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A Primer on PDEs

  • Kartonierter Einband
  • 504 Seiten
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This book offers students a solid introduction to numerical methods, such as finite differences and finite elements. Each chapter ... Weiterlesen
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This book offers students a solid introduction to numerical methods, such as finite differences and finite elements. Each chapter ends with a brief introduction to numerical approximation techniques for the specific problem at hand.

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.

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 26) of this book is entitled Differential models. Part II (Chapters 79) 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. (Viceniu D. Rdulescu, zbMATH, Vol. 1270, 2013)

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.


Titel: A Primer on PDEs
Untertitel: Models, Methods, Simulations
EAN: 9788847028616
ISBN: 8847028612
Format: Kartonierter Einband
Anzahl Seiten: 504
Gewicht: 756g
Größe: H235mm x B155mm x T26mm
Jahr: 2013
Auflage: 2013