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\u7de8\u8f2f\u63a8\u85a6\uff1a<\/strong><\/span><\/p>\n\n

\u672c\u66f8\u662f\u4e16\u5716\u201c\u4fc4\u7f85\u65af\u6578\u5b78\u7d93\u5178\u201d\u66f8\u7cfb\u4e2d\u7684\u4e00\u7a2e\uff0c\u88ab\u6c83\u723e\u592b\u734e\u5f97\u4e3b\u3001\u4fc4\u7f85\u65af\u79d1\u5b78\u9662\u9662\u58eb\u963f\u8afe\u723e\u5fb7\uff08V. I. Arnold\uff09\u8b7d\u70ba\u662f\u73fe\u6709\u6578\u5b78\u5206\u6790\u73fe\u4ee3\u6559\u6750\u7684best\u3002\u8207\u5176\u4ed6\u6578\u5b78\u5206\u6790\u6559\u79d1\u66f8\u76f8\u6bd4\uff0c\u5b83\u66f4\u591a\u5730\u904b\u7528\u4e86\u73fe\u4ee3\u6578\u5b78\uff08\u5305\u62ec\u4ee3\u6578\u5b78\u3001\u5e7e\u4f55\u5b78\u548c\u62d3\u64b2\u5b78\uff09\u7684\u601d\u60f3\u548c\u65b9\u6cd5\uff0c\u800c\u4e14\u4e5f\u66f4\u8cbc\u8fd1\u81ea\u7136\u79d1\u5b78\uff08\u7279\u5225\u662f\u7269\u7406\u5b78\u548c\u529b\u5b78\uff09\u7684\u61c9\u7528\u3002\u672c\u66f8\u88ab\u6e05\u83ef\u5927\u5b78\u6578\u7406\u57fa\u790e\u79d1\u5b78\u73ed\u7cbe\u54c1\u8ab2\u7a0b\u9078\u7528\u70ba\u6388\u8ab2\u6559\u6750\u3002<\/p>\n

 \u5167\u5bb9\u7c21\u4ecb\uff1a<\/span><\/strong><\/p>\n

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\u300a\u5353\u91cc\u5947\u6578\u5b78\u5206\u6790\u6559\u7a0b\u300b\u5171\u5169\u5377\uff0c\u7b2c\uff11\u5377\u5167\u5bb9\u5305\u62ec\uff1a\u96c6\u5408\u3001\u908f\u8f2f\u7b26\u865f\u7684\u904b\u7528\u3001\u5be6\u6578\u7406\u8ad6\u3001\u6975\u9650\u548c\u9023\u7e8c\u6027\u3001\u4e00\u5143\u51fd\u6578\u5fae\u5206\u5b78\u3001\u7a4d\u5206\u3001\u591a\u5143\u51fd\u6578\u53ca\u5176\u6975\u9650\u8207\u9023\u7e8c\u6027\u3001\u591a\u5143\u51fd\u6578\u5fae\u5206\u5b78\u3002<\/p>\n

\u7b2c\uff12\u5377\u5167\u5bb9\u5305\u62ec\uff1a\u9023\u7e8c\u6620\u5c04\u7684\u4e00\u822c\u7406\u8ad6\u3001\u8ce6\u7bc4\u7a7a\u9593\u4e2d\u7684\u5fae\u5206\u5b78\u3001\u91cd\u7a4d\u5206\u3001Rn\u4e2d\u7684\u66f2\u9762\u548c\u5fae\u5206\u5f62\u5f0f\u3001\u66f2\u7dda\u7a4d\u5206\u8207\u66f2\u9762\u7a4d\u5206\u3001\u5411\u91cf\u5206\u6790\u8207\u5834\u8ad6\u3001\u5fae\u5206\u5f62\u5f0f\u5728\u6d41\u5f62\u4e0a\u7684\u7a4d\u5206\u3001\u7d1a\u6578\u548c\u542b\u53c3\u8b8a\u91cf\u7684\u51fd\u6578\u65cf\u7684\u4e00\u81f4\u6536\u6582\u6027\u548c\u57fa\u672c\u904b\u7b97\u3001\u542b\u53c3\u8b8a\u91cf\u7684\u7a4d\u5206\u3001\u5085\u91cc\u8449\u7d1a\u6578\u8207\u5085\u91cc\u8449\u8b8a\u63db\u3001\u6f38\u8fd1\u5c55\u958b\u5f0f\u3002<\/p>\n

