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Book
ISBN: 9783642012877 9783642012860 Year: 2010 Publisher: Heidelberg ; New York : Springer,
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As long as algebra and geometry proceeded along separate paths, their advance was slow and their applications limited. But when these sciences joined company they drew from each other fresh vitality and thenceforward marched on at rapid pace towards perfection Joseph L. Lagrange The theory of differential equations is one of the largest elds within mathematics and probably most graduates in mathematics have attended at least one course on differentialequations. But differentialequationsare also offundamentalimportance in most applied sciences; whenever a continuous process is modelled mathem- ically, chances are high that differential equations appear. So it does not surprise that many textbooks exist on both ordinary and partial differential equations. But the huge majority of these books makes an implicit assumption on the structure of the equations: either one deals with scalar equations or with normal systems, i. e. with systems in Cauchy-Kovalevskaya form. The main topic of this book is what happens, if this popular assumption is dropped. This is not just an academic exercise; non-normal systems are ubiquitous in - plications. Classical examples include the incompressible Navier-Stokes equations of uid dynamics, Maxwell's equations of electrodynamics, the Yang-Mills eq- tions of the fundamental gauge theories in modern particle physics or Einstein's equations of general relativity. But also the simulation and control of multibody systems, electrical circuits or chemical reactions lead to non-normal systems of - dinary differential equations, often called differential algebraic equations. In fact, most of the differentialequationsnowadaysencounteredby engineersand scientists are probably not normal.
Book
ISBN: 9780898716962 0898716969 Year: 2010 Publisher: Philadelphia : Society for Industrial and Applied Mathematics,
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ISBN: 9780821848043 0821848046 Year: 2010 Volume: 528 Publisher: Providence, R.I. : American Mathematical Society,
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Differential equations, Elliptic --- Symmetry (Mathematics) --- Equations différentielles elliptiques --- Symétrie (Mathématiques) --- Congresses. --- Congrès --- Equations différentielles elliptiques --- Symétrie (Mathématiques) --- Congrès --- Differential equations, Elliptic - Congresses --- Symmetry (Mathematics) - Congresses
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ISBN: 9780821847268 Year: 2010 Publisher: Providence American Mathematical Society
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Differential equations --- Differential equations, Elliptic. --- Radiative transfer --- Initial value problems --- Heat --- Earthquake prediction --- Equations différentielles elliptiques --- Transfert radiatif --- Problèmes aux valeurs initiales --- Chaleur --- Tremblements de terre --- Mathematical models --- Transmission --- Mathematical models. --- Modèles mathématiques --- Prévision --- 51 <082.1> --- Mathematics--Series --- Radiative transfer. --- Initial value problems. --- Equations différentielles elliptiques --- Problèmes aux valeurs initiales --- Modèles mathématiques --- Prévision --- Numerical solutions. --- Differential equations, Elliptic --- Transfer, Radiative --- Astrophysics --- Geophysics --- Radiation --- Transport theory --- Problems, Initial value --- Boundary value problems --- Electromagnetic waves --- Physics --- Cold --- Combustion --- Fire --- Temperature --- Thermochemistry --- Thermodynamics --- Earthquakes --- Prediction, Earthquake --- Geophysical prediction --- Elliptic differential equations --- Elliptic partial differential equations --- Linear elliptic differential equations --- Differential equations, Linear --- Differential equations, Partial --- Transmission&delete& --- Radiation and absorption --- Forecasting --- Prediction
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