f(x) = sin¹ (π

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 77E
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Calculate the Fourier Transforms for: f(x) = sin² (πk¸x)
f(x) = sinª (πk¸x)
Transcribed Image Text:Calculate the Fourier Transforms for: f(x) = sin² (πk¸x) f(x) = sinª (πk¸x)
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Follow-up Question
dy
Find the periodic solutions of the differential equations (a)- + ky = f(x), (b) -+ky = f(x)
dx
where k is a constant and f (x) is a 2π - periodic function.
Consider a Fourier series expansion for f(x) using the complex form, f(x) = [ƒ₂e¹x
inx
n=+∞o
d³y
d³x
and try a solution of the form y(x) = Σy ex
11=+00
n=-00
Transcribed Image Text:dy Find the periodic solutions of the differential equations (a)- + ky = f(x), (b) -+ky = f(x) dx where k is a constant and f (x) is a 2π - periodic function. Consider a Fourier series expansion for f(x) using the complex form, f(x) = [ƒ₂e¹x inx n=+∞o d³y d³x and try a solution of the form y(x) = Σy ex 11=+00 n=-00
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