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9 matching pages
1: 1.9 Calculus of a Complex Variable
2: 19.25 Relations to Other Functions
3: 22.18 Mathematical Applications
4: 7.20 Mathematical Applications
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§7.20(ii) Cornu’s Spiral
►Let the set be defined by , , . Then the set is called Cornu’s spiral: it is the projection of the corkscrew on the -plane. …Then the arc length between the origin and equals , and is directly proportional to the curvature at , which equals . … ► …5: Sidebar 9.SB1: Supernumerary Rainbows
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►The faint line below the main colored arc is a ‘supernumerary rainbow’, produced by the interference of different sun-rays traversing a raindrop and emerging in the same direction.
…Airy invented his function in 1838 precisely to describe this phenomenon more accurately than Young had done in 1800 when pointing out that supernumerary rainbows require the wave theory of light and are impossible to explain with Newton’s picture of light as a stream of independent corpuscles.
The house in the picture is Newton’s birthplace.
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6: 4.42 Solution of Triangles
7: Bibliography B
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A monotonicity property involving and comparisons of the classical approximations of elliptical arc length.
SIAM J. Math. Anal. 32 (2), pp. 403–419.
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Ramanujan’s Notebooks. Part II.
Springer-Verlag, New York.
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Ramanujan’s Notebooks. Part III.
Springer-Verlag, Berlin-New York.
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Waves and Thom’s theorem.
Advances in Physics 25 (1), pp. 1–26.
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Uniform asymptotic smoothing of Stokes’s discontinuities.
Proc. Roy. Soc. London Ser. A 422, pp. 7–21.
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8: 1.10 Functions of a Complex Variable
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►If , analytic in , equals on an arc in , or on just an infinite number of points with a limit point in , then they are equal throughout and is called an analytic continuation of .
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►Suppose , , is an arc and .
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