| Document Type
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BL
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| Record Number
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629795
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| Doc. No
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dltt
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| Main Entry
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Arthur, John W.,1949-
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| Title & Author
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Understanding geometric algebra for electromagnetic theory /\ John W. Arthur
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| Publication Statement
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Hoboken, N.J. :: Wiley-IEEE Press,, c2011
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| Series Statement
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IEEE Press series on electromagnetic wave theory ;; 21
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| Page. NO
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xvi, 301 p. :: ill. ;; 25 cm
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| ISBN
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9780470941638
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: 0470941634
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| Bibliographies/Indexes
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Includes bibliographical references (p. 287-289) and index
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| Contents
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1. Introduction -- 2. A Quick Tour of Geometric Algebra : 2.1 The basic rules geometric algebra -- 2.2 3D geometric algebra -- 2.3 Developing the rules -- 2.4 Comparison with traditional 3D tools -- 2.5 New possibilities -- 2.6 Exercises -- 3. Applying the Abstraction : 3.1 Space and time -- 3.2 Electromagnetics -- 3.3 The Vector derivative -- 3.4 The integral equations -- 3.5 The role of the dual -- 3.6 Exercises -- 4. Generalisation : 4.1 Homogeneous and inhomogeneous multivectors -- 4.2 Blades -- 4.3 Reversal -- 4.4 Maximum grade -- 4.5 Inner and outer products involving a multivector -- 4.6 Inner and outer products between higher grades -- 4.7 Summary so far -- 4.8 Exercises -- 5. (3+1)D Electromagnetics : 5.1 The Lorentz Force -- 5.2 Maxwell's equations in free space -- 5.3 Simplified equations -- 5.4 The Connexion between the electric and magnetic fields -- 5.5 Plane electromagnetic waves -- 5.6 Charge conservation -- 5.7 Multivector potential -- 5.8 Energy and momentum -- 5.9 Maxwell's equations on polarizable media -- 5.10 Exercises
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10. Further Spacetime Concepts -- 10.1 Review of frames and time vectors -- 10.2 Frames in general -- 10.3 Maps and grids -- 10.4 Proper time -- 10.5 Proper velocity -- 10.6 Relative vectors and paravectors -- 10.7 Frame dependent v. frame independent scalars -- 10.8 Change of basis for any object in component form -- 10.9 Velocity as seen in different frames -- 10.10 Frame free form of the Lorentz transformation -- 10.11 Exercises -- 11. Application of Spacetime Geometric Algebra to Basic Electromagnetics : 11.1 The vector potential and some spacetime splits -- 11.2 Maxwell's equations in spacetime form -- 11.3 Charge conservation and the wave equation -- 11.4 Plane electromagnetic waves -- 11.5 Transformation of the electromagnetic field -- 11.6 Lorentz Force -- 11.7 The spacetime approach to electrodynamics -- 11.8 The electromagnetic field of a moving point charge -- 11.9 Exercises
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12. The Electromagnetic Field of a Point Charge Undergoing Acceleration : 12.1 Working with null vectors -- 12.2 Finding F for a moving point charge -- 12.3Frad in the charge's rest frame -- 12.4 Frad in the Observer's rest frame -- 12.5 Exercises -- 13. Conclusion -- 14. Appendices -- 14.1 Glossary -- 14.2 Axial v true vectors -- 14.3 Complex numbers and the 2D geometric algebra -- 14.4 The structure of vector spaces and geometric algebras -- 14.5 Quaternions compared -- 14.6 Evaluation of an integral in equation (5.14) -- 14.7 Formal derivation of the spacetime vector derivative
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| Abstract
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"This book aims to disseminate geometric algebra as a straightforward mathematical tool set for working with and understanding classical electromagnetic theory. It's target readership is anyone who has some knowledge of electromagnetic theory, predominantly ordinary scientists and engineers who use it in the course of their work, or postgraduate students and senior undergraduates who are seeking to broaden their knowledge and increase their understanding of the subject. It is assumed that the reader is not a mathematical specialist and is neither familiar with geometric algebra or its application to electromagnetic theory. The modern approach, geometric algebra, is the mathematical tool set we should all have started out with and once the reader has a grasp of the subject, he or she cannot fail to realize that traditional vector analysis is really awkward and even misleading by comparison"--
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| Subject
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Electromagnetic theory-- Mathematics
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| Subject
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Geometry, Algebraic
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| LC Classification
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QC670.A76 2011
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