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

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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
Back Matter....Pages 173-392

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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
Back Matter....Pages 173-392
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