LEADER 04567nam 22007095 450 001 996466771503316 005 20200630031401.0 010 $a3-642-33149-1 024 7 $a10.1007/978-3-642-33149-7 035 $a(CKB)3400000000102775 035 $a(SSID)ssj0000810092 035 $a(PQKBManifestationID)11456156 035 $a(PQKBTitleCode)TC0000810092 035 $a(PQKBWorkID)10826405 035 $a(PQKB)11180734 035 $a(DE-He213)978-3-642-33149-7 035 $a(MiAaPQ)EBC3070794 035 $a(PPN)168323672 035 $a(EXLCZ)993400000000102775 100 $a20121116d2013 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aStochastic Calculus with Infinitesimals$b[electronic resource] /$fby Frederik S. Herzberg 205 $a1st ed. 2013. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2013. 215 $a1 online resource (XVIII, 112 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2067 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-642-33148-3 320 $aIncludes bibliographical references (p.107-110) and index. 327 $a1 Infinitesimal calculus, consistently and accessibly -- 2 Radically elementary probability theory -- 3 Radically elementary stochastic integrals -- 4 The radically elementary Girsanov theorem and the diffusion invariance principle -- 5 Excursion to nancial economics: A radically elementary approach to the fundamental theorems of asset pricing -- 6 Excursion to financial engineering: Volatility invariance in the Black-Scholes model -- 7 A radically elementary theory of Itô diffusions and associated partial differential equations -- 8 Excursion to mathematical physics: A radically elementary definition of Feynman path integrals -- 9 A radically elementary theory of Lévy processes -- 10 Final remarks. 330 $aStochastic analysis is not only a thriving area of pure mathematics with intriguing connections to partial differential equations and differential geometry. It also has numerous applications in the natural and social sciences (for instance in financial mathematics or theoretical quantum mechanics) and therefore appears in physics and economics curricula as well. However, existing approaches to stochastic analysis either presuppose various concepts from measure theory and functional analysis or lack full mathematical rigour. This short book proposes to solve the dilemma: By adopting E. Nelson's "radically elementary" theory of continuous-time stochastic processes, it is based on a demonstrably consistent use of infinitesimals and thus permits a radically simplified, yet perfectly rigorous approach to stochastic calculus and its fascinating applications, some of which (notably the Black-Scholes theory of option pricing and the Feynman path integral) are also discussed in the book. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v2067 606 $aMathematical logic 606 $aProbabilities 606 $aEconomic theory 606 $aGame theory 606 $aMathematical physics 606 $aMathematical Logic and Foundations$3https://scigraph.springernature.com/ontologies/product-market-codes/M24005 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aEconomic Theory/Quantitative Economics/Mathematical Methods$3https://scigraph.springernature.com/ontologies/product-market-codes/W29000 606 $aGame Theory, Economics, Social and Behav. Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13011 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 615 0$aMathematical logic. 615 0$aProbabilities. 615 0$aEconomic theory. 615 0$aGame theory. 615 0$aMathematical physics. 615 14$aMathematical Logic and Foundations. 615 24$aProbability Theory and Stochastic Processes. 615 24$aEconomic Theory/Quantitative Economics/Mathematical Methods. 615 24$aGame Theory, Economics, Social and Behav. Sciences. 615 24$aMathematical Physics. 676 $a511.3 700 $aHerzberg$b Frederik S$4aut$4http://id.loc.gov/vocabulary/relators/aut$0521683 906 $aBOOK 912 $a996466771503316 996 $aStochastic calculus with infinitesimals$9837746 997 $aUNISA LEADER 05063nam 2200673 a 450 001 9911019935803321 005 20251126235649.0 010 $a9786612990212 010 $a9781282990210 010 $a1282990217 010 $a9783527633784 010 $a3527633782 010 $a9783527633760 010 $a3527633766 010 $a9783527633777 010 $a3527633774 035 $a(CKB)2670000000066460 035 $a(EBL)661852 035 $a(OCoLC)707067694 035 $a(SSID)ssj0000470147 035 $a(PQKBManifestationID)12231146 035 $a(PQKBTitleCode)TC0000470147 035 $a(PQKBWorkID)10410411 035 $a(PQKB)10536394 035 $a(MiAaPQ)EBC661852 035 $a(PPN)15874408X 035 $a(Perlego)1009185 035 $a(EXLCZ)992670000000066460 100 $a20110127d2011 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aHydromechanics $etheory and fundamentals /$fEmmanuil G. Sinaiski 210 $aWeinheim, Germany $cWiley-VCH Verlag$d2011 215 $a1 online resource (520 p.) 300 $aDescription based upon print version of record. 