Fourier Series and Boundary Value Problems

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For example, if it is known that the initial distribution of temperature was u(0,x)=g(x) for a function g(x)∈L2[−π,π] then cn(0) is the n-th Fourier coefficient of g(x). 2. 12 The best approximation to x by a linear combination ∑k=1nλkek is ∑k=1n ⟨ x,ek⟩ ek if the ek are orthonormal. We do not require prior knowledge of statistics, applied mathematics or computing, as these are taught from scratch.

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Publisher: McGraw Hill Book Co; Early edition (1941)


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