《微積分（第1卷）》是2015-9-1 出版的圖書，作者是張彪，張雅卓。
基本介紹
- 書名：微積分（第1卷）
- 作者：張彪，張雅卓
- 出版時間：2015-9-1
基本介紹,內容提要,目錄,
基本介紹
作者： 張彪，張雅卓 責編：張永芹
I S B N：978-7-5603-5516-0 定價：48.00
出版日期：2015-9-1 開本：16
所屬叢書： 頁數：350
圖書分類：Q.數學類 中圖分類：O數理科學和化學
內容提要
本書為《微積分》一書的第一卷，適用於工科院校非數學專業本科新生，亦可作為工程技術人員的參考書籍。本卷包含七個章節，內容涵蓋函式、極限與連續、微分及其套用、定積分、不定積分及其套用以及微分方程。本書包含大量例題及習題。
目錄
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
Ⅰ Several Fundamental Theorems//320
Ⅱ Superior and Inferior Limits//326
Ⅲ Calculus in Economics//327
