Project presentation times

RandomSample[{a,b,c,d},2]

RandomSample[{a,b,c,d},4]

RandomSample[{Anastasia,Taylor,Michael,Nathan,Greg,Dylan,Dakota,Joe},8]

Bessel functions

Sum[x^k/k!,{k,0,Infinity}]

Sum[(-1)^k/(2k)!x^(2k),{k,0,Infinity}]

Sum[(-1)^k/4^k/(k!)^2 x^(2k),{k,0,Infinity}]

Plot[BesselJ[0,z],{z,0,30}]

Plot[BesselY[0,z],{z,0,30}]

Timing[FindRoot[BesselJ[0,z],{z,0.1}]]

α[1]=z/.%

Plot[BesselJ[0,α[1]r],{r,0,1}]

FindRoot[BesselJ[0,z],{z,5}]

α[2]=z/.%

Plot[BesselJ[0,α[2]r],{r,0,1}]

BesselJZero[0,1]

N[%]

α[n_]=N[BesselJZero[0,n]]

α5=N[BesselJZero[0,5]]

Plot[BesselJ[0,α[5] r],{r,0,1}]

RevolutionPlot3D[BesselJ[0,α[1] r],{r,0,1},{θ,0,2Pi}]

Animate[
RevolutionPlot3D[BesselJ[0,α[2] r]Cos[α[2] t],{r,0,1},{θ,0,2Pi},PlotRange->{-1,1},Mesh->True],{t,0,20,0.1},AnimationRunning->False]