1)2)By explicitly expanding the summations, show the substitution rule oipci =Obtain the resultsOff...

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1)2)By explicitly expanding the summations, show the substitution rule oipci =Obtain the resultsOff = 3, bk;bk = Oil,With u(r) being a vector field, and 0(x) and 0(x) being scalar fields. write in Cartesian tensor suffix notation (a) u = V0, (b) 0 = V • u, and (c) an equation, deduced from (a) and (b), relating 0. to 0. The quantities ui, Au, B,,,,, and Coe are given tensors (not tensor fields). In each of (a)—(e), use every one of these tensors to complete a valid equation for the indicated quantity: (a) a scalar: 0 = (b) a first-order tensor: vj = (c) a second-order tensor: TM = (d) a third-order tensor: F,„„ = (e) a fourth-order tensor: V, = (for example, a possible answer to (a) is 4) =• A„ + u,Bpj +3) Show that the product of two first order tensors a and 17, is a second order tensor
	
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3) Show that the product of two first order tensors  and  is a second order tensor

David · Accepted Answer

Microsoft Word - solution
Problem-1:- 
In the given eq. putting j=i gives that 1 
Also, ∗ ∗ 	 	
Problem-2:- 
 
(a) u ∅ ı̂ ∅ ȷ̂ ∅ k 
u ∂∅∂x ı̂
∂∅
∂y ȷ̂
∂∅
∂z k 
u ∂∅∂x ı̂
∂∅
∂y ȷ̂
∂∅
∂z k 
(b) 	 	 	   
 
(c) We have 	 ∙ 	 ∙ ∅ 	 ∅ 
Hence, we have 	 ∅ ∅ ∅ 
Now. We have given ui ,

1) 2) By explicitly expanding the summations, show the substitution rule oipci = Obtain the results Off = 3, bk;bk = Oil, With u(r) being a vector field, and 0(x) and 0(x) being scalar fields. write...

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