\u300a\u5353\u91cc\u5947\u6578\u5b78\u5206\u6790\u6559\u7a0b\u300b\u89c0\u9ede\u8f03\u9ad8\uff0c\u5167\u5bb9\u8c50\u5bcc\u65b0\u7a4e\uff0c\u6240\u9078\u7fd2\u984c\u6975\u5177\u7279\u8272\uff0c\u662f\u6559\u6750\u7406\u8ad6\u90e8\u5206\u7684\u6709\u76ca\u88dc\u5145\u3002\u9019\u5957\u6559\u7a0b\u66f8\u53ef\u4f5c\u70ba\u7d9c\u5408\u6027\u5927\u5b78\u548c\u5e2b\u7bc4\u5927\u5b78\u6578\u5b78\u3001\u7269\u7406\u3001\u529b\u5b78\u53ca\u76f8\u95dc\u5c08\u696d\u7684\u6559\u5e2b\u548c\u5b78\u751f\u7684\u6559\u6750\u6216\u4e3b\u8981\u53c3\u8003\u66f8\uff0c\u4e5f\u53ef\u4f9b\u5de5\u79d1\u5927\u5b78\u61c9\u7528\u6578\u5b78\u5c08\u696d\u7684\u6559\u5e2b\u548c\u5b78\u751f\u53c3\u8003\u4f7f\u7528\u3002<\/p>\n

\u4f5c\u8005\u7c21\u4ecb\uff1a<\/strong><\/p>\n\n

\u5f17\u62c9\u57fa\u7c73\u723e\u00b7\u5353\u91cc\u5947\uff08Vladimir A. Zorich\uff09<\/strong>\u662f\u83ab\u65af\u79d1\u570b\u7acb\u5927\u5b78\u6559\u6388\uff0c\u4e3b\u8981\u5f9e\u4e8b\u5206\u6790\u3001\u4fdd\u89d2\u5e7e\u4f55\u3001\u64ec\u5171\u5f62\u6620\u7167\u65b9\u9762\u7684\u7814\u7a76\u5de5\u4f5c\u3002\u4ed6\u89e3\u6c7a\u4e86\u7a7a\u9593\u64ec\u5171\u5f62\u6620\u7167\u4e0b\u7684\u7403\u9762\u540c\u80da\u554f\u984c\uff0c\u4e26\u56e0\u8a72\u7814\u7a76\u6210\u679c\u7372\u5f97\u4e86\u201c\u9752\u5e74\u6578\u5b78\u5bb6\u570b\u5bb6\u734e\u201d\u3002\u4f5c\u70ba\u83ab\u65af\u79d1\u570b\u7acb\u5927\u5b78\u6578\u5b78\u529b\u5b78\u7cfb\u9ad8\u7d1a\u5be6\u9a57\u8ab2\u7a0b\u7684\u7d44\u7e54\u8005\u4e4b\u4e00\uff0c\u4ed6\u5728\u4e00\u4e9b\u5927\u5b78\u4e2d\u958b\u8a2d\u4e26\u6559\u6388\u73fe\u4ee3\u5206\u6790\u5b78\u8ab2\u7a0b\uff0c\u4e26\u767c\u8868\u4e86\u5927\u91cf\u7684\u6578\u5b78\u7814\u7a76\u6210\u679c\u3002<\/p>\n

\u5a92\u9ad4\u8a55\u8ad6\uff1a<\/strong><\/span><\/p>\n\n

\u5a92\u9ad4\u63a8\u85a6\/\u540d\u4eba\u63a8\u85a6\/\u8b80\u8005\u63a8\u85a6<\/p>\n

