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The book serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the emphasis on how to create software for scaled models, based on existing software for unscaled models. Scaling (or nondimensionalization) is a mathematical technique that greatly simplifies the setting of input parameters in numerical simulations. Moreover, scaling enhances the understanding of how different physical processes interact in a differential equation model. Compared to the existing literature, where the topic of scaling is frequently encountered, but very often in only a brief and shallow setting, the present book gives much more thorough explanations of how to reason about finding the right scales. This process is highly problem dependent, and therefore the book features a lot of worked examples, from very simple ODEs to systems of PDEs, especially from fluid mechanics. The text is easily accessible and exampledriven. The first part on ODEs fits even a lower undergraduate level, while the most advanced multiphysics fluid mechanics examples target the graduate level. The scientific literature is full of scaled models, but in most of the cases, the scales are just stated without thorough mathematical reasoning. This book explains how the scales are found mathematically. This book will be a valuable read for anyone doing numerical simulations based on ordinary or partial differential equations.
Mathematics.  Computer simulation.  Differential equations.  Partial differential equations.  Computer mathematics.  Mathematical models.  Ordinary Differential Equations.  Partial Differential Equations.  Mathematical Modeling and Industrial Mathematics.  Computational Science and Engineering.  Simulation and Modeling.  Math  Models, Mathematical  Computer mathematics  Discrete mathematics  Electronic data processing  Partial differential equations  517.91 Differential equations  Differential equations  Computer modeling  Computer models  Modeling, Computer  Models, Computer  Simulation, Computer  Mathematics  Science  Simulation methods  Electromechanical analogies  Mathematical models  Modelintegrated computing  Differential Equations.  Differential equations, partial.  Computer science.  Informatics
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Ordinary differential equations  Partial differential equations  Difference equations  Equations aux différences  Periodicals  Périodiques  Mathématiques  Difference equations.  Mathematical Sciences  Applied Mathematics  Calculus  Differential Geometry  differential equations  applicable analysis  Mathématiques  Calculus of differences  Differences, Calculus of  Equations, Difference  Mathematics
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Differential equations, Partial  Differentiable dynamical systems  Differentiable dynamical systems.  Differential equations, Partial.  Mathematical Sciences  Applied Mathematics  General and Others  Partial differential equations  Differential dynamical systems  Dynamical systems, Differentiable  Dynamics, Differentiable  Differential equations  Global analysis (Mathematics)  Topological dynamics  Calculus
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These Proceedings offer a selection of peerreviewed research and survey papers by some of the foremost international researchers in the fields of finance, energy, stochastics and risk, who present their latest findings on topical problems. The papers cover the areas of stochastic modeling in energy and financial markets; risk management with environmental factors from a stochastic control perspective; and valuation and hedging of derivatives in markets dominated by renewables, all of which further develop the theory of stochastic analysis and mathematical finance. The papers were presented at the first conference on “Stochastics of Environmental and Financial Economics (SEFE)”, being part of the activity in the SEFE research group of the Centre of Advanced Study (CAS) at the Academy of Sciences in Oslo, Norway during the 2014/2015 academic year.
Operations Research  Civil & Environmental Engineering  Engineering & Applied Sciences  Mathematics.  Partial differential equations.  Game theory.  System theory.  Calculus of variations.  Probabilities.  Environmental economics.  Systems Theory, Control.  Probability Theory and Stochastic Processes.  Environmental Economics.  Game Theory, Economics, Social and Behav. Sciences.  Partial Differential Equations.  Calculus of Variations and Optimal Control; Optimization.  Economics  Environmental quality  Probability  Statistical inference  Combinations  Mathematics  Chance  Least squares  Mathematical statistics  Risk  Isoperimetrical problems  Variations, Calculus of  Maxima and minima  Systems, Theory of  Systems science  Science  Games, Theory of  Theory of games  Mathematical models  Partial differential equations  Math  Environmental aspects  Economic aspects  Philosophy  Distribution (Probability theory.  Differential equations, partial.  Mathematical optimization.  Optimization (Mathematics)  Optimization techniques  Optimization theory  Systems optimization  Mathematical analysis  Operations research  Simulation methods  System analysis  Distribution functions  Frequency distribution  Characteristic functions  Probabilities  Systems theory.
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