عنوان

Understanding geometric algebra for electromagnetic theory /

شابک

0470941634

شابک

9780470941638

شماره

dltt

عنوان اصلي

Understanding geometric algebra for electromagnetic theory /

نام عام مواد

[Book]

نام نخستين پديدآور

John W. Arthur

محل نشرو پخش و غیره

Hoboken, N.J. :

نام ناشر، پخش کننده و غيره

Wiley-IEEE Press,

تاریخ نشرو بخش و غیره

c2011

نام خاص و کميت اثر

xvi, 301 p. :

ساير جزييات

ill. ;

ابعاد

25 cm

عنوان فروست

IEEE Press series on electromagnetic wave theory ;

مشخصه جلد

21

متن يادداشت

Includes bibliographical references (p. 287-289) and index

متن يادداشت

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

متن يادداشت

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

متن يادداشت

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

بدون عنوان

0

بدون عنوان

0

بدون عنوان

0

متن يادداشت

"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"--

موضوع مستند نشده

Electromagnetic theory-- Mathematics

موضوع مستند نشده

Geometry, Algebraic

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

Arthur, John W.,1949-

تاريخ عمليات

20130826232147.0

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y