01275aam 2200373I 450 991071010070332120151118015318.0GOVPUB-C13-0b471f448f2ce27619fdf8f9ef05bc08(CKB)5470000002475265(OCoLC)929879621(EXLCZ)99547000000247526520151118d1973 ua 0engrdacontentrdamediardacarrierFractographic examination of Sabreliner landing gear fracture /T. Robert ShivesGaithersburg, MD :U.S. Dept. of Commerce, National Institute of Standards and Technology,1973.1 online resourceNBSIR ;73-1171973.Contributed record: Metadata reviewed, not verified. Some fields updated by batch processes.Title from PDF title page.Includes bibliographical references.Shives T. R313782Shives T. R313782United States.National Bureau of Standards.NBSNBSGPOBOOK9910710100703321Fractographic examination of Sabreliner landing gear fracture3449763UNINA01443nam0 22003613i 450 SBL033980420231121125821.0IT7612069 20141107d1975 ||||0itac50 baitaitz01i xxxe z01n˜L'œultima oratoria di CiceroneEmanuele CastorinaCataniaN. Giannotta1975216 p.21 cm.Cicerone, Marco TullioFIRRMLC115280N875.01Discorsi latini. Periodo romano, fino al 499 ca.22Castorina, EmanueleRAVV078129070182205Cicero, Marcus TulliusCFIV006643072Cicerone, Marco TullioCFIV006644Cicero, Marcus TulliusCiceroneCFIV030674Cicero, Marcus TulliusCicéronCFIV068480Cicero, Marcus TulliusCicerone, M. TullioCFIV150753Cicero, Marcus TulliusCyceronCFIV254495Cicero, Marcus TulliusITIT-0120141107IT-FR0017 Biblioteca umanistica Giorgio ApreaFR0017 NSBL0339804Biblioteca umanistica Giorgio Aprea 52DFA A 243 52FLS0000347845 VMB RS Con dedica autografa dell'A.C 2014110720141107 52Ultima oratoria di Cicerone556237UNICAS05189nam 22004333 450 991079923090332120240105080300.03-031-39524-7(MiAaPQ)EBC31051520(Au-PeEL)EBL31051520(MiAaPQ)EBC31048481(Au-PeEL)EBL31048481(EXLCZ)992951021950004120240105d2024 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierA Short Introduction to Partial Differential Equations1st ed.Cham :Springer,2024.©2023.1 online resource (225 pages)CMS/CAIMS Books in Mathematics Series ;v.11Print version: Novruzi, Arian A Short Introduction to Partial Differential Equations Cham : Springer,c2024 9783031395239 Intro -- Preface -- Contents -- 1 Notations and review -- 1.1 Continuous differentiable functions -- 1.2 Domains and Ck (∂Ω) spaces -- 1.2.1 Partition of unity -- 1.2.2 Domains and Ck (∂Ω) spaces -- 1.3 Review of some important results -- 1.3.1 Some results from Lp(Ω) spaces -- 1.3.2 Some results from (Functional) Analysis -- 1.3.3 An application: Ordinary Differential Equations -- Problems -- 2 Partial differential equations -- 2.1 Some prototypes of PDEs -- Problems -- 3 First-order PDEs: classical and weak solutions -- 3.1 Method of characteristics -- 3.2 Classical local solutions to first-order PDEs -- 3.2.1 Classical local solutions: flat boundary -- 3.2.1.1 Boundary and initial conditions -- 3.2.1.2 Classical local solutions -- 3.2.2 Classical local solutions: non-flat boundary -- 3.3 Conservation laws and weak solutions -- Problems -- 4 Second-order linear elliptic PDEs: maximum principle and classical solutions -- 4.1 Laplace equation and the method of separation of variables -- 4.2 Dirichlet problem in a ball -- 4.3 Maximum principle for Laplacian -- 4.4 Solution to the Dirichlet problem -- 4.4.1 Sub(super) harmonic functions and sub(super) solutions -- 4.4.2 Solution to the Dirichlet problem -- Problems -- 5 Distributions -- 5.1 Motivation -- 5.2 Distributions -- 5.2.1 Test functions -- 5.2.2 Distributions -- 5.2.3 Derivatives of distributions -- 5.3 Convolution of distributions and fundamental solutions -- 5.4 Tempered distributions and Fourier transform -- 5.4.1 Fourier transform -- 5.4.2 Tempered distributions and Fourier transform -- Problems -- 6 Sobolev spaces -- 6.1 Definitions and some first properties -- 6.1.1 Density of D in Wk,p -- 6.1.2 Some applications -- 6.2 Hs spaces and Fourier transform: Ws,p and Ws,p0 spaces -- 6.3 Continuous, compact, and dense embedding theorems in Hs(Ω) -- 6.3.1 Case Ω = RN -- 6.3.2 Case Ω RN.6.4 Boundary traces in Sobolev spaces -- 6.5 Poincaré inequality -- 6.6 H−s(Ω) and W−s,q(Ω) spaces -- Problems -- 7 Second-order linear elliptic PDEs: weak solutions -- 7.1 Introduction -- 7.2 Existence and uniqueness of weak solutions -- 7.2.1 Preliminary results -- 7.2.2 Dirichlet problem -- 7.2.3 Neumann problem -- 7.3 Nonlinear second-order elliptic PDEs -- Problems -- 8 Second-order parabolic and hyperbolic PDEs -- 8.1 Heat and wave equations and the method of separation of variables -- 8.1.1 Heat equation and the method of separation of variables -- 8.1.2 Wave equation and the method of separation of variables -- 8.2 Some preliminary results -- 8.3 Weak solution to the heat equation -- 8.4 Weak solution to the wave equation -- Problems -- 9 Annex -- 9.1 Annex: Chapter 1 -- 9.1.1 Continuous differentiable functions -- 9.1.2 Some results from Lp(Ω) spaces -- 9.1.3 An application: Ordinary Differential Equations -- 9.2 Annex: Chapter 3 -- 9.2.1 Classical local solutions to first-order PDEs -- 9.2.2 Conservation laws and weak solutions -- 9.3 Annex: Chapter 4 -- 9.3.1 Dirichlet problem in a ball -- 9.3.2 Maximum principle for second-order linear elliptic PDEs -- 9.3.3 Solution to the Dirichlet problem -- 9.3.3.1 Sub(super) harmonic functions and sub(super) solutions -- 9.3.3.2 Some auxiliary results from Analysis -- 9.3.3.3 Proof of Theorem 4.4.7 -- 9.4 Annex: Chapter 5 -- 9.4.1 Some useful inequalities -- 9.4.2 More operations with distributions. Examples -- 9.4.3 Convergence of distributions. Distributions of finite order -- 9.4.4 Convolution of distributions -- 9.4.5 Tempered distributions and Fourier transform -- 9.4.6 Tempered distributions and convolution -- 9.5 Annex: Chapter 6 -- 9.5.1 Continuous and compact embeddings -- 9.5.2 Extension and density results in Sobolev spaces -- 9.5.3 Boundary traces in Sobolev spaces.9.6 Annex: Chapter 7 -- 9.6.1 Regularity of weak solutions -- 9.6.1.1 Regularity in the interior -- 9.6.1.2 Regularity near the boundary.CMS/CAIMS Books in Mathematics Series515.353Novruzi Arian1585650MiAaPQMiAaPQMiAaPQBOOK9910799230903321A Short Introduction to Partial Differential Equations3871168UNINA