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This book is based on lectures given in a one-quarter course at UCLA. The aim. is to present som.e of the basic concepts and techniques of Functional Analys.is of relevance to optim.ization problem.s in Control. Com.m.unication and other areas in System. Science. The students are expected to have had an introductory course in Hilbert Space theory. Som.e effort has been m.ade to be self-contained m.ainly in order that the vocabularly used can be clarified. A m.inim.al bibliography is appended. The author is indebted to Jiri Ruzicka and Jerom.e Mersky for help with proof-reading. Profes sor L. Berkovitz looked over and m.ade m.any helpful corn.rn.ents on parts of an early version. Thanks are also due to Trudy Cook for typing the m.anuscript. Grateful acknowledgem.ent is also m.ade of partial support under AFOSR Grant No. 68-1408, Applied Mathem.atics Division, United Stat s Air Force.

Mathematical control systems --- Analytical spaces --- Probability theory --- 681.3*G16 --- Optimization: constrained optimization; gradient methods; integer programming; least squares methods; linear programming; nonlinear programming (Numericalanalysis) --- Business & Economics --- Economic Theory --- Hilbert space. --- Mathematical optimization. --- 681.3*G16 Optimization: constrained optimization; gradient methods; integer programming; least squares methods; linear programming; nonlinear programming (Numericalanalysis) --- Hilbert space --- Mathematical optimization --- Espace de Hilbert --- Optimisation mathématique --- Functional analysis --- Analyse fonctionnelle --- 517.98 --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Banach spaces --- Hyperspace --- Inner product spaces --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- 517.98 Functional analysis and operator theory --- Functional analysis and operator theory --- Functional analysis. --- Programmation (mathématiques)

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681.3*G16 --- Optimization: constrained optimization; gradient methods; integer programming; least squares methods; linear programming; nonlinear programming (Numericalanalysis) --- 681.3*G16 Optimization: constrained optimization; gradient methods; integer programming; least squares methods; linear programming; nonlinear programming (Numericalanalysis) --- Programmation (mathématiques)

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The author's approach is one of continuum models of the aerodynamic flow interacting with a flexible structure whose behavior is governed by partial differential equations. Both linear and nonlinear models are considered although much of the book is concerned with the former while keeping the latter clearly in view. A complete chapter is also devoted to nonlinear theory. The author has provided new insights into the classical inviscid aerodynamics and raises novel and interesting questions on fundamental issues that have too often been neglected or forgotten in the development of the early history of the subject. The author contrasts his approach with discrete models for the unsteady aerodynamic flow and the finite element model for the structure. Much of the aeroelasticity has been developed with applications formerly in mind because of its enormous consequences for the safety of aircraft. Aeroelastic instabilities such as divergence and flutter and aeroelastic responses to gusts can pose a significant hazard to the aircraft and impact its performance. Yet, it is now recognized that there are many other physical phenomena that have similar characteristics ranging from flows around flexible tall buildings and long span bridges, alternate energy sources such as electric power generation by smart structures to flows internal to the human body.  From the foreword:  "For the theorist and applied mathematician who wishes an introduction to this fascinating subject as well as for the experienced aeroelastician who is open to new challenges and a fresh viewpoint, this book and its author have much to offer the reader." Earl Dowell, Duke University, USA.

Aeroelasticity -- Mathematical models. --- Flutter (Aerodynamics) -- Mathematical models. --- Mathematics. --- Aeroelasticity --- Mathematics --- Mechanical Engineering --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Calculus --- Aeronautics Engineering & Astronautics --- Mathematical models --- Aeroelasticity. --- Functional analysis. --- Partial differential equations. --- Fluids. --- Continuum mechanics. --- Engineering design. --- Functional Analysis. --- Engineering Design. --- Continuum Mechanics and Mechanics of Materials. --- Fluid- and Aerodynamics. --- Partial Differential Equations. --- Aerodynamics --- Elastic waves --- Elasticity --- Mechanics. --- Mechanics, Applied. --- Differential equations, partial. --- Solid Mechanics. --- Partial differential equations --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Design, Engineering --- Engineering --- Industrial design --- Strains and stresses --- Design --- Hydraulics --- Mechanics --- Hydrostatics --- Permeability

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Mathematical control systems

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Business economics