1. Use of the Einstein summation convention is a very efficient way to write a series of equations in a compact form. a) What are the two essential components of the convention, as applied with a 3 dimensional Cartesian frame of reference. Explain the Kroneker delta, ðj. b) Write the following 3 equations in compact form using the Einstein convention. Xi= (a¡bı+a2bz+a3c3)yı + 5c1 X2= (a¡bı+a2bz+a3c3)y2 + 5c2 X3= (a,bı+a2b>+a;C:)y3 + 5c3 c) Expand the (Navier-Stokes for a constant density fluid) equation below into its component form for i = 1. du/ôt + ug ôu;/ôxk = -(1/p)ôp/ôx¡ – gði3 + (µ/p)ô²u/(ôxmôxm)

1. Use of the Einstein summation convention is a very efficient way to write a series of equations in a compact form. a) What are the two essential components of the convention, as applied with a 3 dimensional Cartesian frame of reference. Explain the Kroneker delta, ðj. b) Write the following 3 equations in compact form using the Einstein convention. Xi= (a¡bı+a2bz+a3c3)yı + 5c1 X2= (a¡bı+a2bz+a3c3)y2 + 5c2 X3= (a,bı+a2b>+a;C:)y3 + 5c3 c) Expand the (Navier-Stokes for a constant density fluid) equation below into its component form for i = 1. du/ôt + ug ôu;/ôxk = -(1/p)ôp/ôx¡ – gði3 + (µ/p)ô²u/(ôxmôxm)