Erscheinungsjahr:	2019
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	241
Inhalt:	xxv 241 S. 88 s/w Illustr. 1 farbige Illustr. 241 p. 89 illus. 1 illus. in color.
ISBN-13:	9783030017552
ISBN-10:	3030017559
Sprache:	Englisch
Herstellernummer:	978-3-030-01755-2
Einband:	Kartoniert / Broschiert
Autor:	Josipovic, Miroslav
Hersteller:	Springer-Verlag GmbH Springer International Publishing Birkhäuser
Abbildungen:	90 farbige Abbildungen, Bibliographie
Maße:	235 x 155 x 15 mm
Von/Mit:	Miroslav Josipovic
Erscheinungsdatum:	13.12.2019
Gewicht:	0,417 kg

preigu-id: 114334689