LEADER 06134nam 2200493 450 001 996466394503316 005 20230508102028.0 010 $a3-030-77834-7 035 $a(CKB)4100000011982279 035 $a(MiAaPQ)EBC6680480 035 $a(Au-PeEL)EBL6680480 035 $a(OCoLC)1261364257 035 $a(PPN)269146504 035 $a(EXLCZ)994100000011982279 100 $a20220403d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDifferentiability in Banach spaces, differential forms and applications /$fCelso Melchiades Doria 210 1$aCham, Switzerland :$cSpringer,$d[2021] 210 4$d©2021 215 $a1 online resource (369 pages) 311 $a3-030-77833-9 327 $aIntro -- Preface -- Introduction -- Contents -- 1 Differentiation in mathbbRn -- 1 Differentiability of Functions f:mathbbRnrightarrowmathbbR -- 1.1 Directional Derivatives -- 1.2 Differentiable Functions -- 1.3 Differentials -- 1.4 Multiple Derivatives -- 1.5 Higher Order Differentials -- 2 Taylor's Formula -- 3 Critical Points and Local Extremes -- 3.1 Morse Functions -- 4 The Implicit Function Theorem and Applications -- 5 Lagrange Multipliers -- 5.1 The Ultraviolet Catastrophe: The Dawn of Quantum Mechanics -- 6 Differentiable Maps I -- 6.1 Basics Concepts -- 6.2 Coordinate Systems -- 6.3 The Local Form of an Immersion -- 6.4 The Local Form of Submersions -- 6.5 Generalization of the Implicit Function Theorem -- 7 Fundamental Theorem of Algebra -- 8 Jacobian Conjecture -- 8.1 Case n=1 -- 8.2 Case nge2 -- 8.3 Covering Spaces -- 8.4 Degree Reduction -- 2 Linear Operators in Banach Spaces -- 1 Bounded Linear Operators on Normed Spaces -- 2 Closed Operators and Closed Range Operators -- 3 Dual Spaces -- 4 The Spectrum of a Bounded Linear Operator -- 5 Compact Linear Operators -- 6 Fredholm Operators -- 6.1 The Spectral Theory of Compact Operators -- 7 Linear Operators on Hilbert Spaces -- 7.1 Characterization of Compact Operators on Hilbert Spaces -- 7.2 Self-adjoint Compact Operators on Hilbert Spaces -- 7.3 Fredholm Alternative -- 7.4 Hilbert-Schmidt Integral Operators -- 8 Closed Unbounded Linear Operators on Hilbert Spaces -- 3 Differentiation in Banach Spaces -- 1 Maps on Banach Spaces -- 1.1 Extension by Continuity -- 2 Derivation and Integration of Functions f:[a,b]rightarrowE -- 2.1 Derivation of a Single Variable Function -- 2.2 Integration of a Single Variable Function -- 3 Differentiable Maps II -- 4 Inverse Function Theorem (InFT) -- 4.1 Prelude for the Inverse Function Theorem -- 4.2 InFT for Functions of a Single Real Variable. 327 $a4.3 Proof of the Inverse Function Theorem (InFT) -- 4.4 Applications of InFT -- 5 Classical Examples in Variational Calculus -- 5.1 Euler-Lagrange Equations -- 5.2 Examples -- 6 Fredholm Maps -- 6.1 Final Comments and Examples -- 7 An Application of the Inverse Function Theorem to Geometry -- 4 Vector Fields -- 1 Vector Fields in mathbbRn -- 2 Conservative Vector Fields -- 3 Existence and Uniqueness Theorem for ODE -- 4 Flow of a Vector Field -- 5 Vector Fields as Differential Operators -- 6 Integrability, Frobenius Theorem -- 7 Lie Groups and Lie Algebras -- 8 Variations over a Flow, Lie Derivative -- 9 Gradient, Curl and Divergent Differential Operators -- 5 Vector Integration, Potential Theory -- 1 Vector Calculus -- 1.1 Line Integral -- 1.2 Surface Integral -- 2 Classical Theorems of Integration -- 2.1 Interpretation of the Curl and Div Operators -- 3 Elementary Aspects of the Theory of Potential -- 6 Differential Forms, Stokes Theorem -- 1 Exterior Algebra -- 2 Orientation on V and on the Inner Product on ?(V) -- 2.1 Orientation -- 2.2 Inner Product in ?(V) -- 2.3 Pseudo-Inner Product, the Lorentz Form -- 3 Differential Forms -- 3.1 Exterior Derivative -- 4 De Rham Cohomology -- 4.1 Short Exact Sequence -- 5 De Rham Cohomology of Spheres and Surfaces -- 6 Stokes Theorem -- 7 Orientation, Hodge Star-Operator and Exterior Co-derivative -- 8 Differential Forms on Manifolds, Stokes Theorem -- 8.1 Orientation -- 8.2 Integration on Manifolds -- 8.3 Exterior Derivative -- 8.4 Stokes Theorem on Manifolds -- 7 Applications to the Stokes Theorem -- 1 Volumes of the (n+1)-Disk and of the n-Sphere -- 2 Harmonic Functions -- 2.1 Laplacian Operator -- 2.2 Properties of Harmonic Functions -- 3 Poisson Kernel for the n-Disk DnR -- 4 Harmonic Differential Forms -- 4.1 Hodge Theorem on Manifolds -- 5 Geometric Formulation of the Electromagnetic Theory. 