Recent content by Anowar

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    Proving |f(z)|≤ M in a Closed Contour C

    I think the question doesn't want to arrive at maximum modulus principle, it is asking to proof that a function is bounded within the region if its bounded on the boundary. Am I missing something here?
  2. A

    Proving |f(z)|≤ M in a Closed Contour C

    The first problem asks to show that |f(z)|≤ M if f(z)≠0 within C and the second one asks to show that, |f(z)|≤ M does not hold if f(z)= 0 within C. If the f(z) has its minimum on the boundary, how can it help me to show that |f(z)| is bounded within the region? Thanks for you help, I really...
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    Proving |f(z)|≤ M in a Closed Contour C

    But, in the text, the right next problem is, If f(z) = 0 within the contour C, show that the foregoing result (the statement of the previous problem) does not hold and that it is possible to have |f(z)| = 0 at one or more points in the interior with |f(z)| > 0 over the entire bounding...
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    Proving |f(z)|≤ M in a Closed Contour C

    This problem is from Mathematical methods for physicists by Arfken, problem 6.4.7. A function f(z) is analytic within a closed contour C (and continuous on C). If f(z) ≠ 0 within C and |f(z)|≤ M on C, show that |f(z)|≤ M for all points within C. The hint is to consider w(z) = 1/f(z). I have...