b.) Using Mathematica, find the image under the Joukowsky Trans- 1 1 5 form of the circle with center-+-i which passes through z = 1. The resulting image is called a Joukowsky airfoil. These airfoils were historically important in understanding airfoil design. (You should investigate the Mathematica commands ComplexExpand and ParametricPlot.) 2.) The Joukowsky Transform is defined by f(z) = 2 + =. Z ainama.) Show that the region in the upper half-plane outside the unit circle maps to the full upper half-plane under the Joukowsky Transform. The points below are B = -1, C = i, and D = 1 (A and E are generic points on the real axis on either side of the unit circle). Be sure to find the image points B', C', and D', show that the upper unit circle gets mapped to the real axis, and any generic point in the gray region on the left (i.e. |z| = |x + iy| > 1 and y > 0) gets mapped into the gray region on the right (w = u+iv with v > 0). Y f AB DE a 1 ข U A' B' C' D'E'
b.) Using Mathematica, find the image under the Joukowsky Trans- 1 1 5 form of the circle with center-+-i which passes through z = 1. The resulting image is called a Joukowsky airfoil. These airfoils were historically important in understanding airfoil design. (You should investigate the Mathematica commands ComplexExpand and ParametricPlot.) 2.) The Joukowsky Transform is defined by f(z) = 2 + =. Z ainama.) Show that the region in the upper half-plane outside the unit circle maps to the full upper half-plane under the Joukowsky Transform. The points below are B = -1, C = i, and D = 1 (A and E are generic points on the real axis on either side of the unit circle). Be sure to find the image points B', C', and D', show that the upper unit circle gets mapped to the real axis, and any generic point in the gray region on the left (i.e. |z| = |x + iy| > 1 and y > 0) gets mapped into the gray region on the right (w = u+iv with v > 0). Y f AB DE a 1 ข U A' B' C' D'E'
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:b.) Using Mathematica, find the image under the Joukowsky Trans-
1 1
5
form of the circle with center-+-i which passes through z = 1.
The resulting image is called a Joukowsky airfoil. These airfoils
were historically important in understanding airfoil design. (You
should investigate the Mathematica commands ComplexExpand
and ParametricPlot.)
Transcribed Image Text:2.) The Joukowsky Transform is defined by
f(z) = 2 + =.
Z
ainama.) Show that the region in the upper half-plane outside the unit circle
maps to the full upper half-plane under the Joukowsky Transform.
The points below are B = -1, C = i, and D = 1 (A and E are
generic points on the real axis on either side of the unit circle). Be
sure to find the image points B', C', and D', show that the upper
unit circle gets mapped to the real axis, and any generic point in
the gray region on the left (i.e. |z| = |x + iy| > 1 and y > 0) gets
mapped into the gray region on the right (w = u+iv with v > 0).
Y
f
AB
DE
a
1
ข
U
A' B'
C' D'E'
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 1 steps with 1 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
