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The functions
{sinmx; cosmx}; m = 0,....∞
form a complete set over the interval x ∈ [ -Π, Π]. That is, any function f(x) can be expressed as a linear superposition of these with a unique set of coecients. For f(x) = x, we have
To show that the above holds for x = 1, study the dierence between the left- and right-hand sides of the equality as a function of the number of terms included in the sum. Write an octave program to compute and plot the truncated sum approximation (expansion vs x) for n =4 and 16 together with the function x. Make a table showing the error (dierence between two sides) for n =1, 2, 4, 16, 64, 256, 1024. Plot the result of the expansion for 2 values of n together with the original function. Comment on your results. You should submit an octave script or function le I can use to reproduce your results and a separate document (plain text le preferred) for your comments.
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The sum of the digit number is 7. If the digits are reversed , the number formed is less than the original number. find the number
Under this section we will be looking at the previous case for the constant coefficient and linear and homogeneous second order differential equations. In this case we need soluti
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The twenty-third Jaina teacher, Parsva, the immediate predecessor of Mahavira enjoined on his disciples four great vows. To these Mahavira addes which of the followings as the fift
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