Divergence and Curl

I have defined divergence and curl functions (separate from Mathematica's versions. I think these versions make it easier to evaluate using different variables. These are in the notebook "initialization.ma"
div2[f_]:=D[f[#1,#2][[1]],#1]+D[f[#1,#2][[2]],#2]&

div3[f_]:=D[f[#1,#2,#3][[1]],#1]+D[f[#1,#2,#3][[2]],#2]+D[f[#1,#2,#3][[3]],#3]&

curl2[f_]:=- D[f[#1,#2][[1]],#2] + D[f[#1,#2][[2]],#1]&

curl3[f_]:={- D[f[#1,#2,#3][[2]],#3] + D[f[#1,#2,#3][[3]],#2], D[f[#1,#2,#3][[1]],#3] - D[f[#1,#2,#3][[3]],#1], - D[f[#1,#2,#3][[1]],#2] + D[f[#1,#2,#3][[2]],#1]}&

Examples

Important Properties

Divergence

We will have more to say about divergence and curl when we discuss integration.

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