Overview

Nach seinem bekannten und viel verwendeten Buch über gewöhnliche Differentialgleichungen widmet sich der berühmte Mathematiker Vladimir Arnold nun den partiellen Differentialgleichungen in einem neuen Lehrbuch. In seiner unnachahmlich eleganten Art führt er über einen geometrischen, anschaulichen Weg in das Thema ein, und ermöglicht den Lesern so ein vertieftes Verständnis der Natur der partiellen Differentialgleichungen. Für Studierende der Mathematik und Physik ist dieses Buch ein Muss. Wie alle Bücher Vladimir Arnolds ist dieses Buch voller geometrischer Erkenntnisse. Arnold illustriert jeden Grundsatz mit einer Abbildung. Das Buch behandelt die elementarsten Teile des Fachgebiets and beschränkt sich hauptsächlich auf das Cauchy-Problem und das Neumann-Problems für die klassischen Lineargleichungen der mathematischen Physik, insbesondere auf die Laplace-Gleichung und die Wellengleichung, wobei die Wärmeleitungsgleichung und die Korteweg-de-Vries-Gleichung aber ebenfalls diskutiert werden. Die physikalische Intuition wird besonders hervorgehoben. Eine große Anzahl von Problemen ist übers ganze Buch verteilt, und ein ganzer Satz von Aufgaben findet sich am Ende. Was dieses Buch so einzigartig macht, ist das besondere Talent Arnolds, ein Thema aus einer neuen, frischen Perspektive zu beleuchten. Er lüftet gerne den Schleier der Verallgemeinerung, der so viele mathematische Texte umgibt, und enthüllt die im wesentlichen einfachen, intuitiven Ideen, die dem Thema zugrunde liegen. Das kann er besser als jeder andere mathematische Autor.

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9783540435785

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Reviews

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

<p>Aus Rezensionen der englischen Ausgabe: <p>.. . 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. ...<p>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. ...<p>... 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. <p>Prof. Arnold's book ... connects with the roots of the field and brings in concepts from geometry, continuum mechanics, and a

Aus Rezensionen der englischen Ausgabe: <p>.,. 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. ... <p>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. ... <p>... 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. <p>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. ... <p>R.B. Guenther, E.A.Thomann, SIAM Review, Vol. 47, No. 1, 2005 <p> [...] 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 asthose 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. <p>J.Chabrowski, Gazette, Australian Mathematical Society, Vol. 31, Issue 5, 2004 <p> 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. [...] <p>Markus Kunze, Zentralblatt fA1/4r Mathematik 1076.35001 <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

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 fur Mathematik 1076.35001 ________________________________________

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