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A Primer on PDEs [electronic resource] :Models, Methods, Simulations / by Sandro Salsa, Federico M. G. Vegni, Anna Zaretti, Paolo Zunino.

by Salsa, Sandro [author.]; Vegni, Federico M. G [author.]; Zaretti, Anna [author.]; Zunino, Paolo [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: UNITEXT: Publisher: Milano : Springer Milan : 2013.Description: XIV, 489 p. online resource.ISBN: 9788847028623.Subject(s): Mathematics | Global analysis (Mathematics) | Differential equations, partial | Mathematics | Mathematics, general | Partial Differential Equations | AnalysisDDC classification: 510 Online resources: Click here to access online
Contents:
Introduction -- Scalar Conservation Laws -- Diffusion -- The Laplace Equation -- Reaction-diffusion models -- Waves and vibrations -- Elements of Functional Analysis -- Variational formulation of elliptic problems -- Weak formulation of evolution problems -- Solutions -- Fourier Series -- Notes on ordinary differential equations -- Finite difference approximation of time dependent problems -- Identities and Formulas.
In: Springer eBooksSummary: This book is designed as an advanced undergraduate or a first-year graduate course for students from various disciplines like applied mathematics, physics, engineering. It has evolved while teaching courses on partial differential equations during the last decade at the Politecnico of Milan. The main purpose of these courses was twofold: on the one hand, to train the students to appreciate the interplay between theory and modelling in problems arising in the applied sciences and on the other hand to give them a solid background for numerical methods, such as finite differences and finite elements.
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Introduction -- Scalar Conservation Laws -- Diffusion -- The Laplace Equation -- Reaction-diffusion models -- Waves and vibrations -- Elements of Functional Analysis -- Variational formulation of elliptic problems -- Weak formulation of evolution problems -- Solutions -- Fourier Series -- Notes on ordinary differential equations -- Finite difference approximation of time dependent problems -- Identities and Formulas.

This book is designed as an advanced undergraduate or a first-year graduate course for students from various disciplines like applied mathematics, physics, engineering. It has evolved while teaching courses on partial differential equations during the last decade at the Politecnico of Milan. The main purpose of these courses was twofold: on the one hand, to train the students to appreciate the interplay between theory and modelling in problems arising in the applied sciences and on the other hand to give them a solid background for numerical methods, such as finite differences and finite elements.

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