Calculus (2nd Edition)
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Summary
The book covers functions, limits and continuity, derivatives and differentials, the mean value theorem and applications of derivatives, indefinite integrals, definite integrals, calculus of functions of several variables, infinite series, and elementary differential and difference equations, as well as applications of MATLAB in calculus. Each chapter is followed by a selection of exercises, with answers provided via QR codes placed after the exercises in each chapter; an appendix and commonly used elementary mathematics formulas are included at the end of the book.
This book is intended as a textbook or teaching reference for economics and management majors in higher education institutions; different majors may select material according to their own characteristics and needs. The second edition adds QR codes linking to digital resources that accompany the textbook content, along with new material on applications of MATLAB in calculus and some commonly used calling commands.
Editor's review
The book's defining features are its "application orientation" and its principle of "sufficiency rather than excess." It systematically introduces core content such as functions, limits, derivatives, differentials, integrals, and their applications, but omits some overly theoretical proofs and replaces them with numerous examples set in economic and engineering contexts. For example, when explaining applications of derivatives, it introduces economic concepts such as marginal analysis and elasticity analysis; in the section on integrals, it focuses on how to calculate areas and volumes and solve simple differential equations. This arrangement lowers the learning threshold and helps students quickly connect calculus with practical problems and understand its power as an analytical tool.
In terms of quality, the logical structure is clear, the chapters progress step by step, and each chapter includes a summary and exercises of moderate difficulty, suitable for both classroom teaching and self-study. The language is kept plain and avoids obscurity. Of course, for mathematics majors seeking mathematical rigor and theoretical depth, the book may not go far enough. But as the title suggests, its positioning is clear: it serves the teaching of "calculus" for non-mathematics majors, with the goal of mastering basic ideas and methods and applying them initially in related fields.
Overall, this is a highly complete introductory textbook. For beginners who need to learn calculus but are intimidated by its abstraction, or for readers who need to refresh their basic knowledge of calculus at work, this book offers a friendly and effective entry point. It is like a patient guide, intended to help you cross the threshold and see the most practical and central scenery in the world of calculus.
Who it's for
A good fit for
- Students in engineering, economics, and management majors at application-oriented undergraduate institutions who are currently taking a calculus course
- Students at vocational colleges who need to master basic higher mathematics
- Non-mathematics professionals who need to review or apply basic calculus concepts at work
- Introductory self-learners who want to understand the core ideas of calculus from an applied perspective
Not a good fit for
- Students in mathematics, physics, and other majors with very high requirements for theoretical rigor (as a main textbook)
- Advanced learners seeking cutting-edge calculus theory or in-depth mathematical analysis
Reading tips
- It is recommended to study the chapters in order, focusing on the introduction of concepts and practical application cases in each chapter
- Completing the exercises after each section is key to consolidating understanding; there is no need to rush
- Consider how the economic or engineering cases in the book may relate to your own field, in light of your professional background
About the publisher
Chongqing University Press is a comprehensive university press whose publishing areas span social and cultural studies, industrial technology, finance and economics, medicine, social psychology, and theory. Judging from its catalog, the press publishes both academic works and popular science titles. Representative books include E. H. Gombrich's Shadows: The Depiction of Cast Shadows in Western Art, Magnesium-Based Hydrogen Storage Materials by Pan Fusheng et al., Research on China's Regional Spatial Development Models by Sun Jiuwen, and titles from the Gynecologic Oncology Committee of the Chinese Anti-Cancer Association, such as the Guidelines for Diagnosis and Treatment of Common Gynecologic Malignancies in China (2019) and Bipolar Disorder: What You and Your Family Need to Know. Its authors work in art history, materials science, regional economics, clinical medicine, and social research methods. Public information is limited, but its publishing profile combines academic translation, industrial technology, and practical medical guides.
Contents
- 版权信息
- 内容提要
- 第1版前言
- 第2版前言
- 第1章 函数
- 1.1 集合
- 1.2 实数
- 1.3 函数
- 1.4 反函数与复合函数
- 1.5 基本初等函数与初等函数
- 1.6 经济学中几个常见函数
- 习题1
- 第2章 极限与连续
- 2.1 数列
- 2.2 函数的极限
- 2.2 函数的极限
- 2.3 无穷小与无穷大
- 2.4 极限运算法则
- 2.5 极限存在性定理与两个重要极限
- 2.6 函数的连续性
- 习题2
- 第3章 导数与微分
- 3.1 导数的概念
- 3.2 求导法则
- 3.3 高阶导数
- 3.4 函数的微分
- 习题3
- 第4章 微分中值定理与导数的应用
- 4.1 微分中值定理
- 4.2 洛必达法则
- 4.3 函数的单调性、极值与最值
- 4.4 曲线的凸性与拐点
- 4.5 函数作图
- 4.6 导数在经济学中的应用
- 习题4
- 第5章 不定积分
- 5.1 不定积分的概念与性质
- 5.2 换元积分法
- 5.3 分部积分法
- 5.4 有理函数的积分
- 习题5
- 第6章 定积分
- 6.1 定积分的概念
- 6.2 定积分的性质
- 6.3 微积分基本公式
- 6.4 定积分的换元积分法与分部积分法
- 6.5 反常积分
- 6.6 定积分的几何应用
- 习题6
- 第7章 多元函数微积分
- 7.1 空间解析几何基础知识简介
- 7.2 多元函数的概念
- 7.3 偏导数与全微分
- 7.4 多元复合函数与隐函数微分法
- 7.5 多元函数的极值与最值
- 7.6 二重积分
- 习题7
- 第8章 无穷级数
- 8.1 常数项级数的概念与性质
- 8.2 正项级数的敛散性
- 8.3 任意项级数的敛散性
- 8.4 幂级数
- 8.5 泰勒公式与幂级数展开
- 习题8
- 第9章 微分方程与差分方程初步
- 9.1 微分方程的基本概念
- 9.2 可分离变量的方程
- 9.3 齐次方程
- 9.4 一阶线性微分方程
- 9.5 线性微分方程解的基本性质和结构定理
- 9.6 二阶常系数线性微分方程
- 9.7 差分方程初步
- 习题9
- 第10章 Matlab在微积分中的应用
- 10.1 Matlab简介
- 10.2 Matlab在微积分中的应用
- 附录 初等数学 常用公式
- 参考文献
FAQ
Does this book include calculus of functions of several variables?
Is this book suitable for reviewing for the postgraduate entrance examination in mathematics?
Can I understand it through self-study without a teacher?
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About the author
Ai Yihong is an author about whom limited public information is available. The library holds only one work under this name, Calculus (2nd Edition). Judging from the title and its common classification under "examinations," the book is likely aimed at learners preparing for calculus-related exams and belongs to the category of supplementary materials or textbooks for a foundational mathematics course. Calculus is abstract and formula-heavy, placing high demands on the accurate presentation of concepts and the graded arrangement of worked examples; in preparing a revised edition, an author usually needs to balance the completeness of the knowledge system with the practicality of exam-oriented practice. Because information on the author's life, education, and professional positions is unavailable, it is not possible to determine their academic background or to assess the book's standing in the field. The available clues only indicate that Ai Yihong's name is associated with a calculus exam-preparation book whose approach tends toward helping readers review key points and consolidate computational skills. Readers seeking more information about the author would need to consult original publication details such as the book's preface and copyright page.
