Calculus (Volume 1) cover

Calculus (Volume 1)

Rating 3.5
Word count
90K words
Chapters
50
ISBN
9787568922029

Tags

Summary

This textbook, Calculus, was developed in line with our university's educational reform and its positioning as an application-oriented undergraduate institution, as well as the mission of independent colleges to cultivate applied talents, so as to meet the talent-development needs of various majors.

Editor's review

Calculus (Volume 1) is published by Chongqing University Press and authored by Chen Xiangbing. As a foundational university mathematics textbook, it systematically introduces the core concepts and methods of calculus, covering classic topics such as functions, limits, derivatives, differentials, and their applications. From an editorial perspective, the book is logically organized and progresses from the elementary to the advanced, emphasizing both conceptual explanation and worked examples; it is suitable as an introductory textbook or self-study reference for first-year students in science, engineering, or economics and management. Its distinguishing feature is its emphasis on intuitive understanding of mathematical ideas: numerous diagrams and examples help readers build geometric and physical intuition for calculus rather than pursuing purely formal derivations. For beginners, this intuitive, application-oriented style helps lower the learning threshold and fosters interest and confidence in mathematics. However, the book is relatively conservative in theoretical depth and coverage of advanced topics, making it better suited to building foundations than to exploring abstract analysis in depth. Overall, it is a solid, practical introductory textbook with clear value in helping students master the basic tools of calculus.

Who it's for

A good fit for

  • First-year students in science, engineering, economics, or management at colleges and universities
  • Self-learners who need a systematic review of foundational calculus knowledge
  • Readers who prefer intuitive explanations and applied examples over purely theoretical derivations
  • Readers who treat calculus as a tool subject and want to quickly master core computational methods

Not a good fit for

  • Advanced undergraduate mathematics majors seeking a rigorous theoretical framework and proof details in mathematical analysis
  • Advanced researchers who wish to learn about modern developments or cutting-edge applications of calculus

Reading tips

  1. Read the chapters in order, focusing on the intuitive meaning of core concepts such as limits and derivatives
  2. Practice with the worked examples and exercises in the book, emphasizing proficiency in computation and application
  3. Use geometry or mathematical software alongside the book to visualize the relationship between functions and derivatives

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.

Contents

  1. 版权信息
  2. 内容提要
  3. 前言
  4. 第1章 函数、极限与连续
  5. 1.1 函数的概念
  6. 1.2 初等函数
  7. 1.3 数列的极限
  8. 1.4 函数的极限
  9. 1.5 无穷小与无穷大
  10. 1.6 极限的运算法则
  11. 1.7 极限存在准则 两个重要极限
  12. 1.8 无穷小的比较
  13. 1.9 函数的连续性与间断点
  14. 1.10 连续函数的运算与性质
  15. 总习题 1
  16. 第2章 导数与微分
  17. 2.1 导数的概念
  18. 2.2 函数的求导法则
  19. 2.3 高阶导数
  20. 2.4隐函数和参数方程的求导法则
  21. 2.5 函数的微分
  22. 总习题 2
  23. 第3章 微分中值定理及其应用
  24. 3.1 微分中值定理
  25. 3.2 洛必达法则
  26. 3.3 泰勒公式
  27. 3.4 函数的单调性与凹凸性
  28. 3.5 函数的极值与最值
  29. 3.6 函数图像的描绘
  30. 总习题 3
  31. 第4章 不定积分
  32. 4.1 不定积分的概念与运算法则
  33. 4.2 换元积分法
  34. 4.3 分部积分法
  35. 4.4有理函数的不定积分
  36. 总习题 4
  37. 第5章 定积分及其应用
  38. 5.1 定积分的概念和性质
  39. 5.2 微积分基本公式
  40. 5.3 定积分的计算
  41. 5.4 广义积分
  42. 5.5 定积分的应用
  43. 总习题 5
  44. 第6章 微分方程
  45. 6.1 微分方程的基本概念
  46. 6.2 一阶微分方程
  47. 6.3 几种可降阶的二阶微分方程
  48. 6.4 二阶常系数线性微分方程
  49. 总习题 6
  50. 参考文献

