LEADER 01018nam--2200361---450- 001 990001360700203316 005 20050906090639.0 035 $a000136070 035 $aUSA01000136070 035 $a(ALEPH)000136070USA01 035 $a000136070 100 $a20040121d1960----km-y0itay0103----ba 101 0 $afre 102 $aFR 105 $a||||||||001yy 200 1 $a<> metier de seigneur$fPierre Boulard 210 $aParis$cJulliard$d1960 215 $a256 p.$d17 cm. 225 2 $a<> livre de poche 410 0$12001$a<> livre de poche 454 1$12001 461 1$1001-------$12001 700 1$aBOULLE,$bPierre$0438782 801 0$aIT$bsalbc$gISBD 912 $a990001360700203316 951 $aVI.4. Coll.13/ 48(II f D 1 49)$b13499 L.M.$cIIf D 959 $aBK 969 $aUMA 979 $aSIAV4$b10$c20040121$lUSA01$h1723 979 $aPATRY$b90$c20040406$lUSA01$h1736 979 $aCOPAT5$b90$c20050906$lUSA01$h0906 996 $aMétier de seigneur$9309187 997 $aUNISA LEADER 05599nam 2200685Ia 450 001 9910454312903321 005 20200520144314.0 010 $a1-281-93546-8 010 $a9786611935467 010 $a981-279-499-9 035 $a(CKB)1000000000537813 035 $a(EBL)1223606 035 $a(SSID)ssj0000290724 035 $a(PQKBManifestationID)11211138 035 $a(PQKBTitleCode)TC0000290724 035 $a(PQKBWorkID)10230603 035 $a(PQKB)10843223 035 $a(MiAaPQ)EBC1223606 035 $a(WSP)00005374 035 $a(Au-PeEL)EBL1223606 035 $a(CaPaEBR)ebr10255903 035 $a(CaONFJC)MIL193546 035 $a(OCoLC)853361888 035 $a(EXLCZ)991000000000537813 100 $a20030826d2003 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe calculus of variations and functional analysis$b[electronic resource] $ewith optimal control and applications in mechanics /$fLeonid P. Lebedev, Michael J. Cloud 210 $aSingapore ;$aRiver Edge, N.J. $cWorld Scientific$dc2003 215 $a1 online resource (435 p.) 225 1 $aSeries on stability, vibration, and control of systems. Series A ;$vv. 12 300 $aDescription based upon print version of record. 311 $a981-238-581-9 320 $aIncludes bibliographical references (p. 415-416) and index. 327 $aForeword; 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 Extremals 327 $a1.13 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 Problem 327 $a2.10 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 Spaces 327 $a3.8 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 Mechanics 327 $a4.1 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 Method 327 $a4.10 An Eigenfrequency Boundary Value Problem Arising in Linear Mechanics 330 $aThis is a book for those who want to understand the main ideas in the theory of optimal problems. It provides a good introduction to classical topics (under the heading of "the calculus of variations") and more modern topics (under the heading of "optimal control"). It employs the language and terminology of functional analysis to discuss and justify the setup of problems that are of great importance in applications. The book is concise and self-contained, and should be suitable for readers with a standard undergraduate background in engineering mathematics. 410 0$aSeries on stability, vibration, and control of systems.$nSeries A ;$vv. 12. 606 $aFunctional analysis 606 $aMechanics 608 $aElectronic books. 615 0$aFunctional analysis. 615 0$aMechanics. 676 $a515.7 700 $aLebedev$b L. P$0848913 701 $aCloud$b Michael J$041158 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910454312903321 996 $aThe calculus of variations and functional analysis$92240226 997 $aUNINA LEADER 01152nam a22002891i 4500 001 991004107159707536 005 20031003135133.0 008 031111s1995 it |||||||||||||||||ita 020 $a8806131842 035 $ab12521838-39ule_inst 035 $aARCHE-055510$9ExL 040 $aDip.to Lingue$bita$cA.t.i. Arché s.c.r.l. 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Filosofia$bita$cSocioculturale Scs 041 0 $afre 082 04$a320.01$223 100 1 $aRousseau, Jean-Jacques$d<1712-1778>$0132862 245 10$aDiscours sur l'origine et les fondements de l'inégalité parmi les hommes /$cJ.-J. Rousseau ; introduction, commentaires et notes explicatives par J.-L. Lecercle 260 $aParis :$bEditions sociales,$cstampa 1961 300 $a187 p. ;$c18 cm 490 1 $aLes classiques du peuple 650 4$aFilosofia politica 700 1 $aLecercle, Jean Louis 830 4$aLes classiques du peuple 912 $a991004382125407536 996 $aDiscours sur l'origine et les fondements de l'inégalité parmi les hommes$9202969 997 $aUNISALENTO