00738nam 2200193z- 450 99632082020331620160818152922.03-86576-107-0(CKB)9870000000000813(EXLCZ)99987000000000081320140209c2013uuuu -u- -engStrategie zur mittel- und langfristigen Versorgung mit hochwertigem forstlichem Vermehrungsgut durch Züchtung in DeutschlandBraunschweigJohann Heinrich von Thünen-InstitutLiesebachM1006130BOOK996320820203316Strategie zur mittel- und langfristigen Versorgung mit hochwertigem forstlichem Vermehrungsgut durch Züchtung in Deutschland2314816UNISA05566nam 2200673Ia 450 991078211740332120230617040941.01-281-93546-89786611935467981-279-499-9(CKB)1000000000537813(EBL)1223606(SSID)ssj0000290724(PQKBManifestationID)11211138(PQKBTitleCode)TC0000290724(PQKBWorkID)10230603(PQKB)10843223(WSP)00005374(Au-PeEL)EBL1223606(CaPaEBR)ebr10255903(CaONFJC)MIL193546(OCoLC)853361888(MiAaPQ)EBC1223606(EXLCZ)99100000000053781320030826d2003 uy 0engur|n|---|||||txtccrThe calculus of variations and functional analysis[electronic resource] with optimal control and applications in mechanics /Leonid P. Lebedev, Michael J. CloudSingapore ;River Edge, N.J. World Scientificc20031 online resource (435 p.)Series on stability, vibration, and control of systems. Series A ;v. 12Description based upon print version of record.981-238-581-9 Includes bibliographical references (p. 415-416) and index.Foreword; Preface; Contents; 1. Basic Calculus of Variations; 1.1 Introduction; 1.2 Euler's Equation for the Simplest Problem; 1.3 Some Properties of Extremals of the Simplest Functional; 1.4 Ritz's Method; 1.5 Natural Boundary Conditions; 1.6 Some Extensions to More General Functionals; 1.7 Functionals Depending on Functions in Many Variables; 1.8 A Functional with Integrand Depending on Partial Derivatives of Higher Order; 1.9 The First Variation; 1.10 Isoperimetric Problems; 1.11 General Form of the First Variation; 1.12 Movable Ends of Extremals1.13 Weierstrass-Erdmann Conditions and Related Problems1.14 Sufficient Conditions for Minimum; 1.15 Exercises; 2. Elements of Optimal Control Theory; 2.1 A Variational Problem as a Problem of Optimal Control; 2.2 General Problem of Optimal Control; 2.3 Simplest Problem of Optimal Control; 2.4 Fundamental Solution of a Linear Ordinary Differential Equation; 2.5 The Simplest Problem Continued; 2.6 Pontryagin's Maximum Principle for the Simplest Problem; 2.7 Some Mathematical Preliminaries; 2.8 General Terminal Control Problem; 2.9 Pontryagin's Maximum Principle for the Terminal Optimal Problem2.10 Generalization of the Terminal Control Problem2.11 Small Variations of Control Function for Terminal Control Problem; 2.12 A Discrete Version of Small Variations of Control Function for Generalized Terminal Control Problem; 2.13 Optimal Time Control Problems; 2.14 Final Remarks on Control Problems; 2.15 Exercises; 3. Functional Analysis; 3.1 A Normed Space as a Metric Space; 3.2 Dimension of a Linear Space and Separability; 3.3 Cauchy Sequences and Banach Spaces; 3.4 The Completion Theorem; 3.5 Contraction Mapping Principle; 3.6 Lp Spaces and the Lebesgue Integral; 3.7 Sobolev Spaces3.8 Compactness3.9 Inner Product Spaces Hilbert Spaces; 3.10 Some Energy Spaces in Mechanics; 3.11 Operators and Functional; 3.12 Some Approximation Theory; 3.13 Orthogonal Decomposition of a Hilbert Space and the Riesz Representation Theorem; 3.14 Basis Gram-Schmidt Procedure Fourier Series in Hilbert Space; 3.15 Weak Convergence; 3.16 Adjoint and Self-adjoint Operators; 3.17 Compact Operators; 3.18 Closed Operators; 3.19 Introduction to Spectral Concepts; 3.20 The Fredholm Theory in Hilbert Spaces; 3.21 Exercises; 4. Some Applications in Mechanics4.1 Some Problems of Mechanics from the Viewpoint of the Calculus of Variations the Virtual Work Principle; 4.2 Equilibrium Problem for a Clamped Membrane and its Generalized Solution; 4.3 Equilibrium of a Free Membrane; 4.4 Some Other Problems of Equilibrium of Linear Mechanics; 4.5 The Ritz and Bubnov-Galerkin Methods; 4.6 The Hamilton-Ostrogradskij Principle and the Generalized Setup of Dynamical Problems of Classical Mechanics; 4.7 Generalized Setup of Dynamic Problems for a Membrane; 4.8 Other Dynamic Problems of Linear Mechanics; 4.9 The Fourier Method4.10 An Eigenfrequency Boundary Value Problem Arising in Linear MechanicsThis is a book for those who want to understand the main ideas in the theory of optimal problems. It provides a good introduction to classical topics (under the heading of "the calculus of variations") and more modern topics (under the heading of "optimal control"). It employs the language and terminology of functional analysis to discuss and justify the setup of problems that are of great importance in applications. The book is concise and self-contained, and should be suitable for readers with a standard undergraduate background in engineering mathematics.Series on stability, vibration, and control of systems.Series A ;v. 12.Functional analysisMechanicsFunctional analysis.Mechanics.515.7Lebedev L. P1089225Cloud Michael J41158MiAaPQMiAaPQMiAaPQBOOK9910782117403321The calculus of variations and functional analysis3692686UNINA