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-              v9
+              v10
 [[latex($\frac{d^2 u}{dx^2} = f(x)$)]]
 with the centered (2nd order, as can be verified by above discussion) finite different approximation,
+with the centered (2nd order, as can be verified by above discussion) finite different approximation D2,
 [[latex($\frac{1}{h}[\frac{u(x+h)-u(x)}{h} - \frac{u(x-h)-u(x)}{-h}] = \frac{1}{h^2}[u(x+h)+u(x-h)-2u(x)]$)]]
+[[latex($D2 = \frac{1}{h}[\frac{u(x+h)-u(x)}{h} - \frac{u(x-h)-u(x)}{-h}] = \frac{1}{h^2}[u(x+h)+u(x-h)-2u(x)]$)]]
 (which is easily interpreted as the finite difference version of the derivative of the derivative). Using this, and replacing the function f and the (approximate) solution u with their discrete forms, we have