{"product_id":"understanding-geometric-algebra-for-electromagnetic-theory-isbn-9780470941638","title":"Understanding Geometric Algebra for Electromagnetic Theory","description":"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.  \u003cp\u003e Professors can request a solutions manual by email: \u003ca href=\"mailto:pressbooks@ieee.org\"\u003epressbooks@ieee.org\u003c\/a\u003e\u003c\/p\u003e  \u003cb\u003ePreface xi\u003c\/b\u003e  \u003cp\u003e\u003cb\u003eReading Guide xv\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1. Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2. A Quick Tour of Geometric Algebra 7\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 The Basic Rules of a Geometric Algebra 16\u003c\/p\u003e \u003cp\u003e2.2 3D Geometric Algebra 17\u003c\/p\u003e \u003cp\u003e2.3 Developing the Rules 19\u003c\/p\u003e \u003cp\u003e2.3.1 General Rules 20\u003c\/p\u003e \u003cp\u003e2.3.2 3D 21\u003c\/p\u003e \u003cp\u003e2.3.3 The Geometric Interpretation of Inner and Outer Products 22\u003c\/p\u003e \u003cp\u003e2.4 Comparison with Traditional 3D Tools 24\u003c\/p\u003e \u003cp\u003e2.5 New Possibilities 24\u003c\/p\u003e \u003cp\u003e2.6 Exercises 26\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3. Applying the Abstraction 27\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Space and Time 27\u003c\/p\u003e \u003cp\u003e3.2 Electromagnetics 28\u003c\/p\u003e \u003cp\u003e3.2.1 The Electromagnetic Field 28\u003c\/p\u003e \u003cp\u003e3.2.2 Electric and Magnetic Dipoles 30\u003c\/p\u003e \u003cp\u003e3.3 The Vector Derivative 32\u003c\/p\u003e \u003cp\u003e3.4 The Integral Equations 34\u003c\/p\u003e \u003cp\u003e3.5 The Role of the Dual 36\u003c\/p\u003e \u003cp\u003e3.6 Exercises 37\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4. Generalization 39\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Homogeneous and Inhomogeneous Multivectors 40\u003c\/p\u003e \u003cp\u003e4.2 Blades 40\u003c\/p\u003e \u003cp\u003e4.3 Reversal 42\u003c\/p\u003e \u003cp\u003e4.4 Maximum Grade 43\u003c\/p\u003e \u003cp\u003e4.5 Inner and Outer Products Involving a Multivector 44\u003c\/p\u003e \u003cp\u003e4.6 Inner and Outer Products between Higher Grades 48\u003c\/p\u003e \u003cp\u003e4.7 Summary So Far 50\u003c\/p\u003e \u003cp\u003e4.8 Exercises 51\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5. (3\u003c\/b\u003e+\u003cb\u003e1)D Electromagnetics 55\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 The Lorentz Force 55\u003c\/p\u003e \u003cp\u003e5.2 Maxwell’s Equations in Free Space 56\u003c\/p\u003e \u003cp\u003e5.3 Simplifi ed Equations 59\u003c\/p\u003e \u003cp\u003e5.4 The Connection between the Electric and Magnetic Fields 60\u003c\/p\u003e \u003cp\u003e5.5 Plane Electromagnetic Waves 64\u003c\/p\u003e \u003cp\u003e5.6 Charge Conservation 68\u003c\/p\u003e \u003cp\u003e5.7 Multivector Potential 69\u003c\/p\u003e \u003cp\u003e5.7.1 The Potential of a Moving Charge 70\u003c\/p\u003e \u003cp\u003e5.8 Energy and Momentum 76\u003c\/p\u003e \u003cp\u003e5.9 Maxwell’s Equations in Polarizable Media 78\u003c\/p\u003e \u003cp\u003e5.9.1 Boundary Conditions at an Interface 84\u003c\/p\u003e \u003cp\u003e5.10 Exercises 88\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6. Review of (3\u003c\/b\u003e+\u003cb\u003e1)D 91\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7. Introducing Spacetime 97\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Background and Key Concepts 98\u003c\/p\u003e \u003cp\u003e7.2 Time as a Vector 102\u003c\/p\u003e \u003cp\u003e7.3 The Spacetime Basis Elements 104\u003c\/p\u003e \u003cp\u003e7.3.1 Spatial and Temporal Vectors 106\u003c\/p\u003e \u003cp\u003e7.4 Basic Operations 109\u003c\/p\u003e \u003cp\u003e7.5 Velocity 