Because set? -d cos(nлx/d) cos(max/d)dx = 0, m‡n, the functions cos(nmx/d) for n = 1, 2, 3,... form an orthogonal set. What constant must these funcions be multiplied by to form an orthonormal
Because set? -d cos(nлx/d) cos(max/d)dx = 0, m‡n, the functions cos(nmx/d) for n = 1, 2, 3,... form an orthogonal set. What constant must these funcions be multiplied by to form an orthonormal
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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![d
• 1 confer
сos (nлx/d) cos(mπx/d)dx = 0, m‡n, the functions cos(nπx/d) for n = 1, 2, 3, . . . form an orthogonal set. What constant must these funcions be multiplied by to form an orthonormal
-d
Because
set?
Match the items in the left column to the appropriate blanks in the equations on the right. Make certain each equation is complete before submitting your answer.
cos(-2mm)
d
sin (2ax)
sin(2mT)
0
cos(2ax)
1
-d
sin(-2mT)
cos(2mπ)
Orthonormal functions must satisfy the condition:
d
·Ï
N²
N
cos² (mTx/d)dx
-d
To convert the expression use the standard integral
² (² ₂ +
d
=
=
N²
+
d
4mT
]
d
+
2
² (ax) dx =
Cos²
d
4mT
N|T
·x +
1
4a
Reset
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Transcribed Image Text:d
• 1 confer
сos (nлx/d) cos(mπx/d)dx = 0, m‡n, the functions cos(nπx/d) for n = 1, 2, 3, . . . form an orthogonal set. What constant must these funcions be multiplied by to form an orthonormal
-d
Because
set?
Match the items in the left column to the appropriate blanks in the equations on the right. Make certain each equation is complete before submitting your answer.
cos(-2mm)
d
sin (2ax)
sin(2mT)
0
cos(2ax)
1
-d
sin(-2mT)
cos(2mπ)
Orthonormal functions must satisfy the condition:
d
·Ï
N²
N
cos² (mTx/d)dx
-d
To convert the expression use the standard integral
² (² ₂ +
d
=
=
N²
+
d
4mT
]
d
+
2
² (ax) dx =
Cos²
d
4mT
N|T
·x +
1
4a
Reset
Help
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