# Ara 1 HUZEM 2019 2020 (1) ```Adı Soyadı:
No:
İmza
25.04.2020
MIDTERM-I QUESTIONS
1. What is the image of the circle with radius R centered at the origin on the
1
1
w plane which defined by w =  z −  and find a critical radius for this transformation and
2
z
Sonu&ccedil;:
2. If real part of an analytic function is u = 3x 2 − 2 xy + 8 x − 3 y 2 − 6 y and find the complex
form of f(z) for f(1)=1+i
Sonu&ccedil;:
3. Find the Laurent series for
f ( z) =
1
about the z=1 in annulus 1&lt;|z-1|2a
( z − 1)( z − 2)( z + 1)
Sonu&ccedil;:
4. Calculate the contour integral the function f ( z ) =
z −i
on the contour
( z + 1)( z 3 + 27)
2
| z − i |= 4
Sonu&ccedil;:

 (4n
5. Find the summation of following series
,
n =−
2
1
− 20n + 25)2
Sonu&ccedil;:
6. Calculate following integrals using complex integration method

cos( 2 x)
a) 
dx
x4 + 1
−
Sonu&ccedil;:a)
2
b)
 sin  +
0
d
9 − cos 2 
b)
H. &Uuml;. M&uuml;h. Fak. Fizik B&ouml;l. Uzaktan Eğitim 2019-2020 Bahar D&ouml;nemi i&ccedil;in hazırlanmıştır
A &Ouml;ztaş
```