FAQ

Is this book suitable for students with a weak high school mathematics foundation?
As a university textbook, it assumes readers have foundational knowledge such as high school functions. If your foundation is weak, it is advisable to review the relevant preparatory material first; nevertheless, the book's intuitive explanations of core concepts can still aid understanding.
Does the book include answers to the exercises?
As a textbook, the exercises are generally intended for practice and consolidation; answers may require a companion study guide or the instructor's edition, so it is best to confirm the details for the specific edition.
What are the main features of this book compared with other calculus textbooks?
The book emphasizes explaining concepts through geometric intuition and applied examples; its style is plain and practical, making it suitable for introductory study focused on foundations and applications.

Comments

Find this book

This site is an index: you start “Search all sources” in your browser, and the entries it lists all point to third-party sites; please judge their availability yourself.

About the author

陈相兵 Author

Chen Xiangbing: publicly available information about this author is limited, and the name appears as a credited author on published books. The library holds one work under this name, Calculus (Volume One), commonly classified under examination preparation. Based on this署名 and the work itself, Chen Xiangbing is associated with the compilation of foundational higher mathematics material aimed at study and exam review. Calculus (Volume One) is a typical form of introductory university mathematics textbook, usually covering basic topics such as functions, limits, derivatives, and differentials, and serving course study and examination review. Because verifiable information on biography, positions, and academic background is lacking, this profile makes no speculation about personal experience; it states only the author identity related to calculus textbook compilation based on library facts and advises readers to rely on official publication information, with further details to be added if reliable sources become available.

王妍 Author

Wang Yan: publicly available information is limited, and her full educational background, affiliation, and research focus cannot be confirmed at present. According to the library holdings, she is associated with the book Calculus (Volume 1), which is classified under exam preparation, indicating that its content is oriented toward exam review or course study and serves readers who need to systematically organize basic calculus knowledge. As an important introductory course in higher mathematics, calculus is known for its abstract concepts and high computational demands, and textbook writing often requires balancing rigorous definitions with accessible explanations. This work suggests that the author has invested effort in organizing and presenting fundamental mathematical content, with attention to structured knowledge points and learners' practical needs. Because verifiable personal information is scarce, no speculation is made about her academic experience, teaching background, or writing philosophy; this note records only her connection to exam-oriented mathematics materials based on the available work information, for readers' reference.

何兴 Author

He Xing is an author about whom public information is currently limited; details such as his nationality, dates of birth and death, educational background, and professional positions have not been clearly recorded and remain to be verified. Judging from the three works held in the collection, his writing is mainly oriented toward university teaching and the growth and education of college students. These include Calculus (Volume One), a basic textbook for science and engineering courses, as well as practice-oriented books such as College Students' Self-Management Education and Practice and College Students' Labor Education, which focus on students' daily management and the cultivation of labor literacy. His works span two directions—exam preparation and educational practice—and are plain in language and practical in focus, centering on classroom teaching and the development of students' abilities. They are suitable for reference reading by university teachers, students, and educators.

李玲 Author

Li Ling's publicly available information is limited, yet her writing and editorial work cover a notably broad range. The library holds thirteen of her titles, spanning biography, examination preparation, social culture, medicine, history, and finance. In biography, she has written the three-volume collection Meilanfang Fei as well as the standalone volume Meilanfang Fei: Mei Lanfang in Japan, both centering on the Peking opera master Mei Lanfang's experiences abroad; she is also the author of One Who Refuses to Be a Slave: A Biography of Nie Er, a life of the musician Nie Er. Her practical and instructional works include a cake decorating tutorial, Calculus (Volume One), an experimental guide for materials science, and a pre-service training manual for caregivers. She has also contributed to lighthearted popular history such as Ancient People Knew Better How to Have Fun. Judging from these titles, she handles both historical research and textbooks or popular writing with a practical style aimed at different readerships.

More by the same author

Top rated in the same category