Let f. q, and h be the functions defined on R by if – 1 4, and h(r) = e-2. Consider the following boundary problem (G): u(r,0) = h(x), lim u(r,t) + h(x), ¤€ R, t > 0 (1) I E R = 0, (2) Hint:F(e)= Va , where F(f()) is the fourier transform of f(r). (1) The Fourier Transform of f is given by: a. 2, cos (w). b. , sin (w). c. , sin (#). d. None of the above (2) The Fourier cosine Transform of g is given by: 2 sin(w) + cos(w) – - cos(4w)). b. 유(금sin(4w) +음 cos(4u) --급 cos(w)). a. A sin(w) + cos(w) – - cos(4w). d. None of the above (3) Let U(w, t) be the Fourier Transform of u(x, t) acting to the variable r. By Applying the Fourier Transform to the first equation of (G), we obtain: C. a. Ut – wU = te. b. Ut + w²U = e" c. U – w²U = d. None of the above (4) Solving the linear first order ODE obtained in previous part and using equation (2), we obtain a. U(w,t) = e-[1+(w² – 1)e-w²j. b. U (w, t) = e+[1+ w°e¬w°t]. c. U(w,t) = „3=e+*-*. d. None of the above (5) The general solution of (G) is: 1 a. u(r, t) = V2 Lw² e 1 efwz | 1 b. u(x,t) = 11 + w°e¬w°«]dw. [1 + (w² – 1)e-w*t] dw. roo 1 с. и (т,t) — 2w²e d. None of the above
Let f. q, and h be the functions defined on R by if – 1 4, and h(r) = e-2. Consider the following boundary problem (G): u(r,0) = h(x), lim u(r,t) + h(x), ¤€ R, t > 0 (1) I E R = 0, (2) Hint:F(e)= Va , where F(f()) is the fourier transform of f(r). (1) The Fourier Transform of f is given by: a. 2, cos (w). b. , sin (w). c. , sin (#). d. None of the above (2) The Fourier cosine Transform of g is given by: 2 sin(w) + cos(w) – - cos(4w)). b. 유(금sin(4w) +음 cos(4u) --급 cos(w)). a. A sin(w) + cos(w) – - cos(4w). d. None of the above (3) Let U(w, t) be the Fourier Transform of u(x, t) acting to the variable r. By Applying the Fourier Transform to the first equation of (G), we obtain: C. a. Ut – wU = te. b. Ut + w²U = e" c. U – w²U = d. None of the above (4) Solving the linear first order ODE obtained in previous part and using equation (2), we obtain a. U(w,t) = e-[1+(w² – 1)e-w²j. b. U (w, t) = e+[1+ w°e¬w°t]. c. U(w,t) = „3=e+*-*. d. None of the above (5) The general solution of (G) is: 1 a. u(r, t) = V2 Lw² e 1 efwz | 1 b. u(x,t) = 11 + w°e¬w°«]dw. [1 + (w² – 1)e-w*t] dw. roo 1 с. и (т,t) — 2w²e d. None of the above
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
part 1 2 fourier transform
![Let f. q, and h be the functions defined on R by
if – 1<x< 0,
if 0<r<1,
| 4x,
g(r) = {4 - ,
if 0 < x < 1,
if 1<r < 4,
1+x,
f(x) = {1-x,
0,
otherwise ,
0,
if r > 4,
and h(r) = e-2. Consider the following boundary problem (G):
u(r,0) = h(x),
lim u(r,t)
+ h(x), ¤€ R, t > 0 (1)
I E R
= 0,
(2)
Hint:F(e)=
Va
, where F(f()) is the fourier transform of f(r).
(1) The Fourier Transform of f is given by:
a. 2, cos (w).
b. , sin (w).
c. , sin (#).
d. None of the above
(2) The Fourier cosine Transform of g is given by:
2 sin(w) + cos(w) – - cos(4w)).
b. 유(금sin(4w) +음 cos(4u) --급 cos(w)).
a.
A sin(w) + cos(w) – - cos(4w).
d. None of the above
(3) Let U(w, t) be the Fourier Transform of u(x, t) acting to the variable r. By Applying the
Fourier Transform to the first equation of (G), we obtain:
C.
a. Ut – wU = te.
b. Ut + w²U = e"
c. U – w²U =
d. None of the above
(4) Solving the linear first order ODE obtained in previous part and using equation (2), we obtain
a. U(w,t) = e-[1+(w² – 1)e-w²j.
b. U (w, t) = e+[1+ w°e¬w°t].
c. U(w,t) = „3=e+*-*.
d. None of the above
(5) The general solution of (G) is:
1
a. u(r, t) =
V2
Lw² e
1
efwz |
1
b. u(x,t) =
11 + w°e¬w°«]dw.
[1 + (w² – 1)e-w*t] dw.
roo
1
с. и (т,t) —
2w²e
d. None of the above](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9dcaa84c-83af-4054-aa96-9fc9f674a13b%2F83762819-8aa9-491c-ac17-18ddf54a4ac8%2Fcyu686r_processed.png&w=3840&q=75)
Transcribed Image Text:Let f. q, and h be the functions defined on R by
if – 1<x< 0,
if 0<r<1,
| 4x,
g(r) = {4 - ,
if 0 < x < 1,
if 1<r < 4,
1+x,
f(x) = {1-x,
0,
otherwise ,
0,
if r > 4,
and h(r) = e-2. Consider the following boundary problem (G):
u(r,0) = h(x),
lim u(r,t)
+ h(x), ¤€ R, t > 0 (1)
I E R
= 0,
(2)
Hint:F(e)=
Va
, where F(f()) is the fourier transform of f(r).
(1) The Fourier Transform of f is given by:
a. 2, cos (w).
b. , sin (w).
c. , sin (#).
d. None of the above
(2) The Fourier cosine Transform of g is given by:
2 sin(w) + cos(w) – - cos(4w)).
b. 유(금sin(4w) +음 cos(4u) --급 cos(w)).
a.
A sin(w) + cos(w) – - cos(4w).
d. None of the above
(3) Let U(w, t) be the Fourier Transform of u(x, t) acting to the variable r. By Applying the
Fourier Transform to the first equation of (G), we obtain:
C.
a. Ut – wU = te.
b. Ut + w²U = e"
c. U – w²U =
d. None of the above
(4) Solving the linear first order ODE obtained in previous part and using equation (2), we obtain
a. U(w,t) = e-[1+(w² – 1)e-w²j.
b. U (w, t) = e+[1+ w°e¬w°t].
c. U(w,t) = „3=e+*-*.
d. None of the above
(5) The general solution of (G) is:
1
a. u(r, t) =
V2
Lw² e
1
efwz |
1
b. u(x,t) =
11 + w°e¬w°«]dw.
[1 + (w² – 1)e-w*t] dw.
roo
1
с. и (т,t) —
2w²e
d. None of the above
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 3 steps with 3 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
