Transcription of 3.2 Vector and Tensor Mathematics - …
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3.2 Vector and Tensor Mathematics - …
TensorMathematicsThevariablesusedto describe physicalquantitiesare of a number of types,includingscalars,vectors,and orthas been madein the notestoindicatethesetypes consistently as follows:s= scalar;lightfaceitalicv= Vector ;boldfacewithsingleunderscoreT= Tensor ;boldfacewithdoubleunderscore:( )Scalarsare usedto represent physicalquantitieswithno directionalqualities,such as temperature,volume,and usedfor quantitieswhichhave a singledirectionalquality such as velocity and (we willconsideronlysecond-ordertensors)are associatedwithquantitieswhich havetwo directionalcharacteristics,such as a momentum VectorOperationsGiven a coordinatesystemin threedimensions,a vectormay thus be repre-sented by an orderedset of threecomponents which represent its projectionsv1; v2; v3on the coordinateaxes1;2;3:v= [v1; v2.]
Vector and Tensor Mathematics 23 3.2 Vector and Tensor Mathematics Thevariablesusedtodescribephysicalquantitiesareofanumberoftypes, includingscalars,vectors,andtensors.
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