DIFFERENTIAL FORMS IN ELECTROMAGNETICS
CONTENTS MULTIVECTORS THE GRASSMANN ALGEBRA VECTORS AND DUAL VECTORS BASIC DEFINITIONS DUALITY PRODUCT DYADICS BIVECTORS WEDGE PRODUCT BASIS BIVECTORS INCOMPLETE DUALITY PRODUCT BIVECTOR DYADICS TRIVECTORS BASIS TRIVECTORS TRIVECTOR IDENTITIES P-VECTORS BASIS MULTIVECTORS GENERALIZED BAC CAB RULE GEOMETRIC INTERPRETATION VECTORS AND BIVECTORS DUAL VECTORS DUAL BIVECTORS AND TRIVECTORS DYADIC ALGEBRA PRODUCTS OF DYADICS BASIC NOTATION DOUBLE-DUALITY PRODUCT DOUBLE-WEDGE PRODUCT DOUBLE-WEDGE SQUARE DOUBLE-WEDGE CUBE HIGHER DOUBLE-WEDGE POWERS DOUBLE-INCOMPLETE DUALITY PRODUCT DYADIC IDENTITIES GIBBS’IDENTITY IN THREE DIMENSIONS GIBBS’IDENTITY IN N DIMENSIONS CONSTRUCTING IDENTITIES EIGENPROBLEMS LEFT AND RIGHT EIGENVECTORS EIGENVALUES EIGENVECTORS INVERSE DYADIC RECIPROCAL BASIS THE INVERSE DYADIC INVERSE IN THREE DIMENSIONS METRIC DYADICS DOT PRODUCT PROPERTIES OF THE DOT PRODUCT METRIC IN MULTIVECTOR SPACES HODGE DYADICS COMPLEMENTARY SPACES THREE-DIMENSIONAL EUCLIDEAN HODGE DYADICS TWO-DIMENSIONAL EUCLIDEAN HODGE DYADIC FOUR-DIMENSIONAL MINKOWSKIAN HODGE DYADICS DIFFERENTIAL FORMS DIFFERENTIATION THREE-DIMENSIONAL SPACE FOUR-DIMENSIONAL SPACE SPATIAL AND TEMPORAL COMPONENTS DIFFERENTIATION THEOREMS POINCARɒS LEMMA AND DE RHAM’S THEOREM HELMHOLTZ DECOMPOSITION INTEGRATION MANIFOLDS STOKES’THEOREM EUCLIDEAN SIMPLEXES AFFINE TRANSFORMATIONS TRANSFORMATION OF DIFFERENTIAL FORMS THREE-DIMENSIONAL ROTATION FOUR-DIMENSIONAL ROTATION ELECTROMAGNETIC FIELDS AND SOURCES BASIC ELECTROMAGNETIC QUANTITIES MAXWELL EQUATIONS IN THREE DIMENSIONS MAXWELL–FARADAY EQUATIONS MAXWELL–AMPÈRE EQUATIONS TIME-HARMONIC FIELDS AND SOURCES MAXWELL EQUATIONS IN FOUR DIMENSIONS THE FORCE FIELD THE SOURCE FIELD DESCHAMPS GRAPHS MEDIUM EQUATION MAGNETIC SOURCES TRANSFORMATIONS COORDINATE TRANSFORMATIONS AFFINE TRANSFORMATION SUPER FORMS MAXWELL EQUATIONS MEDIUM EQUATIONS TIME-HARMONIC SOURCES MEDIUM, BOUNDARY, AND POWER CONDITIONS MEDIUM CONDITIONS MODIFIED MEDIUM DYADICS BI-ANISOTROPIC MEDIUM DIFFERENT REPRESENTATIONS ISOTROPIC MEDIUM BI-ISOTROPIC MEDIUM UNIAXIAL MEDIUM Q-MEDIUM GENERALIZED Q-MEDIUM CONDITIONS ON BOUNDARIES AND INTERFACES COMBINING SOURCE-FIELD SYSTEMS INTERFACE CONDITIONS BOUNDARY CONDITIONS HUYGENS’PRINCIPLE POWER CONDITIONS THREE-DIMENSIONAL FORMALISM FOUR-DIMENSIONAL FORMALISM COMPLEX POWER RELATIONS IDEAL BOUNDARY CONDITIONS THE LORENTZ FORCE LAW THREE-DIMENSIONAL FORCE FORCE-ENERGY IN FOUR DIMENSIONS STRESS DYADIC STRESS DYADIC IN FOUR DIMENSIONS EXPANSION IN THREE DIMENSIONS MEDIUM CONDITION COMPLEX FORCE AND STRESS THEOREMS AND TRANSFORMATIONS DUALITY TRANSFORMATION DUAL SUBSTITUTION GENERAL DUALITY SIMPLE DUALITY DUALITY ROTATION RECIPROCITY LORENTZ RECIPROCITY EQUIVALENCE OF SOURCES NONRADIATING SOURCES EQUIVALENT SOURCES ELECTROMAGNETIC WAVES WAVE EQUATION FOR POTENTIALS ELECTRIC FOUR-POTENTIAL MAGNETIC FOUR-POTENTIAL ANISOTROPIC MEDIUM SPECIAL ANISOTROPIC MEDIUM THREE-DIMENSIONAL EQUATIONS EQUATIONS FOR FIELD TWO-FORMS WAVE EQUATION FOR FIELDS THREE-DIMENSIONAL FIELD EQUATIONS FOUR-DIMENSIONAL FIELD EQUATIONS PLANE WAVES WAVE EQUATIONS TE AND TM POLARIZED WAVES PLANE-WAVE EQUATIONS TE AND TM POLARIZATIONS GREEN FUNCTIONS GREEN FUNCTION AS A MAPPING THREE-DIMENSIONAL REPRESENTATION FOUR-DIMENSIONAL REPRESENTATION REFERENCES