Electromagnetic Cource Lecture

I.1. PRELMINARY MATH WORKS forELECTROMAGNETICSIntroductionMain topicstobe handledin thischapter:VectorAlgebraScaling, addition, subtractionandmultiplicationofvectors3D CoordinatesystemsCartesian(Rectangular)CylindricalSphericalVectorCalculusDifferentiationandintegrationof vectorsLine, surfaceandvolumeintegralsDel operatorwithgradient, divergenceandcurloperationsVECTOR CALCULUSQuantitiesof EM fieldsexaminedin 3D space+ time as a parameterora 4D variableGeometryas a toolforspatialfunctionsandvariations. Geometricalelementssortedwithincreasingcomplexityexistingin 1D-3D space:pointslinescurvesplanessurfacesvolumesTherepresentaionof theseelementsin 3D spacegovernedby3D coordinatesystemsBothEM quantitesandthegeometricalelementscan be shownin theform of scalarorvectorrepresentation.ScalarsandVectorsForthefieldquantitiesVectorsVectorDescriptionBasic Lawsof VectorAlgebraScalarandvectorrepresentationsPurpose: pointinga location, andshowingthedirectionwrta referencepoint=: vectorquantity(complexorphasorform): unitvectorquantity(withmagnitudebeing1): scalarquantity(real, complex/ phasor)A=: magnitude of a field(realandpositive)A=Amaynot holdBasic Lawsof VectorAlgebraVectorCalculationsBasic Lawsof VectorAlgebraEqualityof twovectorsBasic Lawsof VectorAlgebraVectorAdditionwhere, etcVectoradditionis commutativeBasic Lawsof VectorAlgebraVectorSubtractionVectorsubtractionis not commutativeDA-B B-ABasic Lawsof VectorAlgebraPositionandDistanceVectorsThedistancevector,zxyBasic Lawsof VectorAlgebraVectorMultiplicationa) Simple Productb) Dot(Scalar) ProductABasic Lawsof VectorAlgebraSince, cos 0= 1Basic Lawsof VectorAlgebrac) Cross (Vector) Product, is unitnormal vectorperpendiculartoAB -plane.Basic Lawsof VectorAlgebraSince, sin 0= 0Right-HandRulegovernsthecyclicorderof ( x) product:Basic Lawsof VectorAlgebraLetmatrixDetA=Basic Lawsof VectorAlgebrae.g.VectorsandAnglesBasic Lawsof VectorAlgebraBasic Lawsof VectorAlgebrae.g.