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Fourier series - Partial Differential Equations
One more application of series arises in the study of Partial Differential Equations. One of the more generally employed methods in that subject use Fourier Series. Several applications of series, particularly those in the differential equations fields, rely on the fact that functions can be presented like a series. In these types of applications it is very hard, if not impossible, to find out the function itself. Though, there are methods of determining the series representation for the not known function.
Characteristics and Limitations of moving average Characteristics of moving average 1) The more the number of periods in the moving average, the greater the smoothing
Absolute Convergence While we first talked about series convergence we in brief mentioned a stronger type of convergence but did not do anything with it as we didn't have any
Consider the wave equation utt - uxx = 0 with u(x, 0) = f(x) = 1 if-1 ut(x, 0) = ?(x) =1 if-1 Sketch snapshots of the solution u(x, t) at t = 0, 1, 2 with justification (Hint: Sket
A number x is chosen at random from the numbers -3, -2, -1, 0 1, 2, 3. What is the probability that | x| Ans : x can take 7 values To get |x| Probability (| x |
Arc Length with Parametric Equations In the earlier sections we have looked at a couple of Calculus I topics in terms of parametric equations. We now require to look at a para
Proper and Improper Fractions: Example: 3/8 proper fraction 8/3 improper fraction 3/3 improper fraction Here an improper fraction expressed as the sum of an in
If i worked 7 1/3 hours and planted 11 trees how many hours did it take to plant each tree?
Suppose a regular polygon , which is an N-sided with equal side lengths S and similar angles at each corner. There is an inscribed circle to the polygon that has center C and ba
Properties of Dot Product - proof Proof of: If v → • v → = 0 then v → = 0 → This is a pretty simple proof. Let us start with v → = (v1 , v2 ,.... , vn) a
a) Let V = f1, 2, :::, 7g and define R on V by xRy iff x - y is a multiple of 3. You should know by now that R is an equivalence relation on V . Suppose that this is so. Explain t
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