Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
ди Эт = c for some real constant ди ди θυ = = 0 for all ду მ Əy 3. Suppose f(z) = u(x, y) + iv(x, y) is analytic on |2| ≤ 1 and |f(z)| c for all || ≤ 1. Use Cauchy-Riemann equations to show that u |2|≤ 1. Hence, f(2) is a constant function on |2|≤ 1. 2 Hint: Consider f(2)|2 and take partial derivatives. 4. Suppose f(z) is analytic on |2| ≤ 1. Suppose |f(2)| is constant on the boundary |2| = 1. Show that either f has a zero in || < 1 or f is a constant function in |2| ≤ 1. Hint: Apply maximum and minimum modulus principle and question 3.

ди Эт = c for some real constant ди ди θυ = = 0 for all ду მ Əy 3. Suppose f(z) = u(x, y) + iv(x, y) is analytic on |2| ≤ 1 and |f(z)| c for all || ≤ 1. Use Cauchy-Riemann equations to show that u |2|≤ 1. Hence, f(2) is a constant function on |2|≤ 1. 2 Hint: Consider f(2)|2 and take partial derivatives. 4. Suppose f(z) is analytic on |2| ≤ 1. Suppose |f(2)| is constant on the boundary |2| = 1. Show that either f has a zero in || < 1 or f is a constant function in |2| ≤ 1. Hint: Apply maximum and minimum modulus principle and question 3.

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
See similar textbooks
icon
Related questions
Question
ди Эт = c for some real constant ди ди θυ = = 0 for all ду მ Əy 3. Suppose f(z) = u(x, y) + iv(x, y) is analytic on |2| ≤ 1 and |f(z)| c for all || ≤ 1. Use Cauchy-Riemann equations to show that u |2|≤ 1. Hence, f(2) is a constant function on |2|≤ 1. 2 Hint: Consider f(2)|2 and take partial derivatives. 4. Suppose f(z) is analytic on |2| ≤ 1. Suppose |f(2)| is constant on the boundary |2| = 1. Show that either f has a zero in || < 1 or f is a constant function in |2| ≤ 1. Hint: Apply maximum and minimum modulus principle and question 3.
Transcribed Image Text:ди Эт = c for some real constant ди ди θυ = = 0 for all ду მ Əy 3. Suppose f(z) = u(x, y) + iv(x, y) is analytic on |2| ≤ 1 and |f(z)| c for all || ≤ 1. Use Cauchy-Riemann equations to show that u |2|≤ 1. Hence, f(2) is a constant function on |2|≤ 1. 2 Hint: Consider f(2)|2 and take partial derivatives. 4. Suppose f(z) is analytic on |2| ≤ 1. Suppose |f(2)| is constant on the boundary |2| = 1. Show that either f has a zero in || < 1 or f is a constant function in |2| ≤ 1. Hint: Apply maximum and minimum modulus principle and question 3.
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
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…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS