Ebook: Problems and Theorems in Analysis I: Series. Integral Calculus. Theory of Functions

From the reviews: "The work is one of the real classics of this century; it has had much influence on teaching, on research in several branches of hard analysis, particularly complex function theory, and it has been an essential indispensable source book for those seriously interested in mathematical problems. These volumes contain many extraordinary problems and sequences of problems, mostly from some time past, well worth attention today and tomorrow. Written in the early twenties by two young mathematicians of outstanding talent, taste, breadth, perception, perseverence, and pedagogical skill, this work broke new ground in the teaching of mathematics and how to do mathematical research. (Bulletin of the American Mathematical Society)

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From the reviews: "The work is one of the real classics of this century; it has had much influence on teaching, on research in several branches of hard analysis, particularly complex function theory, and it has been an essential indispensable source book for those seriously interested in mathematical problems. These volumes contain many extraordinary problems and sequences of problems, mostly from some time past, well worth attention today and tomorrow. Written in the early twenties by two young mathematicians of outstanding talent, taste, breadth, perception, perseverence, and pedagogical skill, this work broke new ground in the teaching of mathematics and how to do mathematical research. (Bulletin of the American Mathematical Society)
Content:
Front Matter....Pages I-XIX
Operations with Power Series....Pages 1-15
Linear Transformations of Series. A Theorem of Ces`ro....Pages 15-23
The Structure of Real Sequences and Series....Pages 23-32
Miscellaneous Problems....Pages 32-45
The Integral as the Limit of a Sum of Rectangles....Pages 46-62
Inequalities....Pages 62-75
Some Properties of Real Functions....Pages 75-84
Various Types of Equidistribution....Pages 85-95
Functions of Large Numbers....Pages 95-102
Complex Numbers and Number Sequences....Pages 103-113
Mappings and Vector Fields....Pages 113-124
Some Geometrical Aspects of Complex Variables....Pages 125-132
Cauchy’s Theorem. The Argument Principle....Pages 133-145
Sequences of Analytic Functions....Pages 145-157
The Maximum Principle....Pages 157-172
Infinite Series and Infinite Sequences....Pages 173-229
Integration....Pages 230-296
Functions of One Complex Variable....Pages 297-384
Back Matter....Pages 385-393

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From the reviews: "The work is one of the real classics of this century; it has had much influence on teaching, on research in several branches of hard analysis, particularly complex function theory, and it has been an essential indispensable source book for those seriously interested in mathematical problems. These volumes contain many extraordinary problems and sequences of problems, mostly from some time past, well worth attention today and tomorrow. Written in the early twenties by two young mathematicians of outstanding talent, taste, breadth, perception, perseverence, and pedagogical skill, this work broke new ground in the teaching of mathematics and how to do mathematical research. (Bulletin of the American Mathematical Society)
Content:
Front Matter....Pages I-XIX
Operations with Power Series....Pages 1-15
Linear Transformations of Series. A Theorem of Ces`ro....Pages 15-23
The Structure of Real Sequences and Series....Pages 23-32
Miscellaneous Problems....Pages 32-45
The Integral as the Limit of a Sum of Rectangles....Pages 46-62
Inequalities....Pages 62-75
Some Properties of Real Functions....Pages 75-84
Various Types of Equidistribution....Pages 85-95
Functions of Large Numbers....Pages 95-102
Complex Numbers and Number Sequences....Pages 103-113
Mappings and Vector Fields....Pages 113-124
Some Geometrical Aspects of Complex Variables....Pages 125-132
Cauchy’s Theorem. The Argument Principle....Pages 133-145
Sequences of Analytic Functions....Pages 145-157
The Maximum Principle....Pages 157-172
Infinite Series and Infinite Sequences....Pages 173-229
Integration....Pages 230-296
Functions of One Complex Variable....Pages 297-384
Back Matter....Pages 385-393
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