為有天分的新生準備的分析學基礎教材

內容簡介

本書是一本引進著作權的國外數學英文原版教材，中文書名可譯為：《為有天分的新生準備的分析學基礎教材》。本書的作者有三位：*位是彼得.M.呂蒂，美國聖文森特山學院教授；第二位是吉多.L.外斯，聖路易斯華盛頓大學教授；第三位是史蒂芬.S.蕭，聖路易斯華盛頓大學教授。

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

編輯手記

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