Sandro Salsa, Federico Vegni, Anna Zaretti, Paolo Zunino

A Primer on PDEs (eBook, PDF)

Models, Methods, Simulations

• Format: PDF

Produktbeschreibung

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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Produktdetails

• Verlag: Springer Milan
• Seitenzahl: 489
• Erscheinungstermin: 13. Mai 2013
• Englisch
• ISBN-13: 9788847028623
• Artikelnr.: 43797386

Autorenporträt

Sandro Salsa is a Emeritus Professor of Mathematical Analysis at Politecnico of Milan, where he has been one of the main founders of the educational program in Mathematical Engineering. His research interest ranges over diverse aspects of nonlinear, nonlocal, singular or degenerate elliptic and parabolic equations, with particular emphasis on boundary behavior, regularity and free boundary problems. He is an author of 14 books and several papers in the most prestigious scientific mathematical journals. Gianmaria Verzini is a Professor of Mathematical Analysis at the Department of Mathematics of the Politecnico of Milan. He is author of 5 books and more than 50 papers, published on prominent international journals. His scientific interests concern the applications of Nonlinear Analysis to the existence, multiplicity, qualitative properties and regularity of solutions to nonlinear differential equations and systems.

Inhaltsangabe

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.

Rezensionen

From the reviews:

"Part I (Chapters 2-6) of this book ... is entitled Differential models. ... Part II (Chapters 7-9) is entitled Functional analysis techniques for differential problems and it is devoted to Hilbert space methods for the variational formulation and the analysis of linear boundary and initial-boundary value problems. ... at the end of each chapter the authors include a brief account of numerical methods, with a discussion of some particular case study. ... recommend this book to students in engineering, applied mathematics and physics." -- Vicen?iu D. R?dulescu, zbMATH, Vol. 1270, 2013

From the book reviews:

"This book, presented at the advanced undergraduate or first year graduate level, takes a very interesting mixed approach to partial differential equations, shining a modern light on a classic subject. In addition to the usual analytic solution methods, the presentation includes both numerical approaches and mathematical techniques for proving rigorous existence and regularity results. ... Each chapter concludes with an informative set of exercises, and solutions to many of them are provided at the end of the book." (Peter Bernard Weichman, Mathematical Reviews, May, 2014)

"The present text is suitable for a two semester introduction to partial differential equations. ... The text is well-written and can be particularly recommended for students who are interested in the interplay between modeling, theory, and numerics." (G. Teschl, Monatshefte für Mathematik, 2013)
"Part I (Chapters 2-6) of this book ... is entitled Differential models.... Part II (Chapters 7-9) is entitled Functional analysis techniques for differential problems and it is devoted to Hilbert space methods for the variational formulation and the analysis of linear boundary and initial-boundary value problems. ... at the end of each chapter the authors include a brief account of numerical methods, with a discussion of some particular case study. ... recommend this book to students in engineering, applied mathematics and physics." (Vicentiu D. Radulescu, zbMATH, Vol. 1270, 2013)