Based on a translation of the 6th edition of Gewöhnliche Differentialgleichungen by Wolfgang Walter, this edition includes additional treatments of important subjects not found in the German text as well as material that is seldom found in textbooks, such as new proofs for basic theorems. This unique feature of the book calls for a closer look at contents and methods with an emphasis on subjects outside the mainstream. Exercises, which range from routine to demanding, are dispersed throughout the text and some include an outline of the solution. Applications from mechanics to mathematical biology are included and solutions of selected exercises are found at the end of the book. It is suitable for mathematics, physics, and computer science graduate students to be used as collateral reading and as a reference source for mathematicians. Readers should have a sound knowledge of infinitesimal calculus and be familiar with basic notions from linear algebra; functional analysis is developed in the text when needed.

Inequalities continue to play an essential role in mathematics. The subject is per haps the last field that is comprehended and used by mathematicians working in all the areas of the discipline of mathematics. Since the seminal work Inequalities (1934) of Hardy, Littlewood and P6lya mathematicians have laboured to extend and sharpen the earlier classical inequalities. New inequalities are discovered ev ery year, some for their intrinsic interest whilst others flow from results obtained in various branches of mathematics. So extensive are these developments that a new mathematical periodical devoted exclusively to inequalities will soon appear; this is the Journal of Inequalities and Applications, to be edited by R. P. Agar wal. Nowadays it is difficult to follow all these developments and because of lack of communication between different groups of specialists many results are often rediscovered several times. Surveys of the present state of the art are therefore in dispensable not only to mathematicians but to the scientific community at large. The study of inequalities reflects the many and various aspects of mathemat ics. There is on the one hand the systematic search for the basic principles and the study of inequalities for their own sake. On the other hand the subject is a source of ingenious ideas and methods that give rise to seemingly elementary but nevertheless serious and challenging problems. There are many applications in a wide variety of fields from mathematical physics to biology and economics."

The sixthInternational Conference on General Inequalities was held from Dec. 9 to Dec. 15, 1990, at the Mathematisches Forschungsinstitut Oberwolfach (Black Fa rest, Germany). The organizing committee was composed of W.N. Everitt (Birm ingham), L. Losonczi (Debrecen) and W. Walter (Karlsruhe). Dr. A. Kovacec ( Coimbra) served cheerfully and efficiently as secretary of the meeting. The con ference was attended by 44 participants from 20 countries. Yet again the importance of inequalities in both pure and applied mathematics was made evident from the wide range of interests of the individual participants, and from the wealth of new results announced. New inequalities were presented in the usual spread of the subject areas now expected for these meetings: Classical and functional analysis, existence and boundary value problems for both ordinary and partial differential equations, with special contributions to computer science, quantum holography and error analysis. More strongly than ever, the role played by modern electronic computers was made clear in testing out and prohing into the validity and structure of certain inequalities. Here the computer acts not only for numerical calculations of great complexity, but also in symbolic manipulation of complex finite structures. Prob lems in inequalities which even a few years ago were intractable, now fall to solution or receive direct and positive guidance as a result of computer applications. The interface between finite and infinite structures in mathematics and the versatility of modern computers is weil developed in the subject of general inequalities."

Based on a translation of the 6th edition of Gewoehnliche Differentialgleichungen by Wolfgang Walter, this edition includes additional treatments of important subjects not found in the German text as well as material that is seldom found in textbooks, such as new proofs for basic theorems. This unique feature of the book calls for a closer look at contents and methods with an emphasis on subjects outside the mainstream. Exercises, which range from routine to demanding, are dispersed throughout the text and some include an outline of the solution. Applications from mechanics to mathematical biology are included and solutions of selected exercises are found at the end of the book. It is suitable for mathematics, physics, and computer science graduate students to be used as collateral reading and as a reference source for mathematicians. Readers should have a sound knowledge of infinitesimal calculus and be familiar with basic notions from linear algebra; functional analysis is developed in the text when needed.

Inequalities continue to play an essential role in mathematics. The subject is per haps the last field that is comprehended and used by mathematicians working in all the areas of the discipline of mathematics. Since the seminal work Inequalities (1934) of Hardy, Littlewood and P6lya mathematicians have laboured to extend and sharpen the earlier classical inequalities. New inequalities are discovered ev ery year, some for their intrinsic interest whilst others flow from results obtained in various branches of mathematics. So extensive are these developments that a new mathematical periodical devoted exclusively to inequalities will soon appear; this is the Journal of Inequalities and Applications, to be edited by R. P. Agar wal. Nowadays it is difficult to follow all these developments and because of lack of communication between different groups of specialists many results are often rediscovered several times. Surveys of the present state of the art are therefore in dispensable not only to mathematicians but to the scientific community at large. The study of inequalities reflects the many and various aspects of mathemat ics. There is on the one hand the systematic search for the basic principles and the study of inequalities for their own sake. On the other hand the subject is a source of ingenious ideas and methods that give rise to seemingly elementary but nevertheless serious and challenging problems. There are many applications in a wide variety of fields from mathematical physics to biology and economics."

