Invariant Imbedding : Proceedings of the Summer Workshop on Invariant Imbedding Held at the University of Southern California, June – August 1970

Imbedding is a powerful and versatile tool for problem­ solving. Rather than treat a question in isolation, we view it as a member of a family of related problems. Each member then becomes a stepping stone in a path to a simultaneous solution of the entire set of problems. As might be expected, there are many ways of accomplishing this imbedding. Time and space variables have been widely employed in the past, while modern approaches combine these structural features with others less immediate. Why should one search for alternate imbeddings when elegant classical formalisms already exist? There are many reasons. To begin with, different imbeddings are useful for different purposes. Some are well suited to the derivation of existence and uniqueness theorems, some to the derivation of conservation relations, some to perturbation techniques and sensitivity analysis, some to computa­ tional studies. The digital computer is designed for initial value problems; the analog computer for boundary-value problems. It is essential then to be flexible and possess the ability to use one device or the other, or both. In economics, engineering, biology and physics, some pro­ cesses lend themselves more easily to one type of imbedding rather than another. Thus, for example, stochastic decision processes are well adapted to dynamic programming. In any case, to go hunting in the wilds of the scientific world armed with only one arrow in one's quiver is quite foolhardy. Front Matter....Pages i-3 Invariant Imbedding and Linear Systems....Pages 4-18 Cauchy Problems for Ordinary Differential, Difference and Integral Equations....Pages 19-33 Invariant Imbedding and Partial Differential Equations....Pages 34-45 Reduction of Matrix Integral Equations with Displacement Kernels on the Half-Line to Cauchy Systems....Pages 46-54 Invariant Imbedding and Optimal Control....Pages 55-67 A Method of Characteristics and Invariant Imbedding for Distributed Control Problems....Pages 68-86 Wave Propagation through Longitudinally and Transversally Inhomogeneous Slabs-I....Pages 87-107 Neutron Transport Theory....Pages 108-117 Dynamic Programming and Invariant Imbedding in Structural Mechanics....Pages 118-148 Back Matter....Pages 149-153