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内容简介
本书是一本引进版权的国外数学英文原版教材，中文书名可译为：《为有天分的新生准备的分析学基础教材》。本书的作者有三位：第一位是彼得.M.吕蒂，美国圣文森特山学院教授；第二位是吉多.L.外斯，圣路易斯华盛顿大学教授；第三位是史蒂芬.S.萧，圣路易斯华盛顿大学教授。
目录
List of Figures
Preface
1 Limits, Continuity, and Compactness
1.1 Number Systems and the Principle of Mathematical Induction
1.2 A Quick Introduction to Cardinal Numbers
1.3 Limits
1.4 Vector Space, Metric Space, Norms, and Inequalities
1.5 Continuous Functions, Open, Closed, and Compact Sets in I~n
2 Differentiation on Rn
2.1 Differentiability on Rn
2.2 Higher Partial Derivatives and Taylor’s Theorem
2.3 Maxima and Minima for Real Valued Functions of Several Variables
2.4 The Implicit Function Theorem
3 One and Several Dimensional Integral Calculus
3.1 Brief Review of Integrals of Real-valued Functions Defined on a Finite Closed Interval in R
3.2 Curves, Arc Length, and Line Integrals
3.3 Higher Dimensional Integrals
3.4 Multiple Integrals and their Reduction to One Dimensional Integrals
3.5 Green’s Theorem
3.6 Integration on Surfaces
Authors’ Biographies
Index
编辑手记
Preface
1 Limits, Continuity, and Compactness
1.1 Number Systems and the Principle of Mathematical Induction
1.2 A Quick Introduction to Cardinal Numbers
1.3 Limits
1.4 Vector Space, Metric Space, Norms, and Inequalities
1.5 Continuous Functions, Open, Closed, and Compact Sets in I~n
2 Differentiation on Rn
2.1 Differentiability on Rn
2.2 Higher Partial Derivatives and Taylor’s Theorem
2.3 Maxima and Minima for Real Valued Functions of Several Variables
2.4 The Implicit Function Theorem
3 One and Several Dimensional Integral Calculus
3.1 Brief Review of Integrals of Real-valued Functions Defined on a Finite Closed Interval in R
3.2 Curves, Arc Length, and Line Integrals
3.3 Higher Dimensional Integrals
3.4 Multiple Integrals and their Reduction to One Dimensional Integrals
3.5 Green’s Theorem
3.6 Integration on Surfaces
Authors’ Biographies
Index
编辑手记