f1[t_] := t ;

f2[t_] := t^2 ;

f3[t_] := t^3 ;

f4[t_] := UnitStep[t + Pi/2] - UnitStep[t - Pi/2] ;

f5[t_] := UnitStep[t] - UnitStep[t - Pi/2] ;

f6[t_] := UnitStep[t] - UnitStep[t - Pi/4] ;

f6[t_] := UnitStep[t] - UnitStep[t - Pi/8] ;

f7[t_] := UnitStep[t] - UnitStep[t - Pi/16] ;

f8[t_] := Sin[t] ;

f9[t_] := Cos[t] ;

f10[t_] := Sin[t] Cos[t] ;

f11[t_] := Sin[t] Cos[t]^2 + Exp[t] ;

f12[t_] := Exp[-Abs[t]] ;

f13[t_] := .5^Abs[t] ;

f14[t_] := 5 ;

f15[t_] := DiracDelta[t] 

ticks = {-4 Pi, -π, -π/2, 0, π/2, π, 4Pi} ;

fticks = {-4 Pi, -π, -π/2, 0, π/2, π, 4Pi} ; <br />

F[u_, T_, from_, to_] := 1/T∫_from^tog[t] ^(-2 π t u/T) t ; <br />

do[f_, T_, from_, to_] := Module[{}, g = f ; freq = Plot[Evaluate[F[u, T, fr ... 62371;Show[GraphicsArray[{p1, freq}], DisplayFunction$DisplayFunction] ]

from = -4Pi ; to = 4 Pi ; T = 8 Pi ;

do[f1, T, from, to] ;

do[f2, T, from, to] ;

do[f3, T, from, to] ;

do[f4, T, from, to] ;

do[f5, T, from, to] ;

do[f6, T, from, to] ;

do[f7, T, from, to] ;

do[f8, T, from, to] ;

do[f9, T, from, to] ;

do[f10, T, from, to] ; 

  do[f15, 4  Pi, -∞, ∞] 

[Graphics:HTMLFiles/index_33.gif]

⁃GraphicsArray⁃

2/(1 + (2 Pi (1/2 Pi))^2)//N

? PlotStyle

? Plot

Transpose[{{1, 2, 3}, {4, 5, 6}}]

{{1, 2, 3}, {4, 5, 6}}//MatrixForm

Transpose {x, N[(Abs[freq])^2]}

? Transpose

? Version

System`Version

System`Version

$Version

? ParametricPlot

? Table

Transpose[Table[i, {i, -Pi, Pi, Pi/8}], mag]

Length[Table[i, {i, -Pi, Pi, Pi/8}]]

Length[mag]

Transpose[{1, 2}, {2, 3}]

Needs["Graphics`Graphics`"]

Clear[pairs, x, y] <br />

y = {1., 0., 1., 2., 1.}

x = {0., 1., 1., 1., 2.}

pairs = Table[{x[[i]], y[[i]]}, {i, 1, 4}] <br />

LabeledListPlot[pairs]

freq = Table[F[u, f2], {u, -Pi, π, π/8}]

N[%]

? Xticks

? Ticks

? Abs

r = FullSimplify[∫_ (-∞)^∞A  ^-u^2/(2σ^2) ^(-  2 Pi x u)   u, Element[{u, x, σ, M}, Integers]]

Limit[%, {M, ∞}]

Erf[∞/Sign[σ]]//N

∫_ (-∞)^∞ A ^(-u^2/(2 a^2)) ^( 2 π u x) u

^(-u^2/(2 a^2)) ^( 2 π u x)

FullSimplify[1/(4 π^2) ∫_ (-∞)^∞^(-u^2/(2 a^2) + 2  π u x) u, Element[a>0]]

Integrate :: gener : Unable to check convergence. More…

Element :: argrx : Element called with 1 arguments; 2 arguments are expected. More…

1/(4 π^2) If[Re[a^2] >0, a^2^(1/2) ^(-2 a^2 π^2 x^2) (2 π)^(1/2), ... /(2 a^2) + 2  π u x), {u, -∞, ∞}, AssumptionsRe[a^2] ≤0]]

FullSimplify[∫_ (-∞)^∞Exp[ 2 π (u x + v y)] u, Element[{u, v}, Reals]]

2  π (u x + v y) Integrate :: idiv : I ... f  does not converge on {-∞, ∞} . More…

∫_ (-∞)^∞^(2  π (u x + v y)) u

Limit[%, M∞]

Limit[(^(2  π v y) Sin[2 M π x])/(π x), M∞]

? DiracDelta*

DiracDelta[x] represents the Dirac delta function δ(x). DiracDelta[x1, x2, ... ] represents the multidimensional Dirac delta function δ(x1, x2, …). More…

Plot[Exp[Abs[x]], {x, -3, 3}]

[Graphics:HTMLFiles/index_80.gif]

⁃Graphics⁃

? Gauss*

System`
GaussianIntegers GaussKronrod GaussPoints

σ = 6 ; α = .4 ; A = 7 ; B = 1 ;

Plot[ B  ^-t^2/(2σ^2) - A ^-t^2/(2α^2) , {t, -3, 3}]

[Graphics:HTMLFiles/index_88.gif]

⁃Graphics⁃

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