In 1964 the author's mono graph "Differential- und Integral-Un gleichungen," with the subtitle "und ihre Anwendung bei Abschatzungs und Eindeutigkeitsproblemen" was published. The present volume grew out of the response to the demand for an English translation of this book. In the meantime the literature on differential and integral in equalities increased greatly. We have tried to incorporate new results as far as possible. As a matter of fact, the Bibliography has been almost doubled in size. The most substantial additions are in the field of existence theory. In Chapter I we have included the basic theorems on Volterra integral equations in Banach space (covering the case of ordinary differential equations in Banach space). Corresponding theorems on differential inequalities have been added in Chapter II. This was done with a view to the new sections; dealing with the line method, in the chapter on parabolic differential equations. Section 35 contains an exposition of this method in connection with estimation and convergence. An existence theory for the general nonlinear parabolic equation in one space variable based on the line method is given in Section 36. This theory is considered by the author as one of the most significant recent applications of in equality methods. We should mention that an exposition of Krzyzanski's method for solving the Cauchy problem has also been added. The numerous requests that the new edition include a chapter on elliptic differential equations have been satisfied to some extent."

With reference to existing fruits of research on Christian Wolff (1679-1754) and the methods employed to describe languages for special purposes, the study analyzes the conditions conducive to the emergence of German as a vehicle of scholarly communication in the early 18th century. Wolffs sophisticated ideas on language, his modern and highly influential concept of science and scholarship and the attendant transformation in the style of scholarly thinking in that period are placed in their historical context, tracing the evolution of his mathesis concept to the status of a universal method and its application in scholarly and scientific teaching manuals. In this way it is possible to present a precise appreciation of the specific contribution made by Wolff to the transition from Latin to German as a vehicle of communication in the various branches of scientific and scholarly endeavour. In the process Christian Wolff is clearly delineated as a precursor of the most influental mode of reasoned thought in existence in Germany and an adumbrator of the language of modernity.

Diese Bibliographie bietet einen umfassenden UEberblick uber die Literatur der letzten 100 Jahre zum Thema Klaviermusik (seit etwa 1550) in deutscher, englischer, franzoesischer und italienischer Sprache. Aufgenommen wurden selbstandige Schriften, Zeitschriftenaufsatze, Artikel in Sammelpublikationen, Jahrbuchern, Festschriften und Kongressberichten sowie Dissertationen. Der erste Teil listet die Literatur zu einzelnen Komponisten auf. Umfangreiche Kapitel werden nach Werkgruppen und einzelnen Werken gegliedert. Der zweite Teil verzeichnet die Literatur zur Klaviermusik einzelner Zeitabschnitte, Lander und zu anderen Stichworten.

in die Analysis des Une n d I i chen. Von Leonhard Euler. Erster Teil. Ins Deutsche ubertragen \'Oll H. Maser. Springer-Verlag Berlin Heidelberg GmbH 1885. Vorwort des U ebersetzers. Meisterwerke uben ihren Einfluss auf die Fortbildung der Wissen- schaft nicht allein durch die in ihnen niedergelegten Resultate des forschenden Geil'ites, es lebt in ihnen eine schoepferische Kraft, die, nie er- sterbend, immer neue Keime weckt und fort und fort bis in die spate Ferne hinaus edle Fruchte zeitigt. Derartige Geistesproducte, wenn sie selten werden, in ihrer ganzen Fulle ohne Unterlass von Neuern weiteren Kreisen zuganglich zu machen, halte ich fiir kein nutzloses Beginnen. Eben dem Zwecke soll auch die Herausgabe der vorliegenden, ganzlich nenen Uebersetzung des ersten Teils von Eu I er' s ", lntt-oductio in Analysin infinitoJ-um" dienen. Diese: durch den Reichtum seine: Inhalts, durch die Feinheit der Methoden und durch die ausserordentliche Klarheit und Pracision der Darstellung ausgezeichnete, in arithmetischer Weise aufgebaute -werk, welches weite Perspectiven eroeffnet, ist h!ltlt- zutage, trotzdem oder vielleicht gerade weil fast alle neueren Lehr- biicher aus ihm als aus einer nie versiegenden Quelle schoepfen, schon halb in Vergcst;enheit geraten, und dies ist um so mehr zu bedauern, als sich dem Anscheine nach die Erkenntnis geltend macht, dass eine scharfere Bestimmung der Begriffe auch eine weitere Entwicklung der Analysi: mit E uler' sehen Reminiscenzen auf rein arithmetischer Grundlage ermoeglichen durfte.

