By K. J. Binns
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Convex research is the calculus of inequalities whereas Convex Optimization is its program. research is inherently the area of the mathematician whereas Optimization belongs to the engineer. In layman's phrases, the mathematical technology of Optimization is the examine of the way to make a sensible choice whilst faced with conflicting specifications.
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Extra resources for Analysis and Computation of Electric and Magnetic Field Problems
Essentially, the direct-solution method involves the determination of a potential function satisfying Laplace's equation and also satisfying imposed boundary and other field conditions for a particular region. This potential function is, in general, the sum of several parts (each of which separately is a solution); one part, usually in the form of a series, describes the effect of the boundary influences, and the others describe the effect of field sources such as currents and charges. (The field solution can, of course, be expressed equally in terms of the flux function, though this is not often done.
1. Introduction The method of images, because of its simplicity, is of considerable value, but for many problems involving multiple boundaries or specified distributions of potential or potential gradient, it is more convenient to solve the field equations directly. In this chapter consideration is given to direct solutions of Laplace's equation, and in the next to solutions of Poisson's equation. Solutions which are available by the use of images are also available by the method discussed here, and the equivalence of solutions obtained using the two methods is demonstrated.
For the inner region, r < b everywhere, so that eqn. 12) is relevant for the expansion of a; whilst, for the outer region, r > b everywhere, and eqn. 11) is relevant. Thus, combining the series parts of these equations with the general series, the terms to be added to the general solutions to account for the effect of the current in these regions can be reduced to 0 and (//2TT)0 respectively. In the middle region, a change of 2 n in a is associated with changes in 0 of 2 n or 0, depending upon whether r is greater or less than b, and so eqns.