Calculus (Volume 1)

Name: Calculus (Volume 1)
ISBN: 9787568934718

赵坤银Chongqing University Press · ChinaJun 2024

3.2

Word count: 114K words
Chapters: 47
ISBN: 9787568934718

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Summary

Calculus is a core general-education course offered to students across disciplines in colleges and universities. It provides the foundation for further mathematics courses and serves as a widely used mathematical tool in the natural and social sciences. Grounded in the talent-development needs of applied private universities, this book aims for moderate depth and a well-structured presentation, making it suitable for students in economics and management as well as readers from other fields who wish to study the subject.

Editor's review

Calculus (Volume 1), written by Professor Zhao Kunyin, is a classic mathematics textbook published by Chongqing University Press; the current edition is the first edition of September 2021. As an introductory textbook for higher mathematics, its greatest strength lies in the organic combination of rigorous mathematical logic with clear teaching practice. From an editor's professional perspective, the book's value lies not only in the complete presentation of the knowledge system but also in its step-by-step narrative approach—starting from the core concepts of functions and limits and gradually moving deeper into derivatives, differentials, the mean value theorem and its applications, and then to indefinite and definite integrals, thereby building a solid cognitive framework of calculus for readers. The selection of worked examples and exercises is thoughtful, including both conventional problems to consolidate basic concepts and stimulating extension problems, helping readers understand the underlying mathematical ideas while mastering computational skills. Compared with similar textbooks, this book stands out in readability: the language is plain, and the derivations of key theorems and formulas are explained in detail, reducing cognitive obstacles for beginners. Particularly noteworthy is the explanation of fundamental calculus ideas, such as 'approximating curves with straight lines' and 'limiting processes,' which are accompanied by intuitive geometric or physical background descriptions, making abstract mathematical concepts vivid and tangible. Overall, this is an excellent textbook with a clear structure, solid content, and a clear teaching orientation, especially suitable as the first calculus course book or self-study reference for non-mathematics undergraduates.

Who it's for

A good fit for

First-year non-mathematics majors currently taking higher mathematics or calculus courses
Upper-level science and engineering students or graduate entrance exam candidates who need a systematic review of calculus fundamentals
Mathematics enthusiasts who wish to study calculus on their own and build a rigorous conceptual framework
Professionals in engineering, economics, management, and related fields who need to strengthen their mathematical foundation

Not a good fit for

Mathematics graduate students seeking advanced theoretical discussion or cutting-edge research topics
Test-oriented readers who only need quick access to formulas or problem-solving techniques and do not intend to understand the concepts in depth

Reading tips

Read the chapters in sequence, and focus on understanding each chapter's core concepts (such as the ε-δ definition of limits, the geometric meaning of derivatives, and the relationship between integrals and area) before doing extensive practice
For key theorems (such as the mean value theorem and the Newton–Leibniz formula), not only memorize the conclusions but also try to understand the ideas behind their proofs and their practical applications
Practice with the worked examples and end-of-chapter exercises: first complete the basic problems independently, then challenge more comprehensive problems to test how well you have integrated the knowledge

About the publisher

Chongqing University Press China · Founded in 1985

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.

版权信息
前言
第1章函数
1.1 函数的基本概念
1.2 具有某些特性的函数
1.3 初等函数
第2章极限与连续
2.1 数列的极限
2.2 函数的极限
2.3 无穷小量、无穷大量、阶的比较
2.4 两个重要极限
2.5 极限在经济中的应用
2.6 函数的连续性
第3章导数与微分
3.1 导数的概念
3.2 导数的运算
3.3 高阶导数
3.4 微分
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 未定式的极限
4.3 函数的单调性与极值
4.4 简单的数学建模
4.5 曲线的凹凸性与拐点
4.6 导数在经济中的应用
4.7 函数图形的描绘
第5章一元函数积分
5.1 原函数与不定积分
5.2 定积分的概念
5.3 定积分的性质
5.4 微积分基本定理
第6章积分方法
6.1 不定积分的第一类换元积分法
6.2 不定积分的第二类换元积分法
6.3 不定积分的分部积分法
6.4 定积分的换元积分法与分部积分法
6.5 有理函数的积分
第7章积分的应用与广义积分
7.1 微元分析法的基本思想
7.2 定积分在几何中的应用
7.3 定积分在经济中的应用
7.4 广义积分与Γ函数
附录
附录1 微积分常用公式
附录2 初等数学部分公式
附录3 习题参考答案
参考文献

FAQ

What are the features of this book compared with the Tongji University edition of Higher Mathematics?

This book places more emphasis on a step-by-step teaching process and accessibility for beginners, and its introduction and presentation of concepts may be plainer and more detailed. The Tongji edition is classic in content and rigorous in system, but relatively more theoretical. Both are excellent textbooks; your choice can depend on your study habits and course requirements.

Is it difficult to self-study this book without a teacher?

As a textbook, this book was written with the possibility of self-study in mind, and its explanations are rather detailed. As long as you have a solid high school mathematics foundation and remain patient, reading step by step and completing the exercises, self-study is feasible. When you encounter difficulties, try to understand them with the help of the book's examples and diagrams.

Are there answer explanations for the exercises in the book?

According to common edition information, this book usually comes with a separate Study Guide or exercise-solution booklet. When reading, it is advisable to complete the exercises independently first and then compare with the answers and reflect on them; this will better improve your problem-solving ability and depth of mastery.

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About the author

赵坤银 Author

Zhao Kunyin is an author about whom little public information is currently available; the only known work is Calculus (Volume 1), classified in the library under education. This work suggests that the author's writing is connected with the teaching of basic higher mathematics and is likely intended for university students or those beginning to study calculus. Textbook writing of this kind generally emphasizes a step-by-step presentation of concepts and a clear connection between worked examples, highlighting the logical links among definitions, theorems and computational methods so that readers can build a basic understanding of limits, derivatives and integrals within a limited space. Because the library holds only one work by this author and no information on nationality, dates of birth and death, education or positions can be confirmed, this introduction makes no speculation about personal experience. On the available evidence, Zhao Kunyin's name is associated with a calculus textbook, and the contribution lies mainly in organizing and presenting foundational mathematical material for teaching, which may serve learners in related courses.