Aus den Besprechungen: "Wodurch unterscheidet sich das hiermit begonnene Lehrwerk der Analysis von zahlreichen anderen ... exzellenten Werken dieser Art? ... (1) die ausfuhrliche Berucksichtigung des Warum und Woher, der historischen Gesichtspunkte ...; (2) die Anerkennung der Existenz des Computers. Der Autor verschliesst sich nicht vor der Tatsache, dass die Computermathematik (hier vor allem verstanden als numerische Mathematik) oft interessante Anwendungen der klassischen Analysis bietet. ... (3) die grosse Fulle von Beispielen und nicht-trivialen (aber losbaren) Ubungsaufgaben, sowie (4) der haufige Bezug zu den Anwendungen. ... Sogar die Theorie der gewohnlichen Differentialgleichungen, vor der manche Lehrbuchautoren eine unuberwindliche Scheu zu haben scheinen, ist gut lesbar dargestellt, mit vernunftigen Anwendungen. ... kann das Buch jedem Studierenden der Mathematik wegen der Fulle des Gebotenen und wegen des geschickten didaktischen Aufbaus auf das Warmste empfohlen werden."
ZAMP "

Hauptthema dieses zweiten Bandes ist die Differential- und Integralrechnung fur Funktionen von mehreren Veranderlichen. Dabei wird auch das Lebesguesche Integral im Rn behandelt. Dem erfolgreichen Konzept von "Analysis 1" folgend, wird viel Wert auf historische Zusammenhange, Ausblicke und die Entwicklung der Analysis gelegt. Zu den Besonderheiten, die uber den kanonischen Stoff des zweiten Semesters hinausgehen, gehoeren das Morsesche und das Sardsche Lemma, die C?-Approximation von Funktionen (Mollifiers) und die Theorie der absolutstetigen Funktionen. Zahlreiche Beispiele, UEbungsaufgaben und Anwendungen, z.B. aus der Physik und Astronomie, runden dieses Lehrbuch ab. Der Abschnitt "Loesungen und Loesungshinweise" wurde fur die Neuauflage wesentlich erweitert, so dass die uberwiegende Zahl der Aufgaben im Buch nun besprochen oder vollstandig geloest wird.

In der nunmehr 7., neu bearbeiteten und erweiterten Auflage legt W. Walter sein Lehrbuch uber Gewoehnliche Differentialgleichungen vor, das schon so etwas wie ein "moderner Klassiker" geworden ist. Das Buch entspricht dem aktuellen Forschungsstand. Es behandelt neben der klassischen Theorie vor allem solche Themen, die fur das Studium dynamischer Systeme und des qualitativen Verhaltens gewoehnlicher Differentialgleichungen unentbehrlich sind. Ein Anhang stellt zentrale Begriffe aus Analysis und Topologie bereit. Dieses Lehrbuch bietet dem Studenten eine optimale Einfuhrung in das Gebiet der Differentialgleichungen, die sich durch UEbersichtlichkeit im Aufbau und Klarheit in der Beweisfuhrung auszeichnet. Viele instruktive Beispiele mit Loesungen zu ausgewahlten Aufgaben runden dieses Werk ab.

Das Hauptthema dieses zweiten Bandes ist die Differential- und Integralrechnung f}r Funktionen von mehreren Ver{nderlichen. Dabei wird auchdas Lebesguesche Integral im Rn behandelt. Dem erfolgreichen Konzept von Analysis I folgend, wird viel Wert auf historische Zusammenh{nge, Ausblicke und die Entwicklung der Analysis gelegt. Zu denBesonderheiten, die }ber den kanonischen Stoff des zweiten Semesters hinausgehen, geh-ren das Morsesche und das Sardsche Lemma, die C (unendlich)-Approximation von Funktionen (Mollifiers) und die Theorie der absolutstetigen Funktionen. Die Grundtatsachen }ber die verschiedenen Integralbegriffe werden allesamt aus S{tzen }ber den Netzlimes abgeleitet. Bei den Fourierreihen wird die klassische Theorie in Weiterf}hrung einer von Chernoff und Redheffer entwickelten Methode behandelt. Zahlreiche Beispiele, ]bungsaufgaben und Anwendungen, z.B. aus der Physik und Astronomie, runden dieses Lehrbuch ab.

This bibliography offers a comprehensive survey of publications on the theme