111\u003c\/p\u003e \u003cp\u003e7.6 Different Basis Vectors and Frames 112\u003c\/p\u003e \u003cp\u003e7.7 Events and Histories 115\u003c\/p\u003e \u003cp\u003e7.7.1 Events 115\u003c\/p\u003e \u003cp\u003e7.7.2 Histories 115\u003c\/p\u003e \u003cp\u003e7.7.3 Straight-Line Histories and Their Time Vectors 116\u003c\/p\u003e \u003cp\u003e7.7.4 Arbitrary Histories 119\u003c\/p\u003e \u003cp\u003e7.8 The Spacetime Form of ∇ 121\u003c\/p\u003e \u003cp\u003e7.9 Working with Vector Differentiation 123\u003c\/p\u003e \u003cp\u003e7.10 Working without Basis Vectors 124\u003c\/p\u003e \u003cp\u003e7.11 Classifi cation of Spacetime Vectors and Bivectors 126\u003c\/p\u003e \u003cp\u003e7.12 Exercises 127\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8. Relating Spacetime to (3\u003c\/b\u003e+\u003cb\u003e1)D 129\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 The Correspondence between the Elements 129\u003c\/p\u003e \u003cp\u003e8.1.1 The Even Elements of Spacetime 130\u003c\/p\u003e \u003cp\u003e8.1.2 The Odd Elements of Spacetime 131\u003c\/p\u003e \u003cp\u003e8.1.3 From (3+1)D to Spacetime 132\u003c\/p\u003e \u003cp\u003e8.2 Translations in General 133\u003c\/p\u003e \u003cp\u003e8.2.1 Vectors 133\u003c\/p\u003e \u003cp\u003e8.2.2 Bivectors 135\u003c\/p\u003e \u003cp\u003e8.2.3 Trivectors 136\u003c\/p\u003e \u003cp\u003e8.3 Introduction to Spacetime Splits 137\u003c\/p\u003e \u003cp\u003e8.4 Some Important Spacetime Splits 140\u003c\/p\u003e \u003cp\u003e8.4.1 Time 140\u003c\/p\u003e \u003cp\u003e8.4.2 Velocity 141\u003c\/p\u003e \u003cp\u003e8.4.3 Vector Derivatives 142\u003c\/p\u003e \u003cp\u003e8.4.4 Vector Derivatives of General Multivectors 144\u003c\/p\u003e \u003cp\u003e8.5 What Next? 144\u003c\/p\u003e \u003cp\u003e8.6 Exercises 145\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9. Change of Basis Vectors 147\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Linear Transformations 147\u003c\/p\u003e \u003cp\u003e9.2 Relationship to Geometric Algebras 149\u003c\/p\u003e \u003cp\u003e9.3 Implementing Spatial Rotations and the Lorentz Transformation 150\u003c\/p\u003e \u003cp\u003e9.4 Lorentz Transformation of the Basis Vectors 153\u003c\/p\u003e \u003cp\u003e9.5 Lorentz Transformation of the Basis Bivectors 155\u003c\/p\u003e \u003cp\u003e9.6 Transformation of the Unit Scalar and Pseudoscalar 156\u003c\/p\u003e \u003cp\u003e9.7 Reverse Lorentz Transformation 156\u003c\/p\u003e \u003cp\u003e9.8 The Lorentz Transformation with Vectors in Component Form 158\u003c\/p\u003e \u003cp\u003e9.8.1 Transformation of a Vector versus a Transformation of Basis 158\u003c\/p\u003e \u003cp\u003e9.8.2 Transformation of Basis for Any Given Vector 162\u003c\/p\u003e \u003cp\u003e9.9 Dilations 165\u003c\/p\u003e \u003cp\u003e9.10 Exercises 166\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10. Further Spacetime Concepts 169\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Review of Frames and Time Vectors 169\u003c\/p\u003e \u003cp\u003e10.2 Frames in General 171\u003c\/p\u003e \u003cp\u003e10.3 Maps and Grids 173\u003c\/p\u003e \u003cp\u003e10.4 Proper Time 175\u003c\/p\u003e \u003cp\u003e10.5 Proper Velocity 176\u003c\/p\u003e \u003cp\u003e10.6 Relative Vectors and Paravectors 178\u003c\/p\u003e \u003cp\u003e10.6.1 Geometric Interpretation of the Spacetime Split 179\u003c\/p\u003e \u003cp\u003e10.6.2 Relative Basis Vectors 183\u003c\/p\u003e \u003cp\u003e10.6.3 Evaluating Relative Vectors 185\u003c\/p\u003e \u003cp\u003e10.6.4 Relative Vectors Involving Parameters 188\u003c\/p\u003e \u003cp\u003e10.6.5 Transforming Relative Vectors and Paravectors to a Different Frame 190\u003c\/p\u003e \u003cp\u003e10.7 Frame-Dependent versus Frame-Independent Scalars 192\u003c\/p\u003e \u003cp\u003e10.8 Change