169(2+1 4.2 Part B Suppose that F(x, y) is a rational function of the real variables and y not having singularity on the unit circle in R2. For z E C, let لورعاة - + (²1 (+²¹²) ²1 ( ² - - )) 2- F = 2 2i 2 22 g(z): Let 2k = k + iyk, k = 1,...,n be the isolated singularities of g enclosed by the un circle y(t): et, t€ [0, 2π]. g(): = iz 4.2.1 Show that - £g(z) dz L's certs 4.2.2 Use the method from (4.2.1) to evaluate • 277 * F (cost, sint) dt = 7.th 0 2π 1 3+ sint dt. 129(z) n GCR²) iz = 2πi Res[g, zk]. k=1 - 2 F F 12-01 = 1
169(2+1 4.2 Part B Suppose that F(x, y) is a rational function of the real variables and y not having singularity on the unit circle in R2. For z E C, let لورعاة - + (²1 (+²¹²) ²1 ( ² - - )) 2- F = 2 2i 2 22 g(z): Let 2k = k + iyk, k = 1,...,n be the isolated singularities of g enclosed by the un circle y(t): et, t€ [0, 2π]. g(): = iz 4.2.1 Show that - £g(z) dz L's certs 4.2.2 Use the method from (4.2.1) to evaluate • 277 * F (cost, sint) dt = 7.th 0 2π 1 3+ sint dt. 129(z) n GCR²) iz = 2πi Res[g, zk]. k=1 - 2 F F 12-01 = 1
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
![log cz +1
те
4.2 Part B
Suppose that F(x, y) is a rational function of the real variables and y not having a
singularity on the unit circle in R2. For z E C, let
xy)
iy
fleit,
g(R)
7
Let zk = xk + iyk, k = 1,...,n be the isolated singularities of g enclosed by the unit
circle y(t) := eſt, t = [0, 2π]. g(); =
4.2.1 Show that
(
1
1
1
*(*) - - - - * * ( ; ( ^ ^ ¹ ) - — ( - - :))
F
4
g(z) :=
2+
Z
2i
iz
**F(cost, sint) dt =
0
عن
• 2п
4.2.2 Use the method from (4.2.1) to evaluate
R
£g(z)
g(z) dz
L's
1
3+ sint
=
dt.
X
izgcz)
S
n
2
2πi Res[g, zk].
k=1
22
R
12
F(2)
12-0) = 1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F904caeb1-cd31-4dcf-9af8-09f5b2d51865%2F4c78b7f0-9341-4deb-bc8a-fc1e8f97de7c%2Fh1i2lyn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:log cz +1
те
4.2 Part B
Suppose that F(x, y) is a rational function of the real variables and y not having a
singularity on the unit circle in R2. For z E C, let
xy)
iy
fleit,
g(R)
7
Let zk = xk + iyk, k = 1,...,n be the isolated singularities of g enclosed by the unit
circle y(t) := eſt, t = [0, 2π]. g(); =
4.2.1 Show that
(
1
1
1
*(*) - - - - * * ( ; ( ^ ^ ¹ ) - — ( - - :))
F
4
g(z) :=
2+
Z
2i
iz
**F(cost, sint) dt =
0
عن
• 2п
4.2.2 Use the method from (4.2.1) to evaluate
R
£g(z)
g(z) dz
L's
1
3+ sint
=
dt.
X
izgcz)
S
n
2
2πi Res[g, zk].
k=1
22
R
12
F(2)
12-0) = 1
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