微积分

Preface xi

To the Student

Diagnostic Tests xxiv

A PREVIEW OF CALCULUS

1 Functions and Models

1．1 Four Ways to Represent a Function

1．2 Mathematical Models：A Catalog of Essential Functions

1．3 New Functions from Old Functions

1．4 Graphing Calculators and Computers

1．5 Exponential Functions

1．6 Inverse Functions and Logarithms

Principles of Problem Solving

2 Limits and Derivatives

2．1 The Tangent and Velocity Problems

2．2 The Limit of a Function

2．3 Calculating Limits Using the Limit Laws

2．4 The Precise Definition of a Limit

2．5 Continuity

2．6 Limits at Infinity；Horizontal Asymptotes

2．7 Derivatives and Rates of Change Writing Project Early Methods for Finding Tangents

2．8 The Derivative as a Function

Review

Problems PlUS

3 Differentiation Rules

4 Aookucatuibs if Dufferebtuatuib

5 Integrals

6 Applications of Integration

7 Techniques of Integration

8 Further Applications of Integration

9 Differential Equations

10 Parametric Equations and Polar Coordinates

11 Infinite Sequences and Series

12 Vectors and the Geometry of Space

13 Vector Functions

14 Partial Derivatives

15 Multiple Integrals

16 Vector Calculus

17 Second-Order Differential Equations

Appendixes

Index

《海外优秀数学类教材系列丛书：微积分（下册 第7版 影印版）》从Cengag eLearning出版公司引进中国，原版书在北美大学中被广泛采用，畅销多年。影印版保留了原版书的全部内容，将其原原本本地呈献给国内教师和学生。该书详细介绍了微积分的概念、理论和方法，语言朴实、流畅、通俗易懂，书中的例题、习题贴近生活实际，能充分调动学生学习的兴趣。《海外优秀数学类教材系列丛书：微积分（下册 第7版 影印版）》分上、下两册，上册内容包括：函数和模型、极限和变化率、微分法则、微分的应用、积分、积分的应用、积分法、积分的进一步应用、微分方程、参数方程和极坐标。下册内容包括：无穷序列和级数、向量和解析几何、向量函数、偏导数、多重积分、向量微积分、二阶微分方程。本书可作为高等学校非数学类专业微积分、高等数学课程双语教学的教材，也可供广大师生教学参考之用。