1- Verify the orthogonality properties of sines and cosines on the interval [—L, L] So, m #n * sin(max/L) sin(näx/L) dx = LL, m = n m #n So, [*cos(max/L) cos(nnx/L) dx = LL, m = n sin(mлx/L) cos(nлx/L) dx = 0 all m, n = 1,2,3,... 7
1- Verify the orthogonality properties of sines and cosines on the interval [—L, L] So, m #n * sin(max/L) sin(näx/L) dx = LL, m = n m #n So, [*cos(max/L) cos(nnx/L) dx = LL, m = n sin(mлx/L) cos(nлx/L) dx = 0 all m, n = 1,2,3,... 7
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![1- Verify the orthogonality properties of sines and cosines on the interval [-L, L]
So,
m #n
sin(max/L) sin(nлx/L) dx = LL,
m = n
[² si
Lo cos(max/L) cos(nnx/L) dx = {
m #n
m = n
L
sin(mлx/L) cos(nлx/L) dx = 0 all m, n = 1,2,3,...](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff09ced9d-af9e-4dd9-997d-dfc5e9537dc9%2F3f57d9db-15fc-4aeb-b7cd-f2fa0a2ec349%2Fm42ue4r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1- Verify the orthogonality properties of sines and cosines on the interval [-L, L]
So,
m #n
sin(max/L) sin(nлx/L) dx = LL,
m = n
[² si
Lo cos(max/L) cos(nnx/L) dx = {
m #n
m = n
L
sin(mлx/L) cos(nлx/L) dx = 0 all m, n = 1,2,3,...
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