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Applied Mathematical Methods by Bhaskar Dasgupta

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Chapter 48

1 Law of reflection also is given as one of the local minima of T, but in that case c(x, y, z) is constant and much of the ‘fun’ is lost.

2 It is important to appreciate that the boundary conditions inflict almost no damage to the arbitrariness of δy. Boundary conditions are only 2n in number, whereas δy(x) has infinite coordinates in (x1,x2).

3 For a three-variable problem, one needs to use divergence theorem at this stage.

4 or, a string, in line with our analogy in a similar context, in Chap. 30

5 Note that yi is involved in two of the terms in the summation.

6 For example, the residual of the Poisson’s equation uxx+uyy = h(x, y) operated over

7 For that matter, not every differential equation possesses an underlying variational ...

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