In the exam, there will be on method of undetermined coefficients for an order three or order four equation. • y " + 2y"+y = 3 sint-Scost etc. • one question Such as:.
In the exam, there will be on method of undetermined coefficients for an order three or order four equation. • y " + 2y"+y = 3 sint-Scost etc. • one question Such as:.
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
![Remarks There will be four questions.
In the exam,
in the final
exam
•The topic of mechanical vibrations is not included
• The topic of eigenvalues/eigenvectors is not included.
• The exam
is open book.
there will be
•one question
on method of undetermined coefficients for an order three or order four equation.
Such as: y+2y"+y = 3 sint-Scost
etc.
.
I
• One question about Laplare transform and ODEs involving impulse functions:
such as:
• y"+y= u(t)+38(t−3π/2) - U₂(1);
62y"+y+4y= 8(t - n/6) sint;
y(0) = 0, y'(0) = 0
y(0) = 0, y'(0) = 0
from the book.
y" + 2y + 2y = cost + 8(t - π/2); y(0) = 0, y'(0)=0
y-y=8(t-1); y(0) = 0, y'(0) = 0, y"(0) = 0, y"(0) = 0
"One question about kernel of operators and matrix representation of operators:
such as:
• Let Ti P₁-P₂ be defined
by
Tlp)=p"-p"!
(a) Determine ker (1).
(b) Find 9€ P4 such that T(q) = 2x.
(c) By using the basis A. {lixixix³} represent T₁9 and 2x as matrices and verify
that [7] [9] = [2x]A
One question about the determinant and the rank.
such as
Let X and Y be constants. Consider the matrices
[0-1
-1 -1
Y 8
B=
-9
A= 3 X 8
02
C= 6 X
-4
03
6
Given that rank(A) <3 and nullity(B) = 1; find the nullity, rank and the null space of C.
• Verify Ronk and Nullity theorem for A and AT
2
3
1
where A-
4
2
-1
6
3 O](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F48965f99-7319-4e8d-a667-7a651107f947%2F043e8ef3-c78f-4717-9849-6197fdb450b3%2Fv67jxrc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Remarks There will be four questions.
In the exam,
in the final
exam
•The topic of mechanical vibrations is not included
• The topic of eigenvalues/eigenvectors is not included.
• The exam
is open book.
there will be
•one question
on method of undetermined coefficients for an order three or order four equation.
Such as: y+2y"+y = 3 sint-Scost
etc.
.
I
• One question about Laplare transform and ODEs involving impulse functions:
such as:
• y"+y= u(t)+38(t−3π/2) - U₂(1);
62y"+y+4y= 8(t - n/6) sint;
y(0) = 0, y'(0) = 0
y(0) = 0, y'(0) = 0
from the book.
y" + 2y + 2y = cost + 8(t - π/2); y(0) = 0, y'(0)=0
y-y=8(t-1); y(0) = 0, y'(0) = 0, y"(0) = 0, y"(0) = 0
"One question about kernel of operators and matrix representation of operators:
such as:
• Let Ti P₁-P₂ be defined
by
Tlp)=p"-p"!
(a) Determine ker (1).
(b) Find 9€ P4 such that T(q) = 2x.
(c) By using the basis A. {lixixix³} represent T₁9 and 2x as matrices and verify
that [7] [9] = [2x]A
One question about the determinant and the rank.
such as
Let X and Y be constants. Consider the matrices
[0-1
-1 -1
Y 8
B=
-9
A= 3 X 8
02
C= 6 X
-4
03
6
Given that rank(A) <3 and nullity(B) = 1; find the nullity, rank and the null space of C.
• Verify Ronk and Nullity theorem for A and AT
2
3
1
where A-
4
2
-1
6
3 O
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