NUMERICAL OPERATIONS

2 + Sqrt[2]

N[%]

Integrate[ Sin[Sin[x]], {x,0,1} ]

N[%]

NIntegrate[ Sin[Sin[x]], {x,0,1} ]

NIntegrate[ Sin[(x-y)^2], {x,0,1}, {y,0,1} ]

NIntegrate[ E^(-x^2), {x,-Infinity, Infinity}]

N[%,11]

N[ Sqrt[Pi], 11]

??NIntegrate

NIntegrate[ 1/z, {z,1,I,-1,-I,1} ]

2 Pi I Residue[ 1/z, {z,0} ]

NSum[ 1/i^4, {i,1,Infinity} ]

N[ Pi^4/90 ]

NSolve[ x^8 + x^3 -1 == 0, x ]

FindRoot[ 2 Sin[x] - E^Cos[x] == 0, {x,1} ]

Plot[ 2 Sin[x] - E^Cos[x], {x,0,4}]

NDSolve[ {y'[x] - y[x]^(2/3) == 0, y[0] == 1 },
         y, {x,0,1} ]

Plot[ Evaluate[ y[x] /. % ], {x,0,1}  ]

Sqrt[x] y''[x] - y[x]^(3/2)

NDSolve[ {% == 0, y[1]==1, y'[1]==1}, y, {x,1,2} ]

Plot[Evaluate[y[x] /. %], {x,1,2}]

??NDSolve

data = Table[ Exp[-0.5 i], {i,10} ]

myfit = Fit[ data, {1,x,x^2}, x ]

?Fit

Plot[ {Exp[-0.5 x], myfit}, {x,0,10}]

data = {-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1}

ListPlot[ data, PlotJoined -> True ]

N[ Fourier[data] ]

ListPlot[ -Re[%], PlotJoined -> True ]