06738nam 22006975 450 991030012380332120200702092027.03-319-70842-210.1007/978-3-319-70842-3(CKB)4100000004834515(DE-He213)978-3-319-70842-3(MiAaPQ)EBC5426704(PPN)229494978(EXLCZ)99410000000483451520180609d2018 u| 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierMathematical Foundations of Computational Electromagnetism /by Franck Assous, Patrick Ciarlet, Simon Labrunie1st ed. 2018.Cham :Springer International Publishing :Imprint: Springer,2018.1 online resource (IX, 458 p. 7 illus.)Applied Mathematical Sciences,0066-5452 ;1983-319-70841-4 Foreword -- Physical framework and models -- Electromagnetic fields and Maxwell’s equations -- Stationary equations -- Coupling with other models -- Approximate models -- Elements of mathematical classifications -- Boundary conditions and radiation conditions -- Energy matters -- Bibliographical notes -- Basic applied functional analysis -- Function spaces for scalar fields -- Vector fields: standard function spaces -- Practical function spaces in the (t, x) variable -- Complements of applied functional analysis -- Vector fields: tangential trace revisited -- Scalar and vector potentials: the analyst’s and topologist’s points of view -- Extraction of scalar potentials and consequences -- Extraction of vector potentials -- Extraction of vector potentials – Vanishing normal trace -- Extraction of vector potentials – Complements -- Helmholtz decompositions -- Abstract mathematical framework -- Basic Results -- Static problems -- Time-dependent problems -- Time-dependent problems: improved regularity results -- Time-harmonic problems -- Summing up -- Analyses of exact problems: first-order models -- Energy matters: uniqueness of the fields -- Well-posedness -- Analyses of approximate models -- Electrostatic problem -- Magnetostatic problem -- Further comments around static problems -- Other approximate models -- Analyses of exact problems: second-order models -- First-order to second-order equations -- Well-posedness of the second-order Maxwell equations -- Second-order to first-order equations -- Other variational formulations -- Compact imbeddings -- Improved regularity for augmented and mixed augmented formulations -- Analyses of time-harmonic problems -- Compact imbeddings: complements -- Free vibrations in a domain encased in a cavity -- Sustained vibrations -- Interface problem between a dielectric and a Lorentz material -- Comments -- Dimensionally reduced models: derivation and analyses -- Two-and-a-half dimensional (2 1/2 2D) models -- Two-dimensional (2D) models -- Some results of functional analysis -- Existence and uniqueness results (2D problems) -- Analyses of coupled models -- The Vlasov–Maxwell and Vlasov–Poisson systems -- Magnetohydrodynamics -- References -- Index of function spaces -- Basic Spaces -- Electromagnetic spaces -- Dimension reduction and weighted spaces -- Spaces measuring time regularity -- List of Figures -- Index.This book presents an in-depth treatment of various mathematical aspects of electromagnetism and Maxwell's equations: from modeling issues to well-posedness results and the coupled models of plasma physics (Vlasov-Maxwell and Vlasov-Poisson systems) and magnetohydrodynamics (MHD). These equations and boundary conditions are discussed, including a brief review of absorbing boundary conditions. The focus then moves to well‐posedness results. The relevant function spaces are introduced, with an emphasis on boundary and topological conditions. General variational frameworks are defined for static and quasi-static problems, time-harmonic problems (including fixed frequency or Helmholtz-like problems and unknown frequency or eigenvalue problems), and time-dependent problems, with or without constraints. They are then applied to prove the well-posedness of Maxwell’s equations and their simplified models, in the various settings described above. The book is completed with a discussion of dimensionally reduced models in prismatic and axisymmetric geometries, and a survey of existence and uniqueness results for the Vlasov-Poisson, Vlasov-Maxwell and MHD equations. The book addresses mainly researchers in applied mathematics who work on Maxwell’s equations. However, it can be used for master or doctorate-level courses on mathematical electromagnetism as it requires only a bachelor-level knowledge of analysis.Applied Mathematical Sciences,0066-5452 ;198Mathematical physicsOpticsElectrodynamicsEngineering mathematicsFunctional analysisPlasma (Ionized gases)Mathematical Applications in the Physical Scienceshttps://scigraph.springernature.com/ontologies/product-market-codes/M13120Classical Electrodynamicshttps://scigraph.springernature.com/ontologies/product-market-codes/P21070Engineering Mathematicshttps://scigraph.springernature.com/ontologies/product-market-codes/T11030Functional Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12066Theoretical, Mathematical and Computational Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P19005Plasma Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P24040Mathematical physics.Optics.Electrodynamics.Engineering mathematics.Functional analysis.Plasma (Ionized gases)Mathematical Applications in the Physical Sciences.Classical Electrodynamics.Engineering Mathematics.Functional Analysis.Theoretical, Mathematical and Computational Physics.Plasma Physics.519Assous Franckauthttp://id.loc.gov/vocabulary/relators/aut767837Ciarlet Patrickauthttp://id.loc.gov/vocabulary/relators/autLabrunie Simonauthttp://id.loc.gov/vocabulary/relators/autBOOK9910300123803321Mathematical Foundations of Computational Electromagnetism2240082UNINA02634oam 22005534a 450 991052486710332120241204165259.00-8018-0147-81-4214-3389-3(CKB)4100000010460859(OCoLC)1122190185(MdBmJHUP)muse78183(oapen)https://directory.doabooks.org/handle/20.500.12854/88909(MiAaPQ)EBC29138870(Au-PeEL)EBL29138870(oapen)doab88909(OCoLC)1526863243(EXLCZ)99410000001046085919801219d1959 uy 0engur|||||||nn|ntxtrdacontentcrdamediacrrdacarrierAn Age of CrisisMan and World in Eighteenth Century French Thought1st ed.Johns Hopkins University Press2019Baltimore,Johns Hopkins Press[1959]©[1959]1 online resource (xx, 496 p. )Goucher Colloquium Series1-4214-3388-5 1-4214-3390-7 Cover -- Copyright -- Contents -- Prefatory Note -- Man in the Universe -- 1. Man's Relation to God -- 2. The Problem of Evil -- 3. Man's Place -- Freedom and Determinism -- 4. The Activity of the Mind -- 5. Freedom of Indifference. Intuition -- 6. The Moral Consequences -- Human Nature and Motivation -- 7. The Theory of Human Nature -- 8. Man's Detractors -- 9. Reason and the Passions -- 10. Forms and Values of Self-Interest (1) -- 11. Forms and Values of Self-Interest (2): Approbation, Esteem, and Pride -- 12. Man's Goodness -- 13. Ethics and Christianity -- 14. Human Nature in the Novel -- Culminations -- Bibliography -- Index.Originally published in 1959. This book examines the French Enlightenment by analyzing critical thought in eighteenth-centruy France. It examines the philosophes' views on evil, free will and determinism, and human nature. This is an interesting group to look at, according to Crocker, because French Enlightenment thinkers straddled two vastly different time periods.Goucher College series. [from old catalog]EnlightenmentEthicsFranceHistoryPhilosophy, FrenchEnlightenment.EthicsHistory.Philosophy, French.Crocker Lester G. [from old catalog]1115796MdBmJHUPMdBmJHUPBOOK9910524867103321An Age of Crisis2642854UNINA