As a point:: moves to the right along that pan of the

Chapter 0, Problem 11.13

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As a point:: moves to the right along that pan of the negative real axis where x ::: -1. its image point is to move lo the right along the negati,e real axis in the ir plane. As :. moves on the real axis to the right along the segment - I ::: x ::: 0 and then along the segment 0 ~ x ~ I. its image point 1r is to move in the direction of increasing t' along the segment 0 ::: 11 .::: I of the t' axis and then in the direction of decrea'\ing 11 along the same segment. Finally. as : moves to the right along that pan of the positive real axis where x ::_- I. its image point is to move to the right along the positive real axis in the 11 plane. l'\ote the changes in direction of the motion of 1J: al the images of the points :: = -1.:: = 0. and : = I. A mapping function whose derivative is where A is some constant. is thus indicated. Obtain formally the mapping function ,. , I Ir = \/ ::- - . \Vhere 0 < arg \/:. 2 - I < ;r. By considering the successive mappings Z = - 2 \V = Z - I. and 1r = JW. verify that the resulting transformation maps the right half plane Re:: > 0 onto the upper half plane Im u~ > 0. with a cul along the segment 0 < t' ::: I of the t' axis.