Applied Mathematical Methods

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 u_xx+u_yy = h(x, y) operated over

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