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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The time interval [0,T] has been marked out in equal steps T/N, and frequency fn = n/T has been replaced by the dimensionless quantity n/N.
Produce a discrete time series y(t i ) by super positioning 5 cosinusoidal components, for your own choice of the amplitudes (a j ) and frequencies (f j ). Add some Gaus
y"+3y''+2y=0
An auto manufacturing company wanted to investigate how the price of one of its car models depreciates with age. The research department at the company took a sample of eight cars
A) Prove the following theorem by considering two distinct cases. For any integer n, n 2 + n is even. B) If x = r 2 - s 2 and y = 2rs for any integers r and s, then x 2 +
y''=2xy/x^2-y^2
Solve the initial value problem 11(t+1)dydt-7y=28t, for t>-1 with y(0)=14. Put the problem in standard form. Then find the integrating factor, ?(t)= , and finally find y(t)=
Find the quadratic that interpolates f(x) = 2x 3 - x + 1 at the nodes x 0 = 0, x 1 = 2, x 2 = 3, a) by solving a set of three equations for the coefficients of p 2 (x) = a 2
#how do you estimate the sum a limit using intrgral test
integral dx/root of sinx using beta and gamma functions
The data in this exam are a set of 6 integers a through f, based on your social security number. Write the LAST 6 digits of your social security or ID number in the spaces below, t
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