Consider the period 4 function -2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:Consider the period 4 function
-2 < x < 0
0 <x < 2
( f(x+4) otherwise.
f(r) = {2 – x
(a) Sketch three periods of f(x).
(b) Show that the Fourier coefficients b1, b2, ... may be written as
1
bam-1 = 0 , bzm
for m = 1, 2, ....
(c) Knowing the Fourier coefficients
4
a2m = 0 ,
d2m-1=
(2m – 1)272
for m = 1,2, ..., write down the Fourier series corresponding to f(r).
(d) Briefly explain why the Dirichlet conditions hold.
(e) By evaluating f(x) at a suitable value of r, find
1.
(2m – 1)2
(f) Given
n=1
using Parseval's theorem and the value of (1), deduce that
1.
(2m – 1)4
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 5 steps with 5 images
Similar questions
- Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
Numerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEY
Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,
