... ... + + ... +

Extremizing (i.e., minimizing or maximizing) Eq. (12.75) is accomplished by setting the first variation M of I[y(x)] equal to zero. This gives

af af af aJ af M[y(x)] = -by, + -bY2 + ... + --bYi_1 + -bYi + ... + -bYI = 0

Since the individual variations bYi (i = I, 2, ... , I) are arbitrary, Eq. (12.76) is satisfied only if

Equation (12.77) yields f equations for the determination of the f nodal values Yi (i = 1, 2, ... , I).