# Tag Info

4

Note the last condition, or consider limit of Riemann sum $\Delta t=\frac{b-a}{n}$. As can be seen the expected integral should be positive: f[x_, y_] := x y/(1 + x + 2 y); p3 = Plot3D[f[x, y], {x, 0, 1}, {y, 0, 1}, MeshFunctions -> (#1^2 + #2^2 &), Mesh -> {{1}}, PlotStyle -> Opacity[0.5]]; pp = ParametricPlot3D[{t, Sqrt[1 - t^2], ...

5

Some time ago I developed a function for these sort of symbolic vector computations, called dotExand. For example, it will expand (2 x + 3 y, x-y) to 2(x,x)+(x,y)-3(y,y). Here I use the, at least in my country more common, notation (x,y) for the inner product of the vectors x and y. The advantage is that complicated expressions become more readable in this ...

3

Here is the best I've got so far. If you can be persuaded to write your vectors in a more distinguishable way, e.g. $v_1$ as v[1], then the following might work for you. I'm not so sure how robust it will be, but play around with it and let me know: Clear[specialDot] specialDot[expr_] := ReplaceAll[ Distribute[expr, Plus, Dot, Plus, Times], v[a_] v[b_] ...

1

I suspect you just need to do that yourself by defining your own div function div[{Power[r_,-2],0,0},{r_,_,_},"Spherical"]=DiracDelta[r]; div[args___]:=Div[args] div[{1/x^2,0,0},{x,y,z},"Spherical"] DiracDelta[x]

Top 50 recent answers are included