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An experiment conducted over time T necessarily produces a windowed view of the phenomenon generating the data. It is a useful strategy to regard the windowed data as one period of a periodic function. Then one may write
and seek to calculate the Fourier coefficients cn from the integral expression
Large values of cn will be regarded as a quantitative indication of a genuine periodic change in the phenomenon under study. In digital form the relevant equations are
The time interval [0,T] has been marked out in equal steps T/N, and frequency fn = n/T has been replaced by the dimensionless quantity n/N.
Draw parallel lines with slope +1.05; one passes through (0,a), and the other passes through (0,b). Suppose φ is a harmonic function between the two lines, with φ = 0 on the line t
You are working as an engineer on a project that involved being able to accurately measure the fluid level change in a large outdoor holding tank. The fluid level rises and falls a
sample problem of maxima application
what are the applications of integration?
the solution of diffusion equation by using separation of variables
Use Lagrange interpolation to estimate f(3), given that f(1) = 1, f(4) = -3, f(2) = 0 and f(-1) = 3.
y''(x)=2*10^-6*y(x)(100000-y(x))
a^n * n *u[n-1]
The system has a solution near (-0.5,-0.7). Set up the matrix equation Jδ = -f for Newton's method and then carry out one iteration, starting with x 0 = -0.5, y 0 = -0.7.
A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y paper i
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