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Partial Differential Equation Add in library

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(a) Write an explicit example of a (non identically zero!) function in C ∞ c (R) (detailed argument). (b) For a ball B(x, R) ⊂ R n , construct an explicit function u ∈ C ∞ c (B(x, R)). 2. Construct a function Ï• so that Ï• ∈ C ∞ c (R) is a function that is identically 1 on [−1, 1], vanishes outside [−2, 2], and 0 ≤ Ï• ≤ 1. 3. Construct an explicit example of a partition of unity {Ï•j} ∞ j=−∞ on R. In other words, {Ï ...

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Tags: United States Fayetteville Engineering Mathematics Advanced Mathematic University of Arkansas Advanced Mathematic 

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