درک تحلیل واقعی

Front Cover; Copyright ; Table of Contents; Preface; Chapter 1; Chapter 2; Chapter 3; Chapter 4; Chapter 5; Solutions. Preface 1 Preliminaries: Numbers, Sets, Proofs, and BoundsNumbers 101: The Very BasicsSets 101: Getting StartedSets 102: The Idea of a FunctionProofs 101: Proofs and Proof-WritingTypes of ProofSets 103: Finite and Infinite Sets; CardinalityNumbers 102: Absolute ValuesBoundsNumbers 103: Completeness2 Sequences and Series SequencesandConvergenceWorkingwithSequencesSubsequencesCauchySequencesSeries 101: Basic IdeasSeries 102: Testing for Convergence and Estimating LimitsLimsupandliminf:AGuidedDiscovery3 Limits and Continuity LimitsofFunctionsContinuous FunctionsWhyContinuityMatters:ValueTheoremsU. Read more... Abstract: Front Cover; Copyright ; Table of Contents; Preface; Chapter 1; Chapter 2; Chapter 3; Chapter 4; Chapter 5; Solutions. Preface 1 Preliminaries: Numbers, Sets, Proofs, and BoundsNumbers 101: The Very BasicsSets 101: Getting StartedSets 102: The Idea of a FunctionProofs 101: Proofs and Proof-WritingTypes of ProofSets 103: Finite and Infinite Sets; CardinalityNumbers 102: Absolute ValuesBoundsNumbers 103: Completeness2 Sequences and Series SequencesandConvergenceWorkingwithSequencesSubsequencesCauchySequencesSeries 101: Basic IdeasSeries 102: Testing for Convergence and Estimating LimitsLimsupandliminf:AGuidedDiscovery3 Limits and Continuity LimitsofFunctionsContinuous FunctionsWhyContinuityMatters:ValueTheoremsU "This book is a one-semester text for an introduction to real analysis. The author's primary aims are to develop ideas already familiar from elementary calculus in a rigorous manner and to help students deeply understand some basic but crucial mathematical ideas, and to see how definitions, proofs, examples, and other forms of mathematical "apparatus" work together to create a unified theory. A key feature of the book is that it includes substantial treatment of some foundational material, including general theory of functions, sets, cardinality, and basic proof techniques." -- Publisher