| 本书特点： 本书丰富：涵盖数学分析、实变函数、近代数学课程内容。 可读性强：概念阐述从简单到复杂，从具体到一般，通俗易懂。 读者范围广：既有基础内容，又饱含了较深入的研究性问题。 |
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| 总算说明 序 PREFACE TO THE STUDENT 1 The Real Number System 1.1 Sets and Operations on Sets 1.2 Functions 1.3 Mathematical Induction 1.4 The Least Upper Bound Property 1.5 Consequences of the Least upper Boud Property 1.6 binary and Ternary Expansions 1.7 Countable and Uncountable Sets Notes Miscellaneous Exercises Supplemental Reading 2 Sequences of Real Numbers 2.1 convergent Sequences 2.2 Limit Therems 2.3 Monotone Sequences 2.4 Subequences and the Bolzano-Veierstrass Thorem 2.5 Limit Superior and Inferior of a Sequence 2.6 Cauchy Sequences 2.7 Series of Real Numbers Notes Miscellaneous Exercises Supplemental Reading 3 Structure of Point Sets 3.1 Open and Closed Sets 3.2 compact Sets 3.3 The Cantor Set Notes Miscellaneous Exercises Supplemental Reading 4 Limits and Continulty 4.1 Limit of a Function 4.2 Continuous Functions 4.3 Uniform Continuity 4.4 Monotone Functions and discontinuties Notes Miscellaneous Exercises Supplemental Reading 5 Differentiation 6 The Riemann and Riemann-Stieltjes Integral 7 Series of Real Numbers 8 Sequences and Series of Functions 9 Orthogonal Functions and Fourier Series 10 Lebesgue Measure and Integration APPENDIX:Logic and Proofs |
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