Vorlesungen über partielle Differentialgleichungen

Allgemeine Theorie einer Gleichung erster Ordnung.- Allgemeine Theorie einer Gleichung erster Ordnung (Fortsetzung).- Das Huygenssche Prinzip in der Theorie der Wellenausbreitung.- Die Saite (Methode von d'Alembert).- Die Methode von Fourier (für eine Saite).- Schwingungstheorie. Das Variationsprinzip.- Schwingungstheorie. Das Variationsprinzip (Fortsetzung).- Eigenschaften harmonischer Funktionen.- Fundamentallösungen des Laplaceoperators. Potentiale.- Das Doppelschichtpotential.- Kugelfunktionen. Der Satz von Maxwell. Der Satz über hebbare Singularitäten.- Randwertprobleme für die Laplacegleichung. Die Theorie linearer Gleichungen und Systeme.

lt;p>Aus Rezensionen der englischen Ausgabe:

"... Professor Arnold's Lectures on Partial Differential Equations is an ambitious, intensely personal effort to reconnect the subject with some of its roots in modeling physical processes. He does so in a lively lecture-style format, resulting in a book that would complement almost any course in PDEs. ...

As can be gleaned from the previous paragraph, we bouth found the book by V.I.Arnold most stimulating and thought provoking, leading to statements such as, "It has been years since I enjoyed a book so much" by RBG and "I cannot point to any other book in mathematics written with the same intensity" by EAT. ...

... what follows [...] is a beautiful book on PDEs, interwoven with the exposition of deep physical, geometrical, and topological insights that contribute to both the understanding and history of PDEs.

Prof. Arnold's book ... connects with the roots of the field and brings in concepts from geometry, continuum mechanics, and analysis. It can be used together with any book on PDEs and students will welcome its directness and freshness. We know of no other book like it on the market and highly recommend it for individual reading and as an accompaniment to any course in PDEs. ..."

R.B. Guenther, E.A.Thomann, SIAM Review, Vol. 47, No. 1, 2005

"[...] In brief, this book contains beautifully structured lectures on classical theory of linear partial differential equations of mathematical physics. Professor Arnold stresses the importance of physical intuitions and offers in his lecture a deep geometric insight into these equations. The book is highly recommended to anybody interested in partial differential equations as well as those involved in lecturing on these topics. I encourage readers of this book to take note of the Preface which contains very interesting comments on the role of Bourbaki's group in mathematics, a theme which resurfaces many times in these lectures."

J.Chabrowski, Gazette, Australian Mathematical Society, Vol. 31, Issue 5, 2004

"This book provides an introductory text (in German) to basic partial differential equations, based on the author's lectures at Moscow University [Moscow: Fazis (1997; Zbl 1055.35500)]. Most of the standard themes are treated (see list below), but some unusual topics are covered as well. For instance, in chapter 10 double layer potentials are considered, and chapters 11 and 13 deal (among others) with Maxwell's theorem on the multipole expansion of spherical functions. The style of the book is quite non-technical (it contains almost no estimates), taking a mainly geometric viewpoint. [...]"

Markus Kunze, Zentralblatt für Mathematik 1076.35001

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