Lagrange undetermined multipliers maximization

The important aspect of (13.70b) is that each pa=Pa(U, V, N) has maximal ( most probable ) character with respect to the natural control variables of S. The constrained maximization procedure to find this optimal distribution by the method of Lagrange undetermined multipliers [see Schrodinger (1949), Sidebar 13.4, for further details] is very similar to that described in Section 5.2. In particular, the pa must be maximal with respect to variations in each control variable, leading to the usual second-derivative curvature conditions such as... 

Hi) Constrained Maximization Method of Lagrange Undetermined Multipliers The problem of constrained maximization may be posed in its most general form as follows ... 

P must be maximized subject to the constraints of equations 2.106 and 2.108. This is accomplished using Lagrange s method of undetermined multipliers. Equation 2.106 is multiplied by the arbitrary constant (a - 1) and equation 2.108 is multiplied by the arbitrary constant p ot the sam/8 as defined in equatioiiL90]. Then these are added to equation 2.104 to give... 

There are a number of problems in physical chemistry for which it is necessary to maximize (or minimize) a function under specific restrictive conditions. For example, suppose we wished to maximize some function/ x, y) subject to the restriction that another function of x and y, 0(jc, y), always equals zero. We can do this by a method known as Lagrange s method of undetermined multipliers. In order to maximize f(x, y) by this method, consider the total differentials... 

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