Part 1: Find the Eigenfunction Expansion Consider the function f (same as in the previous problem) defined on the interval [0, 10] as follows, 3 x, f(x)= x = [0,5], 5 3. x = [5, 10]. Find the coefficients C, of the eigenfunction expansion of function f, 00 f(x) = co+cn Yn(x), where yo=1 (which is not a unit eigenfunction), while yn, for n = 1, 2, 3, ., are unit the eigenfunctions of the Regular Sturm-Liouville system -y" = Ay. y' (0) = 0, y' (10) = 0. Note: The constant eigenfunction yo= 1 is not a unit eigenfunction, since yo yo = 10. Therefore, the formula for co is co= the eigenfunctions yn, for n = 1, 2, 3, ... to be unit eigenfunctions. Therefore, the formula for the coefficients c, is C = fyn- f-yo We choose yo yo Σ Co= Σ Cn =
Part 1: Find the Eigenfunction Expansion Consider the function f (same as in the previous problem) defined on the interval [0, 10] as follows, 3 x, f(x)= x = [0,5], 5 3. x = [5, 10]. Find the coefficients C, of the eigenfunction expansion of function f, 00 f(x) = co+cn Yn(x), where yo=1 (which is not a unit eigenfunction), while yn, for n = 1, 2, 3, ., are unit the eigenfunctions of the Regular Sturm-Liouville system -y" = Ay. y' (0) = 0, y' (10) = 0. Note: The constant eigenfunction yo= 1 is not a unit eigenfunction, since yo yo = 10. Therefore, the formula for co is co= the eigenfunctions yn, for n = 1, 2, 3, ... to be unit eigenfunctions. Therefore, the formula for the coefficients c, is C = fyn- f-yo We choose yo yo Σ Co= Σ Cn =
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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![Part 1: Find the Eigenfunction Expansion
Consider the function f (same as in the previous problem) defined on the interval [0, 10] as follows,
3
x,
f(x)=
x = [0,5],
5
3.
x = [5, 10].
Find the coefficients C, of the eigenfunction expansion of function f,
00
f(x) = co+cn Yn(x),
where yo=1 (which is not a unit eigenfunction), while yn, for n = 1, 2, 3, ., are unit the eigenfunctions of the Regular Sturm-Liouville system
-y" = Ay. y' (0) = 0, y' (10) = 0.
Note:
The constant eigenfunction yo= 1 is not a unit eigenfunction, since yo yo = 10. Therefore, the formula for co is co=
the eigenfunctions yn, for n = 1, 2, 3, ... to be unit eigenfunctions. Therefore, the formula for the coefficients c, is C = fyn-
f-yo
We choose
yo yo
Σ
Co=
Σ
Cn =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F70b0be1d-05d2-4889-9ebe-d10a05ca7046%2F8c283c04-0e82-47bd-88b8-3dfc26d951a5%2Fatk92wc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Part 1: Find the Eigenfunction Expansion
Consider the function f (same as in the previous problem) defined on the interval [0, 10] as follows,
3
x,
f(x)=
x = [0,5],
5
3.
x = [5, 10].
Find the coefficients C, of the eigenfunction expansion of function f,
00
f(x) = co+cn Yn(x),
where yo=1 (which is not a unit eigenfunction), while yn, for n = 1, 2, 3, ., are unit the eigenfunctions of the Regular Sturm-Liouville system
-y" = Ay. y' (0) = 0, y' (10) = 0.
Note:
The constant eigenfunction yo= 1 is not a unit eigenfunction, since yo yo = 10. Therefore, the formula for co is co=
the eigenfunctions yn, for n = 1, 2, 3, ... to be unit eigenfunctions. Therefore, the formula for the coefficients c, is C = fyn-
f-yo
We choose
yo yo
Σ
Co=
Σ
Cn =
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