| 佐里奇，是莫斯科国立大学教授。主要从事分析、保角几何、拟共形映照方面的研究工作。近期从事热力学中的数学问题的研究。他解决了空间拟共形映照下的球面同胚问题，并因该研究成果获得了“青年数学家国家奖”（National Prize for Young Mathematicians）。同时还拥有一项技术专利。
作为莫斯科国立大学数学力学系高级实验课程的组织者之一，他在一些大学中开设并教授现代分析学课程，并发表了大量的数学研究成果。 |
| 1 Some General Mathematical Concepts and Notation. 1.1 Logical Symbolism 1.2 Sets and Elementary Operations on them 1.3 Functions 1.4 Supplementary Material 2 The Real Numbers 2.1 Axioms and Properties of Real Numbers 2.2 Classes of Real Numbers and Computations 2.3 Basic Lemmas on Completeness 2.4 Countable and Uncountable Sets 3 Limits 3.1 The Limit of a Sequence 3.2 The Limit of a Function 4 Continuous Functions 4.1 Basic Definitions and Examples 4.2 Properties of Continuous Functions 5 Differential Calculus 5.1 Differentiable Functions 5.2 The Basic Rules of Differentiation 5.3 The Basic Theorems of Differential Calculus 5.4 Differential Calculus Used to Study Functions 5.5 Complex Numbers and Elementary Functions 5.6 Examples of Differential Calculus in Natural Science 5.7 Primitives 6 Integration 6.1 Definition of the Integral 6.2 Linearity, Additivity and Monotonicity of the Iuntegral 6.3 The Integral and the Derivative 6.4 Some Applications of Integration 6.5 Improper Integrals 7 Functions of Several Variables 7.1 The Space Rm and its Subests 7.2 Limits and Continuity of Functions of Several Variables 8 Differential Calculus in Several Variables 8.1 The Linear Structure on Rm …… Some Problems from the Midterm Examinations Examination Topics References Subject Index Name Index |
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