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Problems and Theorems in Analysis
Series · Integral Calculus · Theory of Functions
Taschenbuch von Georg Polya (u. a.)
Sprache: Englisch

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Beschreibung
The present English edition is not a mere translation of the German original. Many new problems have been added and there are also other changes, mostly minor. Yet all the alterations amount to less than ten percent of the text. We intended to keep intact the general plan and the original flavor of the work. Thus we have not introduced any essentially new subject matter, although the mathematical fashion has greatly changed since 1924. We have restricted ourselves to supplementing the topics originally chosen. Some of our problems first published in this work have given rise to extensive research. To include all such developments would have changed the character of the work, and even an incomplete account, which would be unsatisfactory in itself, would have cost too much labor and taken up too much space. We have to thank many readers who, since the publication of this work almost fifty years ago, communicated to us various remarks on it, some of which have been incorporated into this edition. We have not listed their names; we have forgotten the origin of some contributions, and an incomplete list would have been even less desirable than no list. The first volume has been translated by Mrs. Dorothee Aeppli, the second volume by Professor Claude Billigheimer. We wish to express our warmest thanks to both for the unselfish devotion and scrupulous conscientiousness with which they attacked their far from easy task.
The present English edition is not a mere translation of the German original. Many new problems have been added and there are also other changes, mostly minor. Yet all the alterations amount to less than ten percent of the text. We intended to keep intact the general plan and the original flavor of the work. Thus we have not introduced any essentially new subject matter, although the mathematical fashion has greatly changed since 1924. We have restricted ourselves to supplementing the topics originally chosen. Some of our problems first published in this work have given rise to extensive research. To include all such developments would have changed the character of the work, and even an incomplete account, which would be unsatisfactory in itself, would have cost too much labor and taken up too much space. We have to thank many readers who, since the publication of this work almost fifty years ago, communicated to us various remarks on it, some of which have been incorporated into this edition. We have not listed their names; we have forgotten the origin of some contributions, and an incomplete list would have been even less desirable than no list. The first volume has been translated by Mrs. Dorothee Aeppli, the second volume by Professor Claude Billigheimer. We wish to express our warmest thanks to both for the unselfish devotion and scrupulous conscientiousness with which they attacked their far from easy task.
Inhaltsverzeichnis
One Infinite Series and Infinite Sequences.- 1 Operations with Power Series.- 2 Linear Transformations of Series. A Theorem of Cesàro.- 3 The Structure of Real Sequences and Series.- 4 Miscellaneous Problems.- Two Integration.- 1 The Integral as the Limit of a Sum of Rectangles.- 2 Inequalities.- 3 Some Properties of Real Functions.- 4 Various Types of Equidistribution.- 5 Functions of Large Numbers.- Three Functions of One Complex Variable. General Part.- 1 Complex Numbers and Number Sequences.- 2 Mappings and Vector Fields.- 3 Some Geometrical Aspects of Complex Variables.- 4 Cauchy's Theorem The Argument Principle.- 5 Sequences of Analytic Functions.- 6 The Maximum Principle.- Author Inde.- Subject Inde.
Details
Erscheinungsjahr: 1976
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 416
Reihe: Springer Study Edition
Inhalt: xix
392 S.
1 s/w Illustr.
392 p. 1 illus.
ISBN-13: 9780387902241
ISBN-10: 0387902244
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Polya, Georg
Szegö, Gabor
Übersetzung: Aeppli, Dorothee
Auflage: 1972
Hersteller: Springer New York
Springer US, New York, N.Y.
Springer Study Edition
Maße: 244 x 170 x 23 mm
Von/Mit: Georg Polya (u. a.)
Erscheinungsdatum: 20.12.1976
Gewicht: 0,715 kg
preigu-id: 107102282
Inhaltsverzeichnis
One Infinite Series and Infinite Sequences.- 1 Operations with Power Series.- 2 Linear Transformations of Series. A Theorem of Cesàro.- 3 The Structure of Real Sequences and Series.- 4 Miscellaneous Problems.- Two Integration.- 1 The Integral as the Limit of a Sum of Rectangles.- 2 Inequalities.- 3 Some Properties of Real Functions.- 4 Various Types of Equidistribution.- 5 Functions of Large Numbers.- Three Functions of One Complex Variable. General Part.- 1 Complex Numbers and Number Sequences.- 2 Mappings and Vector Fields.- 3 Some Geometrical Aspects of Complex Variables.- 4 Cauchy's Theorem The Argument Principle.- 5 Sequences of Analytic Functions.- 6 The Maximum Principle.- Author Inde.- Subject Inde.
Details
Erscheinungsjahr: 1976
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 416
Reihe: Springer Study Edition
Inhalt: xix
392 S.
1 s/w Illustr.
392 p. 1 illus.
ISBN-13: 9780387902241
ISBN-10: 0387902244
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Polya, Georg
Szegö, Gabor
Übersetzung: Aeppli, Dorothee
Auflage: 1972
Hersteller: Springer New York
Springer US, New York, N.Y.
Springer Study Edition
Maße: 244 x 170 x 23 mm
Von/Mit: Georg Polya (u. a.)
Erscheinungsdatum: 20.12.1976
Gewicht: 0,715 kg
preigu-id: 107102282
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