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Stochastic processes --- Partial differential equations --- Stochastic partial differential equations --- Differential equations, Nonlinear --- Convergence --- Numerical solutions --- Congresses. --- Probabilities --- Congresses --- Differential equations [Nonlinear ] --- Differential equations [Partial ] --- Stochastic partial differential equations - Numerical solutions - Congresses. --- Differential equations, Nonlinear - Numerical solutions - Congresses. --- Convergence - Congresses.

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Financial Mathematics is an exciting, emerging field of application. The five sets of course notes in this book provide a bird's eye view of the current "state of the art" and directions of research. For graduate students it will therefore serve as an introduction to the field while reseachers will find it a compact source of reference. The reader is expected to have a good knowledge of the basic mathematical tools corresponding to an introductory graduate level, and sufficient familiarity with probabilistic methods, in particular stochastic analysis. B. Biais, J.C. Rochet: Risk-sharing, adverse selection and market structure.- T. Björk: Interest-rate theory.- J. Cvitanic: Optimal trading under constraints.- N. El Karoui, M.C. Quenez: Nonlinear pricing theory and backward stochastic differential equations.- E. Jouini: Market imperfections, equilibrium and arbitrage.

Stochastic processes --- Quantitative methods (economics) --- Business mathematics. --- Business mathematics --- Mathematical Theory --- Mathematics --- Physical Sciences & Mathematics --- Bedrijfswiskunde --- Mathématiques financières --- Probabilities. --- Public finance. --- Economics, Mathematical . --- Partial differential equations. --- Functional analysis. --- Probability Theory and Stochastic Processes. --- Public Economics. --- Business Mathematics. --- Quantitative Finance. --- Partial Differential Equations. --- Functional Analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Partial differential equations --- Economics --- Mathematical economics --- Econometrics --- Arithmetic, Commercial --- Business --- Business arithmetic --- Business math --- Commercial arithmetic --- Finance --- Cameralistics --- Public finance --- Public finances --- Currency question --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Methodology

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This volume contains the texts of the four series of lectures presented by B.Cockburn, C.Johnson, C.W. Shu and E.Tadmor at a C.I.M.E. Summer School. It is aimed at providing a comprehensive and up-to-date presentation of numerical methods which are nowadays used to solve nonlinear partial differential equations of hyperbolic type, developing shock discontinuities. The most effective methodologies in the framework of finite elements, finite differences, finite volumes spectral methods and kinetic methods, are addressed, in particular high-order shock capturing techniques, discontinuous Galerkin methods, adaptive techniques based upon a-posteriori error analysis.

Differential equations, Hyperbolic --- Differential equations, Nonlinear --- Numerical solutions --- Congresses --- Differential equations [Hyperbolic] --- Differential equations [Nonlinear ] --- Partial differential equations. --- Numerical analysis. --- Thermodynamics. --- Computational intelligence. --- Partial Differential Equations. --- Numerical Analysis. --- Computational Intelligence. --- Chemistry, Physical and theoretical --- Dynamics --- Mechanics --- Physics --- Heat --- Heat-engines --- Quantum theory --- Mathematical analysis --- Partial differential equations --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Differential equations, Hyperbolic - Numerical solutions - Congresses --- Differential equations, Nonlinear - Numerical solutions - Congresses

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Algebraic geometry --- Algebraïsche meetkunde --- Geometry [Algebraic ] --- Géométrie algébrique --- Meetkunde [Algebraïsche ] --- Geometry, Algebraic. --- 514.76 --- 51 --- Geometry, Algebraic --- 512.7 --- Geometry --- Geometry of differentiable manifolds and of their submanifolds --- Mathematics --- Algebraic geometry. Commutative rings and algebras --- 512.7 Algebraic geometry. Commutative rings and algebras --- 51 Mathematics --- 514.76 Geometry of differentiable manifolds and of their submanifolds

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This book is devoted to the presentation of some flow problems in porous media having relevant industrial applications. The main topics covered are: the manufacturing of composite materials, the espresso coffee brewing process, the filtration of liquids through diapers, various questions about flow problems in oil reservoirs and the theory of homogenization. The aim is to show that filtration problems arising in very practical industrial context exhibit interesting and highly nontrivial mathematical aspects. Thus the style of the book is mathematically rigorous, but specifically oriented towards applications, so that it is intended for both applied mathematicians and researchers in various areas of technological interest. The reader is required to have a good knowledge of the classical theory of PDE and basic functional analysis.

Filters and filtration --- Fluid dynamics --- Porous materials --- Industrial applications --- Mathematical models --- Mathematical Theory --- Applied Mathematics --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Congresses --- Condensed matter. --- Partial differential equations. --- Thermodynamics. --- Mechanics. --- Applied mathematics. --- Engineering mathematics. --- Condensed Matter Physics. --- Partial Differential Equations. --- Classical Mechanics. --- Applications of Mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Chemistry, Physical and theoretical --- Mechanics --- Heat --- Heat-engines --- Partial differential equations --- Condensed materials --- Condensed media --- Condensed phase --- Materials, Condensed --- Media, Condensed --- Phase, Condensed --- Liquids --- Matter --- Solids --- Fluid dynamics - Congresses. --- Filters and filtration - Mathematical models - Congresses. --- Filters and filtration - Industrial applications - Congresses. --- Porous materials - Congresses.