327 $a5.1 Electromagnetic Potentials -- 5.2 Geometric Formulation -- 5.3 Variational Formulation -- 6 Helmholtz's Decomposition Theorem -- Appendix A Basics of Analysis -- 1 Sets -- 2 Finite-dimensional Linear Algebra: V=mathbbRn -- 2.1 Matrix Spaces -- 2.2 Linear Transformations -- 2.3 Primary Decomposition Theorem -- 2.4 Inner Product and Sesquilinear Forms -- 2.5 The Sylvester Theorem -- 2.6 Dual Vector Spaces -- 3 Metric and Banach Spaces -- 4 Calculus Theorems -- 4.1 One Real Variable Functions -- 4.2 Functions of Several Real Variables -- 5 Proper Maps -- 6 Equicontinuity and the Ascoli-Arzela? Theorem -- 7 Functional Analysis Theorems -- 7.1 Riesz and Hahn-Banach Theorems -- 7.2 Topological Complementary Subspace -- 8 The Contraction Lemma -- Appendix B Differentiable Manifolds, Lie Groups -- 1 Differentiable Manifolds -- 2 Bundles: Tangent and Cotangent -- 3 Lie Groups -- Appendix C Tensor Algebra -- 1 Tensor Product -- 2 Tensor Algebra -- Appendix References -- -- Index. 606 $aBanach spaces 606 $aEspais de Banach$2thub 606 $aStokes' theorem 608 $aLlibres electrònics$2thub 615 0$aBanach spaces. 615 7$aEspais de Banach 615 0$aStokes' theorem. 676 $a515.732 700 $aDoria$b Celso Melchiades$0846200 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466394503316 996 $aDifferentiability in Banach Spaces, Differential Forms and Applications$91890197 997 $aUNISA LEADER 02869oam 2200673I 450 001 9910784001303321 005 20230617001915.0 010 $a1-351-83666-8 010 $a1-315-22077-6 010 $a1-62870-647-3 010 $a1-280-19517-7 010 $a9786610195176 010 $a0-203-99738-7 024 7 $a10.1201/9781420030907 035 $a(CKB)1000000000251919 035 $a(EBL)243239 035 $a(OCoLC)191036804 035 $a(SSID)ssj0000202412 035 $a(PQKBManifestationID)11166842 035 $a(PQKBTitleCode)TC0000202412 035 $a(PQKBWorkID)10252211 035 $a(PQKB)11421386 035 $a(MiAaPQ)EBC243239 035 $a(Au-PeEL)EBL243239 035 $a(CaPaEBR)ebr10162244 035 $a(CaONFJC)MIL19517 035 $a(OCoLC)935228262 035 $a(OCoLC)1000433832 035 $a(EXLCZ)991000000000251919 100 $a20180331d2005 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMicrooptics technology /$fNicholas F. Borrelli 205 $a2nd ed. 210 1$aNew York :$cMarcel Dekker,$d2005. 215 $a1 online resource (543 p.) 225 1 $aOptical engineering ; v. 93 300 $aDescription based upon print version of record. 311 $a1-4200-3090-6 311 $a0-8247-5921-4 320 $aIncludes bibliographical references and index. 327 $aBook Cover; Title; Copyright; Dedication; Preface to Second Edition; Contents; 1 Introduction; 2 Refractive Elements; 3 Gradient Index; 4 Diffractive Element Lenses; 5 Erect One-to-One Imaging; 6 Two-Dimensional Arrays; 7 Gratings; 8 Optical Isolators; 9 Photonic Crystals; 10 Femtosecond-Laser Interaction in Glasses; 11 Negative Refractive Index Materials; Index 330 $aIt has been five years since the publication of the first edition of Microoptics Technology. In that time, optical technology has experienced an unparalleled burst of activity that has produced a body of significant real results that have advanced new materials, devices, and systems. Building on the foundation of the first edition, this comprehensive reference presents an introduction and review of the optics and methods of microoptic elements with particular emphasis on lenses and lens arrays.The author explores advances that emerged from the flurry of activity over the last five year 410 0$aOptical engineering (Marcel Dekker, Inc.) ;$vv. 93. 606 $aLenses$xDesign and construction 606 $aOptics 615 0$aLenses$xDesign and construction. 615 0$aOptics. 676 $a621.36 700 $aBorrelli$b Nicholas F.$f1936,$01550913 801 0$bFlBoTFG 801 1$bFlBoTFG 906 $aBOOK 912 $a9910784001303321 996 $aMicrooptics technology$93810126 997 $aUNINA LEADER 05107nam 22007455 450 001 9910624302903321 005 20251009105822.0 010 $a9783031130489 (electronic book) 010 $z9783031130472 024 7 $a10.1007/978-3-031-13048-9 035 $a(MiAaPQ)EBC7133744 035 $a(Au-PeEL)EBL7133744 035 $a(CKB)25299362300041 035 $a(OCoLC)1350688504 035 $a(DE-He213)978-3-031-13048-9 035 $a(EXLCZ)9925299362300041 100 $a20221108d2022 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$a"Invisible Cities" and the Urban Imagination /$fedited by Benjamin Linder 205 $a1st ed. 2022. 