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2011005744 contributor B12106183.
2011005744 created "c2011.".
2011005744 date "2011".
2011005744 date "c2011.".
2011005744 dateCopyrighted "c2011.".
2011005744 description "Includes bibliographical references (p. 287-289) and index.".
2011005744 description "Machine generated contents note: Preface. -- Reading Guide. -- 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. -- Understanding Geometric Algebra for Electromagnetic Theory. -- 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 Polarisable Media. -- 5.10 Exercises. -- 6. Review of (3+1)D. -- 7. Introducing Spacetime. -- 7.1 Background and Key Concepts. -- 7.2 Time as a Vector. -- 7.3 The Spacetime Basis Elements. -- 7.4 Basic Operations. -- 7.5 Velocity. -- 7.6 Different Basis Vectors and Frames. -- 7.7 Events and Hstories. -- Understanding Geometric Algebra for Electromagnetic Theory. -- 7.8 The Spacetime Form of. -- 7.9 Working with Vector Differentiation. -- 7.10 Working without Basis Vectors. -- 7.11 Classification of Spacetime Vectors and Bivectors. -- 7.12 Exercises. -- 8. Relating Spacetime to (3+1)D. -- 8.1 The Correspondence between the Elements. -- 8.2 Translations in General. -- 8.3 Introduction to Spacetime Splits. -- 8.4 Some Important Spacetime Splits. -- 8.5 What Next? -- 8.6 Exercises. -- 9. Change of Basis Vectors. -- 9.1 Linear transformations. -- Understanding Geometric Algebra for Electromagnetic Theory. -- 9.2 Relationship to Geometric Algebras. -- 9.3 Implementing Spatial Rotations and the Lorentz Transformation. -- 9.4 Lorentz Transformation of the Basis Vectors. -- 9.5 Lorentz Transformation of the Basis Bivectors. -- 9.6 Transformation of the Unit Scalar and Pseudoscalar. -- 9.7 Reverse Lorentz Transformation. -- 9.8 The Lorentz Transformation with Vectors in Component Form. -- 9.9 Dilations. -- 9.10 Exercises. -- 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. -- Understanding Geometric Algebra for Electromagnetic Theory. -- 11. Application of Spacetime Geometric Algebra to Basic Electromagnetics. -- 11.1 The Spacetime Approach to Electrodynamics. -- 11.2 The Vector Potential and some Spacetime Splits. -- 11.3 Maxwell's Equations in Spacetime Form. -- 11.4 Charge Conservation and the Wave Equation. -- 11.5 Plane Electromagnetic Waves. -- 11.6 Transformation of the Electromagnetic Field. -- 11.7 Lorentz Force. -- 11.8 The Electromagnetic Field of a Moving Point Charge. -- 11.9 Exercises. -- 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. -- 12.3 Frad 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. -- Understanding Geometric Algebra for Electromagnetic Theory. -- 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. -- 15. Table and Figure Captions. -- 16. Further Reading on Geometric Algebra. -- 17. References. -- 18. Tables and Figures.".
2011005744 extent "xvi, 301 p. :".
2011005744 identifier "9780470941638".
2011005744 identifier 2011005744-d.html.
2011005744 identifier 2011005744-t.html.
2011005744 identifier 2011005744-b.html.
2011005744 isPartOf "IEEE Press series on electromagnetic wave theory ; 38".
2011005744 issued "2011".
2011005744 issued "c2011.".
2011005744 language "eng".
2011005744 publisher "Hoboken, N.J. : Wiley-IEEE Press,".
2011005744 subject "530.14/10151635 22".
2011005744 subject "Electromagnetic theory Mathematics.".
2011005744 subject "Geometry, Algebraic.".
2011005744 subject "QC670 .A76 2011".
2011005744 subject "SCIENCE / Electromagnetism bisacsh.".
2011005744 tableOfContents "Machine generated contents note: Preface. -- Reading Guide. -- 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. -- Understanding Geometric Algebra for Electromagnetic Theory. -- 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 Polarisable Media. -- 5.10 Exercises. -- 6. Review of (3+1)D. -- 7. Introducing Spacetime. -- 7.1 Background and Key Concepts. -- 7.2 Time as a Vector. -- 7.3 The Spacetime Basis Elements. -- 7.4 Basic Operations. -- 7.5 Velocity. -- 7.6 Different Basis Vectors and Frames. -- 7.7 Events and Hstories. -- Understanding Geometric Algebra for Electromagnetic Theory. -- 7.8 The Spacetime Form of. -- 7.9 Working with Vector Differentiation. -- 7.10 Working without Basis Vectors. -- 7.11 Classification of Spacetime Vectors and Bivectors. -- 7.12 Exercises. -- 8. Relating Spacetime to (3+1)D. -- 8.1 The Correspondence between the Elements. -- 8.2 Translations in General. -- 8.3 Introduction to Spacetime Splits. -- 8.4 Some Important Spacetime Splits. -- 8.5 What Next? -- 8.6 Exercises. -- 9. Change of Basis Vectors. -- 9.1 Linear transformations. -- Understanding Geometric Algebra for Electromagnetic Theory. -- 9.2 Relationship to Geometric Algebras. -- 9.3 Implementing Spatial Rotations and the Lorentz Transformation. -- 9.4 Lorentz Transformation of the Basis Vectors. -- 9.5 Lorentz Transformation of the Basis Bivectors. -- 9.6 Transformation of the Unit Scalar and Pseudoscalar. -- 9.7 Reverse Lorentz Transformation. -- 9.8 The Lorentz Transformation with Vectors in Component Form. -- 9.9 Dilations. -- 9.10 Exercises. -- 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. -- Understanding Geometric Algebra for Electromagnetic Theory. -- 11. Application of Spacetime Geometric Algebra to Basic Electromagnetics. -- 11.1 The Spacetime Approach to Electrodynamics. -- 11.2 The Vector Potential and some Spacetime Splits. -- 11.3 Maxwell's Equations in Spacetime Form. -- 11.4 Charge Conservation and the Wave Equation. -- 11.5 Plane Electromagnetic Waves. -- 11.6 Transformation of the Electromagnetic Field. -- 11.7 Lorentz Force. -- 11.8 The Electromagnetic Field of a Moving Point Charge. -- 11.9 Exercises. -- 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. -- 12.3 Frad 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. -- Understanding Geometric Algebra for Electromagnetic Theory. -- 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. -- 15. Table and Figure Captions. -- 16. Further Reading on Geometric Algebra. -- 17. References. -- 18. Tables and Figures.".
2011005744 title "Understanding geometric algebra for electromagnetic theory / John W. Arthur.".
2011005744 type "text".