HW2a - Page 512, problem 2: πx / 2 0 < x < 1...

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Unformatted text preview: Page 512, problem 2: πx / 2 0 < x < 1 ∞ 1 2 2 πv sin(ω ) − ω ⋅ cos(ω ) f ( x) = π / 4 x = 1 ⇒ B (ω ) = ∫ f (v ) sin(ωv)dv = ∫ sin(ωv)dv = π0 π02 ω2 0 x >1 ∞ ∞ sin(ω ) − ω ⋅ cos(ω ) sin(ωx)dω ω2 0 ⇒ f ( x ) = ∫ B (ω ) sin(ωx)dω = ∫ 0 Page 512, problem 9: ∞ 1 x 0 < x < 1 2 2 2 cos(ω ) + ω ⋅ sin(ω ) − 1 f ( x) = ⇒ A(ω ) = ∫ f (v ) cos(vω )dv = ∫ v ⋅ cos(vω )dv = π0 π0 π ω2 0 x > 1 ∞ 2 cos(ω ) + ω ⋅ sin(ω ) − 1 cos(ωx)dω π∫ ω2 0 Page 512, problem 15: ⇒ f ( x) = ∞ π sin( x) 0 < x < π 2 2 2 f ( x) = ⇒ B (ω ) = ∫ f (v) sin(vω )dv = ∫ sin(v ) sin(vω ) dv = sin(πω) x >π π0 π0 1− ω2 0 ∞ 2 sin(πω) sin( xω )dω 2 0 1−ω ⇒ f ( x) = ∫ ...
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