simple closed curve
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4 matching pages
1: 1.6 Vectors and Vector-Valued Functions
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►The geometrical image of a path is called a simple
closed curve if is one-to-one, with the exception .
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►and be the closed and bounded point set in the plane having a simple closed curve
as boundary.
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2: 1.9 Calculus of a Complex Variable
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►A simple closed contour is a simple contour, except that .
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►Any simple closed contour divides into two open domains that have as common boundary.
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►If is continuous within and on a simple closed contour and analytic within , then
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►If is continuous within and on a simple closed contour and analytic within , and if is a point within , then
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3: 10.21 Zeros
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►Each curve that represents an infinite string of nonreal zeros should be located on the opposite side of its straight line asymptote.
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►In Figures 10.21.1, 10.21.3, and 10.21.5 the two continuous curves that join the points are the boundaries of , that is, the eye-shaped domain depicted in Figure 10.20.3.
These curves therefore intersect the imaginary axis at the points , where .
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►In Figures 10.21.2, 10.21.4, and 10.21.6 the continuous curve that joins the points is the lower boundary of .
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►are simple and the asymptotic expansion of the th positive zero as is given by
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