## Problems and Theorems in Analysis I: Series. Integral Calculus. Theory of FunctionsFrom 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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### Contents

Infinite Series and Infinite Sequences | 1 |

Linear Transformations of Series A Theorem of Cesŕro | 15 |

The Structure of Real Sequences and Series | 23 |

Miscellaneous Problems | 32 |

Integration | 46 |

Inequalities | 62 |

Some Properties of Real Functions | 75 |

Various Types of Equidistribution | 85 |

Functions of Large Numbers | 95 |

Functions of One Complex Variable General Part | 103 |

Mappings and Vector Fields | 113 |

Some Geometrical Aspects of Complex Variables | 125 |

Cauchys Theorem The Argument Principle | 133 |

Sequences of Analytic Functions | 145 |

The Maximum Principle | 157 |

### Other editions - View all

Problems and Theorems in Analysis II: Theory of Functions. Zeros ... George Polya,Gabor Szegö Limited preview - 1997 |

Problems and Theorems in Analysis I: Series. Integral Calculus. Theory of ... George Polya,Gabor Szegö No preview available - 1978 |

Problems and Theorems in Analysis I: Series. Integral Calculus. Theory of ... George Polya,Gabor Szegö No preview available - 1978 |

### Common terms and phrases

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