\u201c…Complete logical rigor of discussion…is combined with simplicity and completeness as well as with the development of the habit to work with real problems from natural sciences. \u201d<\/p>\n


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<\/strong><\/span><\/p>\n

<\/strong><\/span><\/p>\n

\u57fa\u672c\u4fe1\u606f\uff1a<\/strong><\/span><\/p>\n\n

\u5546\u54c1\u540d\u7a31\uff1a\u5353\u91cc\u5947\u6578\u5b78\u5206\u6790\u6559\u7a0b( \u7b2c1\u5377\u7b2c2\u7248\u82f1\u6587\u7248)(\u7cbe)\/\u4fc4\u7f85\u65af\u6578\u5b78\u7d93\u5178<\/p>\n

\u4f5c\u8005\uff1a(\u4fc4\u7f85\u65af)\u5f17\u62c9\u57fa\u7c73\u723e\u00b7\u5353\u91cc\u5947|\u8cac\u7de8:\u9673\u4eae<\/p>\n

\u958b\u672c\uff1a16\u958b                                   \u9801\u6578\uff1a616<\/p>\n

\u51fa\u7248\u793e\uff1a\u4e16\u5716\u51fa\u7248\u516c\u53f8<\/span>                   ISBN\u865f\uff1a9787519296612<\/span>  <\/p>\n

\u51fa\u7248\u6642\u9593\uff1a2022-10-01   \u7248\u6b21\uff1a1  <\/span>\u5370\u5237\u6642\u9593\uff1a2022-10-01 \u5370\u6b21\uff1a1<\/p>\n

\u5167\u5bb9\u7c21\u4ecb\uff1a<\/strong><\/p>\n\n

\u672c\u66f8\u662f\u4e00\u90e8\u4ecb\u7d39\u6578\u5b78\u5206\u6790\u7684\u6559\u6750\uff0c\u5167\u5bb9\u6d89\u53ca\u5f9e\u5be6\u6578\u5230\u6d41\u5f62\u4e0a\u7684\u5fae\u5206\u5f62\u5f0f\uff0c\u5176\u4e2d\u5305\u62ec\u6f38\u8fd1\u65b9\u6cd5\u3001\u5085\u91cc\u8449\u5206\u6790\u3001\u62c9\u666e\u62c9\u65af\u8b8a\u63db\u3001\u52d2\u8b93\u5fb7\u8b8a\u63db\u3001\u6a62\u5713\u51fd\u6578\u4ee5\u53ca\u983b\u7387\u5206\u4f48\u3002\u672c\u66f8\u8a9e\u8a00\u901a\u4fd7\uff0c\u8868\u9054\u6e05\u6670\uff0c\u5404\u7ae0\u6709\u5927\u91cf\u7684\u7df4\u7fd2\u3001\u601d\u8003\u984c\u4ee5\u53ca \u61c9\u7528\u5be6\u4f8b\uff0c\u6536\u9304\u4e86\u57fa\u672c\u6578\u5b78\u6982\u5ff5\u8207\u7b26\u865f\uff1b\u5be6\u6578\uff1b\u6975\u9650\uff1b\u9023\u7e8c\u51fd\u6578\uff1b\u5fae\u5206\uff1b\u7a4d\u5206\uff1b\u591a\u8b8a\u91cf\u51fd\u6578\uff1b\u591a\u8b8a\u91cf\u4e2d\u7684\u5fae\u5206\uff1b\u671f\u4e2d\u8a66\u984c\uff1b\u8003\u8a66\u63d0\u7db1\u3002<\/p>\n