311 08$a9783527410262 311 08$a3527410260 320 $aIncludes bibliographical references and index. 327 $aHydromechanics; Dedication; Contents; Preface; List of Symbols; 1 Introduction; 1.1 Goals and Methods of Continuum Mechanics; 1.2 The Main Hypotheses of Continuum Mechanics; 2 Kinematics of the Deformed Continuum; 2.1 Dynamics of the Continuum in the Lagrangian Perspective; 2.2 Dynamics of the Continuum in the Eulerian Perspective; 2.3 Scalar and Vector Fields and Their Characteristics; 2.4 Theory of Strains; 2.5 The Tensor of Strain Velocities; 2.6 The Distribution of Velocities in an Infinitesimal Continuum Particle; 2.7 Properties of Vector Fields. Theorems of Stokes and Gauss 327 $a3 Dynamic Equations of Continuum Mechanics3.1 Equation of Continuity; 3.2 Equations of Motion; 3.3 Equation of Motion for the Angular Momentum; 4 Closed Systems of Mechanical Equations for the Simplest Continuum Models; 4.1 Ideal Fluid and Gas; 4.2 Linear Elastic Body and Linear Viscous Fluid; 4.3 Equations in Curvilinear Coordinates; 4.3.1 Equation of Continuity; 4.3.2 Equation of Motion; 4.3.3 Gradient of a Scalar Function; 4.3.4 Laplace Operator; 4.3.5 Complete System of Equations of Motion for a Viscous, Incompressible Medium in the Absence of Heating 327 $a5 Foundations and Main Equations of Thermodynamics5.1 Theorem of the Living Forces; 5.2 Law of Conservation of Energy and First Law of Thermodynamics; 5.3 Thermodynamic Equilibrium, Reversible and Irreversible Processes; 5.4 Two Parameter Media and Ideal Gas; 5.5 The Second Law of Thermodynamics and the Concept of Entropy; 5.6 Thermodynamic Potentials of Two-Parameter Media; 5.7 Examples of Ideal and Viscous Media, and Their Thermodynamic Properties, Heat Conduction; 5.7.1 The Model of the Ideal, Incompressible Fluid; 5.7.2 The Model of the Ideal, Compressible Gas 327 $a5.7.3 The Model of Viscous Fluid5.8 First and Second Law of Thermodynamics for a Finite Continuum Volume; 5.9 Generalized Thermodynamic Forces and Currents, Onsager's Reciprocity Relations; 6 Problems Posed in Continuum Mechanics; 6.1 Initial Conditions and Boundary Conditions; 6.2 Typical Simplifications for Some Problems; 6.3 Conditions on the Discontinuity Surfaces; 6.4 Discontinuity Surfaces in Ideal Compressible Media; 6.5 Dimensions of Physical Quantities; 6.6 Parameters that Determine the Class of the Phenomenon; 6.7 Similarity and Modeling of Phenomena; 7 Hydrostatics 327 $a7.1 Equilibrium Equations7.2 Equilibrium in the Gravitational Field; 7.3 Force and Moment that Act on a Body from the Surrounding Fluid; 7.4 Equilibrium of a Fluid Relative to a Moving System of Coordinates; 8 Stationary Continuum Movement of an Ideal Fluid; 8.1 Bernoulli's Integral; 8.2 Examples of the Application of Bernoulli's Integral; 8.3 Dynamic and Hydrostatic Pressure; 8.4 Flow of an Incompressible Fluid in a Tube of Varying Cross Section; 8.5 The Phenomenon of Cavitation; 8.6 Bernoulli's Integral for Adiabatic Flows of an Ideal Gas 327 $a8.7 Bernoulli's Integral for the Flow of a Compressible Gas 330 $aWritten by an experienced author with a strong background in applications of this field, this monograph provides a comprehensive and detailed account of the theory behind hydromechanics. He includes numerous appendices with mathematical tools, backed by extensive illustrations. The result is a must-have for all those needing to apply the methods in their research, be it in industry or academia. 606 $aFluid mechanics 615 0$aFluid mechanics. 676 $a532 700 $aSinai?skii?$b E?. G$g(E?mmanuil Genrikhovich)$0866154 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911019935803321 996 $aHydromechanics$94458982 997 $aUNINA