微积分(第1卷)

  • 作者:张彪,张雅卓
  • 责编:张永芹
  • ISBN:978-7-5603-5516-0
  • 出版日期:2015-9-1
  • 所属丛书:
  • 定价:48.00
  • 开本:16
  • 页数:350
  • 图书分类:Q.数学类
  • 中图分类:O数理科学和化学
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【内容提要】

本书为《微积分》一书的第一卷,适用于工科院校非数学专业本科新生,亦可作为工程技术人员的参考书籍。本卷包含七个章节,内容涵盖函数、极限与连续、微分及其应用、定积分、不定积分及其应用以及微分方程。本书包含大量例题及习题。

【目  录】

Chapter 1 Function//1

1.1 Concepts of Functions//1

1.2 Some Important Properties of Functions//7

1.3 Implicit Functions and Inverse Functions//9

1.4 Basic Elementary Functions//11

1.5 Composite Functions and Elementary Functions//14

1.6 Polar Coordinate System//15

1.7 Examples//17

Exercises 1//21

Chapter 2 Limits and Continuity//27

2.1 The Limit of a sequence//27

2.2 Properties and Operation of Convergent Sequences//31

2.3 Existence Discriminances of Sequence Limit//35

2.4 The Limit of a Function//38

2.5 Properties of Function Limits//44

2.6 Infinitesimal and Infinity//49

2.7 Continuity//56

2.8 Examples//65

Exercises 2//69

Chapter 3 Derivatives//77

3.1 Definition of Derivatives//77

3.2 Differentiation Rules//87

3.3 Higher-Order Derivatives//102

3.4 Linearization and Differentials//107

3.5 Examples//113

Exercises3//116

Chapter 4 Applications of Derivatives//127

4.1 The Mean Value Theorem//127

4.2 L' Hospital's Rule//134

4.3 Taylor Formula//140

4.4 Maximum and Minimum Values//146

4.5 Curve Sketching//154

4.6 Examples//160

Exercises 4//164

Chapter 5 The Indefinite Integral//174

5.1 The Antiderivative and the Indefinite Integral//174

5.2 Integration by Substitution//179

5.3 Integration by Parts//184

5.4 The Integration of Several Kinds of Functions//188

5.5 Examples//194

Exercises 5//198

Chapter 6 The Definite Integral and Its Applications//204

6.1 Concepts and Properties//204

6.2 The Fundamental Theorem of Calculus//204

6.3 Evaluating the Definite Integral//216

6.4 The Improper Integral//221

6.5 Applications of Definite Integrals Examples//227

6.6 Examples//245

Exercises 6

Chapter 7 Differential Equations//268

7.1 Basic Concepts of Differential Equations//268

7.2 The First-Order Differential Equations//270

7.3 Some Order-Reducible Higher-Order Differential Equations//280

7.4 Linear Differential Equations of Higher Order//286

7.5 The Second-Order Linear Differential Equations with Constant Coefficients//294

Exercise 7//311

Appendix//320

Several Fundamental Theorems//320

Superior and Inferior Limits//326

Calculus in Economics//327