(a) Find a Schwarz-Christoffel transformation of the upper half-plane onto the do-main D = {ret E C: r > 0, -T/3 0 is a positive constant, and the infinitehorizontal segment H = {x+ Li: x <0}.(c) Use a computer to visualize the above transformations by plotting the image ofthe Cartesian grid relative to the mappings in (a) and (b).

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Answered: (a) Find a Schwarz-Christoffel…

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(a) Find a Schwarz-Christoffel transformation of the upper half-plane onto the do- main D = {reite C: r > 0, -7/3

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.4: Linear Transformations

Problem 12EQ

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Question

(a) Find a Schwarz-Christoffel transformation of the upper half-plane onto the do-
main D = {ret E C: r > 0, -T/3 <t <n}.
(b) Find a Schwarz-Christoffel transformation of the upper half-plane (UHP) onto
the subset of the UHP bordered by the positive real axis, the vertical segment
V = {iy: 0 < y < L} where L > 0 is a positive constant, and the infinite
horizontal segment H = {x+ Li: x <0}.
(c) Use a computer to visualize the above transformations by plotting the image of
the Cartesian grid relative to the mappings in (a) and (b).

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