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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The time interval [0,T] has been marked out in equal steps T/N, and frequency fn = n/T has been replaced by the dimensionless quantity n/N.
A manager has determined the cost C, in dollars, for manufacturing is C(q) =85log 10 (10+q/2) for manufacturing, where q is the number of units produced in a given day. (a
Prove that the Lagrangian coef?cient polynomials for p n (x) satisfy ∑ n k=0 l k (x) = 1. Hint: It is only a 3-line proof. Consider the interpolating polynomial for a constan
sample problem of maxima application
Below are the conditions specified by the institution: a) If the temperature sensor shows 30 degree Celsius or higher, the air-conditioner will be turned ON regardless of the othe
i need a quote in analytical methods for engineers (Algebraic methods)
A scientist calculates the temperature of melting platinum using a new type of thermometer. The temperature of the metal is called to be exactly 1768.3 centigrade. The measurements
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 +
Define a mapping from the x,y plane to the u,v plane by u = 2x + y, v = -x +2y . If a temperature function is given in the x,y plane by T(x,y) = x+y, what is the value, to 3 de
A Pew Research poll was conducted to investigate opinions about global warming. The respondents who answered yes when asked if there is solid evidence that the earth is getting wa
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
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