Transcription of Index Notation for Vector Calculus
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Index Notation for Vector Calculus
Index Notation for Vector CalculusbyIlan Ben-Yaacov and Francesc RoigCopyrightc 2006 Index Notation , also commonly known as subscript Notation or tensor Notation ,is an extremely useful tool for performing Vector algebra . Consider the coordinatesystem illustrated in Figure 1. Instead of using the typical axis labelsx,y, andz,we usex1,x2, andx3, orxii= 1,2,3 The corresponding unit basis vectors are then e1, e2, and e3, or eii= 1,2,3 The basis vectors e1, e2, and e3have the following properties: e1 e1= e2 e2= e3 e3= 1(1) e1 e2= e1 e3= e2 e3= 0(2)x1x2x3a1a2a3ae1e2e3 Figure 1: Reference coordinate NotationWe now introduce theKronecker deltasymbol ij.
Using index notation, we can express the vector ~A as ... Eqn 20 is an extremely useful property in vector algebra and vector calculus applications. It can also be …
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