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 make comments. Sonuç: 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 Sonuç: 3. Find the Laurent series for f ( z) = 1 about the z=1 in annulus 1<|z-1|2a ( z − 1)( z − 2)( z + 1) Sonuç: 4. Calculate the contour integral the function f ( z ) = z −i on the contour ( z + 1)( z 3 + 27) 2 | z − i |= 4 Sonuç: (4n 5. Find the summation of following series , n =− 2 1 − 20n + 25)2 Sonuç: 6. Calculate following integrals using complex integration method cos( 2 x) a) dx x4 + 1 − Sonuç:a) 2 b) sin + 0 d 9 − cos 2 b) H. Ü. Müh. Fak. Fizik Böl. Uzaktan Eğitim 2019-2020 Bahar Dönemi için hazırlanmıştır A Öztaş