\u76ee\u3000\u3000\u9304\uff1a<\/strong><\/span><\/p>\n\n

1 Some General Mathematical Concepts and Notation<\/p>\n

1.1 Logical Symbolism<\/p>\n

1.1.1 Connectives and Brackets<\/p>\n

1.1.2 Remarks on Proofs<\/p>\n

1.1.3 Some Special Notation<\/p>\n

1.1.4 Concluding Remarks<\/p>\n

1.1.5 Exercises<\/p>\n

1.2 Sets and Elementary Operations on Them<\/p>\n

1.2.1 The Concept of a Set<\/p>\n

1.2.2 The Inclusion Relation<\/p>\n

1.2.3 Elementary Operations on Sets<\/p>\n

1.2.4 Exercises<\/p>\n

1.3 Functions<\/p>\n

1.3.1 The Concept of a Function \uff08Mapping\uff09<\/p>\n

1.3.2 Elementary Classification of Mappings<\/p>\n

1.3.3 Composition of Functions and Mutually Inverse Mappings<\/p>\n

1.3.4 Functions as Relations. The Graph ofa Function<\/p>\n

1.3.5 Exercises<\/p>\n

1.4 Supplementary Material<\/p>\n

1.4.1 The Cardinality of a Set (Cardinal Numbers\uff09<\/p>\n

1.4.2 Axioms for Set Theory<\/p>\n

1.4.3 Remarks on the Structure of Mathematical Propositions and Their Expression in the Language of Set Theory<\/p>\n

1.4.4 Exercises<\/p>\n

2 The Real Numbers<\/p>\n

2.1 The Axiom System and Some General Properties of the Set of Real Numbers<\/p>\n

2.1.1 Definition of the Set of Real Numbers<\/p>\n

2.1.2 Some General Algebraic Properties of Real Numbers<\/p>\n

2.1.3 The Completeness Axiom and the Existence of a Least Upper (or Greatest Lower\uff09 Bound of a Set of Numbers<\/p>\n

2.2 The Most Important Classes of Real Numbers and Computational Aspects of Operations with Real Numbers<\/p>\n

2.2.1 The Natural Numbers and the Principle of Mathematical Induction<\/p>\n

2.2.2 Rational and Irrational Numbers<\/p>\n

2.2.3 The Principle of Archimedes<\/p>\n

2.2.4 The Geometric Interpretation of the Set of Real Numbers and Computational Aspects of Operations with Real Numbers<\/p>\n

2.2.5 Problems and Exercises<\/p>\n

2.3 Basic Lemmas Connected with the Completeness of the Real Numbers<\/p>\n

2.3.1 The Nested Interval Lemma (Cauchy-Cantor Principle\uff09<\/p>\n

2.3.2 The Finite Covering Lemma (Borel-Lebesgue Principle\uff0c or Heine-Borel Theorem\uff09<\/p>\n

2.3.3 The Limit Point Lemma (Bolzano-Weierstrass Principle\uff09<\/p>\n

2.3.4 Problems and Exercises<\/p>\n

2.4 Countable and Uncountable Sets<\/p>\n

2.4.1 Countable Sets<\/p>\n

2.4.2 The Cardinality of the Continuum<\/p>\n

2.4.3 Problems and Exercises<\/p>\n

3 Limits<\/p>\n

3.1 The Limit of a Sequence<\/p>\n

3.1.1 Definitions and Examples<\/p>\n

3.1.2 Properties of the Limit of a Sequence<\/p>\n

3.1.3 Questions Involving the Existence of the Limit of a Sequence<\/p>\n

3.1.4 Elementary Facts About Series<\/p>\n

3.1.5 Problems and Exercises<\/p>\n

<\/p>\n

<\/span><\/p>\n

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\u57fa\u672c\u4fe1\u606f\uff1a<\/strong><\/span><\/p>\n\n

\u5546\u54c1\u540d\u7a31\uff1a\u5353\u91cc\u5947\u6578\u5b78\u5206\u6790\u6559\u7a0b(\u7b2c2\u5377\u7b2c2\u7248\u82f1\u6587\u7248)(\u7cbe)\/\u4fc4\u7f85\u65af\u6578\u5b78\u7d93\u5178<\/p>\n

\u4f5c\u8005\uff1a(\u4fc4\u7f85\u65af)\u5f17\u62c9\u57fa\u7c73\u723e\u00b7\u5353\u91cc\u5947|\u8cac\u7de8:\u9673\u4eae<\/span><\/p>\n

