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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The time interval [0,T] has been marked out in equal steps T/N, and frequency fn = n/T has been replaced by the dimensionless quantity n/N.
As an engineering student, the ministry of energy and minerals has tasked you to help them model equation(s) that can estimate the amount of crude oil in a reservoir. The governmen
sin2+cos2=
State each of the following arguments in abstract form. Recognize the premises and the conclusion of the argument. Then test whether the argument is valid or invalid. Describe how
1. (i) How many digits does the number 101000 have when written to base 7 ? (ii) Use the prime number theorem to estimate the proportion of prime numbers among the positive inte
WHY IS SINp = 0
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)=
The following are 8 data points that shows the relationship between the number of fishermen and the amount of fish they can catch a day. (Let the number of fishermen be X and the a
A function f(t) is defined as f(t) = p - t for 0 Write down the even extension of f(t) for -p Determine the Fourier cosine series, and hence, calculate the Fourier series approx
Valid objective function for a LPP with x,y,z as decision variables
The integral has an exact answer, viz., sinc(pfT). As T®¥ the sinc function tends to zero. Divide the region from -T/2 to T/2 into N equal parts and sum the rectangles on b
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