210 1$aCham :$cSpringer International Publishing :$cImprint: Palgrave Macmillan,$d2022. 215 $a1 online resource (355 pages) $cillustrations 225 1 $aLiterary Urban Studies,$x2523-7896 311 08$aPrint version: Linder, Benjamin Invisible Cities and the Urban Imagination Cham : Springer International Publishing AG,c2022 9783031130472 320 $aIncludes bibliographical references and index. 327 $a1. Introduction: Invisible Cities and the Urban Imagination -- Part I Cities & Theory -- 2. Invisible Cities: Learning to Recognize Urban Society -- 3. How to Map the Invisible -- 4. Invisible Cities and the Work of Storying the Future -- 5. Paris, Latour, and Calvino -- 6. Queer Cities, Bodies & Desire: Reading Nicole Brossard alongside Italo Calvino -- 7. On the Epistemic Ruins of Existence -- Part II Cities & Cities -- 8. ?The Void not Filled with Words": The Role of Venice in Invisible Cities -- 9. A Tale of Two Ethnographers: Urban Anthropologists Read Invisible Cities -- 10. Fifty Years of Soul City: Lessons of a Black Utopia -- 11. Tirana Visible and Invisible -- 12. The Lost City: The Pathos of Arab Jerusalem -- 13. ?Submerging the City in Its Own Past?: Tracing Glasgow?s Architectures of Inhabitation -- 14. Poetics of the Invisible, Poetics of Rubble -- 15. Encountering Urban Mutualities and Indeterminacy with a Dar es Salaam Taxi Driver -- 16. Reconstructing Memory and Desire in Bhaktapur, Nepal -- 17. The Weight of the City: The Burden and Opportunities of Urban Villages -- 18. Don?t Nuisance the Relented City: Community Barriers and Urban ?Keepers? in the Haedo, Buenos Aires -- Part III Cities & Practice -- 19. The Architect and Invisible Cities -- 20. Visible Cities: Calvino in Performance -- 21. The Pedagogy of Storytelling in Invisible Cities -- 22. Invisible Smart Cities -- 23. Peripheral Visions of Empire: Zagreb, Belgrade, Sarajevo (Homage to Calvino) -- 24. Imagining São Paulo with Invisible Cities -- 25. Desires and Fears in the Invisible Eternal City -- 26. Nyctopolis, the City of Darkness -- 27. Epilogue: A Comparative Palimpsest of Urban Plenitude and Difference. 330 $aIn 1972, Italo Calvino published Invisible Cities, a literary book that masterfully combines philosophy and poetry, rigid structure and free play, theoretical insight and glittering prose. The text is an extended meditation on urban life, and it continues to resonate not only among literary scholars, but among social scientists, architects, and urban planners as well. To commemorate the 50th anniversary of Invisible Cities, this collection of essays serves as both an appreciation and a critical engagement. Drawing from a wide array of disciplinary perspectives and geographical contexts, this volume grapples with the theoretical, pedagogical, and political legacies of Calvino?s work. Each chapter approaches Invisible Cities not only as a novel but as a work of evocative ethnography, place-writing, and urban theory. Fifty years on, what can Calvino?s dreamlike text offer to scholars and practitioners interested in actually existing urban life? 410 0$aLiterary Urban Studies,$x2523-7896 606 $aLiterature, Modern$y20th century 606 $aLiterature, Modern$y21st century 606 $aEuropean literature 606 $aComparative literature 606 $aSpace 606 $aCulture 606 $aCities and towns$xHistory 606 $aContemporary Literature 606 $aEuropean Literature 606 $aComparative Literature 606 $aSpace and Place in Culture 606 $aUrban History 615 0$aLiterature, Modern 615 0$aLiterature, Modern 615 0$aEuropean literature. 615 0$aComparative literature. 615 0$aSpace. 615 0$aCulture. 615 0$aCities and towns$xHistory. 615 14$aContemporary Literature. 615 24$aEuropean Literature. 615 24$aComparative Literature. 615 24$aSpace and Place in Culture. 615 24$aUrban History. 676 $a354.81150006 676 $a853.914 700 $aLinder$b Benjamin$0795748 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910624302903321 996 $aInvisible Cities and the Urban Imagination$92967880 997 $aUNINA