This volume contains an enlarged version of some of the talks presented at the American Mathematical Society Spring Meeting in New York City, May of 1983 in a special session on the Sensitivity of Functionals with Applications to Engineering Sciences. All talks were given by invitation. The enlarged versions of the talks given by professors M. Vogelius and R.V. Kohn, and by A. Fiacco and J. Kyparisis were published elsewhere before the publication of this volume. Only an enlarged abstract exists of Professor W.M. Wonham's presentation. Versions of all other papers presented at that meeting are given in this volume. All of these papers discuss applications of sensitivity theory to design of engineering systems or processes. Applications of sensitivity theory to chemical kinetics are given in the contribution of Professor H. Rabitz.
Applications to structural or mechnaical engineering were offered in the papers of V. Komkov; of J.W. Hou, E.J. Haug and R.L. Benedict, A. Diaz, N. Kikuchi and J.E. Taylor, V. Komkov and C. Irwin and P. Pedersen. All of these papers stress the functional analytic approach to optimization and to sensitivity theory for structural and mechanical systems.
These contributions attempt to clarify some latest developments in sensitivity theory for engineering systems and also present new theoretical solutions to several important problems. For example, the paper of H. Rabitz presents a new insight into the numerical treatment of chemical kinetics and of quantum scattering theory based on the sensitivity density concept. The paper of P. Pedersen deals with the troublesome aspects of nonselfadjoint problems that arise in structural dynamics, such as the dynamic behavior of the Beck column or Hauger column with both external and internal damping. Influence of these theoretical findings on existing numerical techniques is clearly outlined. Grid modification problems for numerical solutions of structural optimization are the main topic of the paper of A.R. Diaz, N. Kikuchi and J. Taylor. The modification of the grid and related sensitivity with respect to numerical errors is the main topic of that paper. It develops a new direction in numerical implementations of optimizing procedures, but more importantly it provides rigorous mathematical justification for such procedures. This aspect has been lacking in almost all previous papers on this subject.

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