\u958b\u672c\uff1a16\u958b                                  \u9801\u6578\uff1a720<\/p>\n

\u51fa\u7248\u793e\uff1a\u4e16\u5716\u51fa\u7248\u516c\u53f8<\/span>                   ISBN\u865f\uff1a9787519296629<\/span>  <\/p>\n

\u51fa\u7248\u6642\u9593\uff1a2022-10-01  \u7248\u6b21\uff1a1  <\/span>\u5370\u5237\u6642\u9593\uff1a2022-10-01 \u5370\u6b21\uff1a1<\/p>\n

\u5167\u5bb9\u7c21\u4ecb\uff1a<\/strong><\/p>\n\n

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\u76ee\u3000\u3000\u9304\uff1a<\/strong><\/span><\/p>\n\n

9 *Continuous Mappings (General Theory)<\/p>\n

9.1 Metric Spaces<\/p>\n

9.1.1 Definition and Examples<\/p>\n

9.1.2 Open and Closed Subsets of a Metric Space<\/p>\n

9.1.3 Subspaces of a Metric Space<\/p>\n

9.1.4 The Direct Product of Metric Spaces<\/p>\n

9.1.5 Problems and Exercises<\/p>\n

9.2 Topological Spaces<\/p>\n

9.2.1 Basic Definitions<\/p>\n

9.2.2 Subspaces of a Topological Space<\/p>\n

9.2.3 The Direct Product of Topological Spaces<\/p>\n

9.2.4 Problems and Exercises<\/p>\n

9.3 Compact Sets<\/p>\n

9.3.1 Definition and General Properties of Compact Sets<\/p>\n

9.3.2 Metric Compact Sets<\/p>\n

9.3.3 Problems and Exercises<\/p>\n

9.4 Connected Topological Spaces<\/p>\n

9.4.1 Problems and Exercises<\/p>\n

9.5 Complete Metric Spaces<\/p>\n

9.5.1 Basic Definitions and Examples<\/p>\n

9.5.2 The Completion of a Metric Space<\/p>\n

9.5.3 Problems and Exercises<\/p>\n

9.6 Continuous Mappings of Topological Spaces<\/p>\n

9.6.1 The Limit of a Mapping<\/p>\n

9.6.2 Continuous Mappings<\/p>\n

9.6.3 Problems and Exercises<\/p>\n

9.7 The Contraction Mapping Principle<\/p>\n

9.7.1 Problems and Exercises<\/p>\n

10 *Differential Calculus from a More General Point of View<\/p>\n

10.1 Normed Vector Spaces<\/p>\n

10.1.1 Some Examples of Vector Spaces in Analysis<\/p>\n

10.1.2 Norms in Vector Spaces<\/p>\n

10.1.3 Inner Products in Vector Spaces<\/p>\n

10.1.4 Problems and Exercises<\/p>\n

10.2 Linear and Multilinear Transformations<\/p>\n

10.2.1 Definitions and Examples<\/p>\n

10.2.2 The Norm of a Transformation<\/p>\n

10.2.3 The Space of Continuous Transformations<\/p>\n

10.2.4 Problems and Exercises<\/p>\n

10.3 The Differential of a Mapping<\/p>\n

10.3.1 Mappings Differentiable at a Point<\/p>\n

10.3.2 The General Rules for Differentiation<\/p>\n

10.3.3 Some Examples<\/p>\n

10.3.4 The Partial Derivatives of a Mapping<\/p>\n

10.3.5 Problems and Exercises<\/p>\n

10.4 The Finite-Increment Theorem and Some Examples of Its Use<\/p>\n

10.4.1 The Finite-Increment Theorem<\/p>\n

10.4.2 Some Applications of the Finite-Increment Theorem<\/p>\n

10.4.3 Problems and Exercises<\/p>\n

10.5 Higher-Order Derivatives<\/p>\n","protected":false},"excerpt":{"rendered":"

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