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6) The image of the infinite strip

6) The image of the infinite strip

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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6) The image of the infinite strip <y< ½, under the bilinear transformation 1 w = u + iv = 7) is given by the region lying between (u + 2)² + v² = 4 and u² + (v + 1)² = 1 in the w- plane O the region lying between u²+ (v + 2)² = 4 and u²+ (v + 1)² = 1 in the w- plane O the region lying between (u + 1)² + v² = 1 and u²+ (v + 2)² = 4 in the w- plane the region lying between u²+ (v- 1)² = 4 and u² + (v + 1)² = 1 in the w- plane Under the bilinear transformation w = u + iv = the real axis of the z – plane is mapped to the imaginary axis of the w- plane the straight line 4u+ 3v = 1 the circle with centre (0, -1) and radius in the w- plane O the circle with centre (0, – 3) and radius in the w- plane 00 iz + 2 4z + i'
Transcribed Image Text:6) The image of the infinite strip <y< ½, under the bilinear transformation 1 w = u + iv = 7) is given by the region lying between (u + 2)² + v² = 4 and u² + (v + 1)² = 1 in the w- plane O the region lying between u²+ (v + 2)² = 4 and u²+ (v + 1)² = 1 in the w- plane O the region lying between (u + 1)² + v² = 1 and u²+ (v + 2)² = 4 in the w- plane the region lying between u²+ (v- 1)² = 4 and u² + (v + 1)² = 1 in the w- plane Under the bilinear transformation w = u + iv = the real axis of the z – plane is mapped to the imaginary axis of the w- plane the straight line 4u+ 3v = 1 the circle with centre (0, -1) and radius in the w- plane O the circle with centre (0, – 3) and radius in the w- plane 00 iz + 2 4z + i'
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