of Basis for Any Object in Component Form 194\u003c\/p\u003e \u003cp\u003e10.9 Velocity as Seen in Different Frames 196\u003c\/p\u003e \u003cp\u003e10.10 Frame-Free Form of the Lorentz Transformation 200\u003c\/p\u003e \u003cp\u003e10.11 Exercises 202\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11. Application of the Spacetime Geometric Algebra to Basic Electromagnetics 203\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 The Vector Potential and Some Spacetime Splits 204\u003c\/p\u003e \u003cp\u003e11.2 Maxwell’s Equations in Spacetime Form 208\u003c\/p\u003e \u003cp\u003e11.2.1 Maxwell’s Free Space or Microscopic Equation 208\u003c\/p\u003e \u003cp\u003e11.2.2 Maxwell’s Equations in Polarizable Media 210\u003c\/p\u003e \u003cp\u003e11.3 Charge Conservation and the Wave Equation 212\u003c\/p\u003e \u003cp\u003e11.4 Plane Electromagnetic Waves 213\u003c\/p\u003e \u003cp\u003e11.5 Transformation of the Electromagnetic Field 217\u003c\/p\u003e \u003cp\u003e11.5.1 A General Spacetime Split for \u003cb\u003e\u003ci\u003eF\u003c\/i\u003e\u003c\/b\u003e 217\u003c\/p\u003e \u003cp\u003e11.5.2 Maxwell’s Equation in a Different Frame 219\u003c\/p\u003e \u003cp\u003e11.5.3 Transformation of \u003cb\u003e\u003ci\u003eF\u003c\/i\u003e\u003c\/b\u003e by Replacement of Basis Elements 221\u003c\/p\u003e \u003cp\u003e11.5.4 The Electromagnetic Field of a Plane Wave Under a Change of Frame 223\u003c\/p\u003e \u003cp\u003e11.6 Lorentz Force 224\u003c\/p\u003e \u003cp\u003e11.7 The Spacetime Approach to Electrodynamics 227\u003c\/p\u003e \u003cp\u003e11.8 The Electromagnetic Field of a Moving Point Charge 232\u003c\/p\u003e \u003cp\u003e11.8.1 General Spacetime Form of a Charge’s Electromagnetic Potential 232\u003c\/p\u003e \u003cp\u003e11.8.2 Electromagnetic Potential of a Point Charge in Uniform Motion 234\u003c\/p\u003e \u003cp\u003e11.8.3 Electromagnetic Field of a Point Charge in Uniform Motion 237\u003c\/p\u003e \u003cp\u003e11.9 Exercises 240\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12. The Electromagnetic Field of a Point Charge Undergoing Acceleration 243\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Working with Null Vectors 243\u003c\/p\u003e \u003cp\u003e12.2 Finding \u003cb\u003e\u003ci\u003eF\u003c\/i\u003e\u003c\/b\u003e for a Moving Point Charge 248\u003c\/p\u003e \u003cp\u003e12.3 \u003cb\u003e\u003ci\u003eFrad\u003c\/i\u003e\u003c\/b\u003e in the Charge’s Rest Frame 252\u003c\/p\u003e \u003cp\u003e12.4 \u003cb\u003e\u003ci\u003eFrad\u003c\/i\u003e\u003c\/b\u003e in the Observer’s Rest Frame 254\u003c\/p\u003e \u003cp\u003e12.5 Exercises 258\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13. Conclusion 259\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14. Appendices 265\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Glossary 265\u003c\/p\u003e \u003cp\u003e14.2 Axial versus True Vectors 273\u003c\/p\u003e \u003cp\u003e14.3 Complex Numbers and the 2D Geometric Algebra 274\u003c\/p\u003e \u003cp\u003e14.4 The Structure of Vector Spaces and Geometric Algebras 275\u003c\/p\u003e \u003cp\u003e14.4.1 A Vector Space 275\u003c\/p\u003e \u003cp\u003e14.4.2 A Geometric Algebra 275\u003c\/p\u003e \u003cp\u003e14.5 Quaternions Compared 281\u003c\/p\u003e \u003cp\u003e14.6 Evaluation of an Integral in Equation (5.14) 283\u003c\/p\u003e \u003cp\u003e14.7 Formal Derivation of the Spacetime Vector Derivative 284\u003c\/p\u003e \u003cp\u003e\u003cb\u003eReferences 287\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eFurther Reading 291\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIndex 293\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eThe IEEE Press Series on Electromagnetic Wave Theory\u003c\/b\u003e\u003c\/p\u003e  \u003cp\u003e\"This book will benefit scientists and engineers who use electromagnetic theory in the course of their work.”  (\u003ci\u003eZentralblatt MATH\u003c\/i\u003e, 1 May 2013)\u003c\/p\u003e \u003cb\u003eJOHN W. ARTHUR\u003c\/b\u003e earned his PhD from Edinburgh University in 1974 for research into light scattering in crystals. He has been involved in academic research, the microelectronics industry, and corporate R\u0026amp;D. Dr. Arthur has published various research papers in acclaimed journals, including \u003ci\u003eIEEE Antennas and Propagation Magazine\u003c\/i\u003e. His 2008 paper entitled \"The Fundamentals of Electromagnetic Theory Revisited\" received the 2010 IEEE Donald G. Fink Prize for Best Tutorial Paper. A senior member of the IEEE, Dr. Arthur was elected a fellow of the Royal Society of Edinburgh and of the United Kingdom's Royal Academy of Engineering in 2002. He is currently an honorary fellow in the School of Engineering at the University of Edinburgh.  \u003cb\u003eProvides insight into classical electromagnetic theory through geometric algebra\u003c\/b\u003e  \u003cp\u003eThis practical book promotes the understanding of geometric algebra as a straightforward mathematical toolset for both working with and appreciating the fundamentals of electromagnetic theory. Taking a non-axiomatic, less formal tutorial approach, the text introduces new ideas gradually and goes into considerable detail in giving explanations and working out equations.\u003c\/p\u003e \u003cp\u003eAfter an introduction to geometric algebra, the book shows how to apply it to some basic concepts. Then, the essential toolset is developed, allowing for the application of geometric algebra more generally—for example, in any dimension of space. After applying the toolset to fundamental electromagnetics in the usual (3+1)D situation where space and time are separate entities, the book prepares the ground for a full 4D treatment in which they are treated equally as spacetime vectors. Through geometric algebra, the reader will discover how to tackle the electromagnetic theory of moving charges in a systematic yet uncomplicated way.\u003c\/p\u003e \u003cp\u003eIn later chapters, the book provides a self-contained primer on the spacetime approach that seeks to avoid the usual conceptual difficulties of special relativity. While this involves some intriguing subtleties, its application is straightforward and readers will see how the toolset unifies previously separate ideas under a single theme: Coulomb's Law + Spacetime = Σ Classical Electromagnetic Theory. The electromagnetic field of an accelerating charge is worked through in detail to show how the toolset is applied.\u003c\/p\u003e \u003cp\u003eMost chapters include exercises. There are figures and tables with detailed captions as well as various appendices that offer explanatory information and background material. In particular, a glossary provides an at-a-glance explanation of key terms and symbols.\u003c\/p\u003e \u003cp\u003eThis book will benefit scientists and engineers who use electromagnetic theory in the course of their work, including those who teach the subject; graduate students and senior undergraduates studying electromagnetics; and electromagnetic theorists.\u003c\/p\u003e \u003cp\u003eProblems and solutions materials are available by sending an email to pressbooks@ieee.org\u003c\/p\u003e","brand":"Wiley-IEEE Press","offers":[{"title":"Default Title","offer_id":47990429810917,"sku":"NP9780470941638","price":156.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780470941638.jpg?v=1761787794","url":"https:\/\/k12savings.com\/es\/products\/understanding-geometric-algebra-for-electromagnetic-theory-isbn-9780470941638","provider":"K12savings","version":"1.0","type":"link"}