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| 为了把系统完全以数学形式表现出来，牛顿发明了微商的概念，并且提出了微分方程形式的运动定律——也许这是个人的最伟大的沉思。 ——爱因斯坦于麦克斯韦诞辰100周年纪念 |
| Patrick M.Fitzpatrick，拥有拉特格大学博士学位，是纽约大学科朗研究院和芝加歌大学的博士后，1975年进入马里兰大学的College Park分校任教，现在是数学系教授和系主任，同时他还是巴黎大学和佛罗伦萨大学的客座教授。他的研究方向是非线性泛函分析。 |
| Preface Preliminaries 1 TOOLS FOR ANALYSIS 2 CONVERGENT SEQUENCES 3 CONTINUOUS FUNCTIONS 4 DIFFERENTIATION 5 ELEMENTARY FUNCTIONS AS SOLUTIONS OF DIFFERENTIAL EQUATIONS 6 INTEGRATION:TWO FUNDAMENTAL THEOREMS 7 INTEGRATION:fURTHER TOPICS 8 APPROXIMATION BY TAYLOR POLYNOMIALS 9 SEQUENCES AND SERIES OF FUNCTIONS 10 THE EUCLIDEAN SPACE 11 CONTINUITY,COMPACTNESS,AND CONNECTEDESS 12 METRIC SPACES 13 DIFFERENTIATING FUNCTIONS OF SEVERAL VARIABLES 14 LOCAL APPROXIMATION OF REAL-VALUED FUNCTIONS 15 APPROXIMATING NONLINEAR MAPPINGS BY LINEAR MAPPINGS 16 IMAGES AND INVERSES:THE INVERSE FUNCTION THEOREM 17 THE IMPLICIT FUNCTION THEOREM AND ITS APPLICATIONS 18 INTEGRATING FUNTIONS OF SEVERAL VARIABLES 19 ITERATED INTEGRATION AND CHANGES OF VARIABLES 20 LINE AND SURFACE INTEGRALS A CONSEQUENCES OF THE FIELD AND POSITIVITY AXIOMS B LINEAR ALGEBRA Index |
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