By quantamania
12/08/2008 - 21:35:36
Type: City Hall building
Rating: -0.94 (Not rated)
Tags: algebra, diffraction, educational, envelope, fresnel, function, half, integral, limit, mathematics, odd, optics, physics, plot, points, quantamania, special function, wavy
Description
This plot is one half of an integral function. The integrand (function being integrated) is cos(pi/2*t^2) dt. The function is based on the value of this integrand from zero to x. Fresnel integrals are used in optics. Described by Augustin-Jean Fresnel. There are two similar integral functions, C(x) and S(x). Both of these functions are odd functions, meaning that they have the same shapes in the lower left quadrant as that in the upper right quadrant. Diffraction phenomena are often described using these integral functions. The limit for both functions as x goes to infinity is (pi/8)^1/2.
By quantamania
Sorry about the half-finished look of this one. C(x) is an odd function so the other half is easily visualized in the lower left quadrant. Complexity limits prevented me from putting it in there. And this is how it often looks in most books.