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计算机科学急救指南v2026.0.0

微积分

学习材料

Section titled “学习材料”

教科书

Section titled “教科书”
  1. [1]
    R. A. Adams and C. Essex, Calculus: A Complete Course, 10th ed. Toronto, ON: Pearson, 2021. Accessed: Apr. 02, 2026. [Online]. Available: https://www.pearson.com/en-ca/subject-catalog/p/calculus-a-complete-course/P200000002479/9780135766781
  2. [2]
    龚昇, 简明微积分, 4th ed. in 普通高等教育“十五”国家级规划教材. 北京市: 高等教育出版社, 2006. Accessed: Apr. 03, 2026. [Online]. Available: https://www.hep.com.cn/book/show/4fbfa3b9-aa86-41c2-be72-84ac7d0b87b2

说明

Section titled “说明”

未被选择的书目

Section titled “未被选择的书目”
  1. [3]
    J. Stewart, S. Watson, and D. K. Clegg, Stewart Calculus, 9th ed. Boston, MA: Cengage Learning, 2020. Accessed: Apr. 03, 2026. [Online]. Available: https://www.cengage.com/c/calculus-9e-stewart-clegg-watson/9781337624183/
  2. [4]
    J. Stewart, S. Watson, and D. K. Clegg, Stewart Calculus: Early Transcendentals, 9th ed. Boston, MA: Cengage Learning, 2020. Accessed: Apr. 03, 2026. [Online]. Available: https://www.cengage.com/c/calculus-early-transcendentals-9e-stewart-clegg-watson/9781337613927/
  3. [5]
    A. D. Banner, The Calculus Lifesaver: All the Tools You Need to Excel at Calculus, 1st ed. Princeton, NJ: Princeton University Press, 2009. Accessed: Apr. 03, 2026. [Online]. Available: https://press.princeton.edu/books/ebook/9781400835782/the-calculus-lifesaver-pdf?srsltid=AfmBOops83rJhcGuw-fa0Bu44xMu49g0lGUuYIANhrxpdDl-qjG2pwW-

说明

Section titled “说明”
  • 本项目推荐的基础必修课《微积分》的难度基准是：不低于同济大学数学系主编《高等数学》[6][7]。
  • Stewart 微积分[3][4]、Princeton 微积分读本[5]的难度低于同济高数。
  • 再次强调：本项目总体的难度基准为荣誉ECE/EECS项目。

其它参考

Section titled “其它参考”
  1. [6]
    同济大学数学科学学院, 高等数学, 8th ed., vol. 1, 2 vols. 北京市: 高等教育出版社, 2023. Accessed: Apr. 03, 2026. [Online]. Available: https://www.hep.com.cn/book/show/9bbb9470-3576-4736-8bf7-018b8b5fb298
  2. [7]
    同济大学数学科学学院, 高等数学, 8th ed., vol. 2, 2 vols. 北京市: 高等教育出版社, 2023. Accessed: Apr. 03, 2026. [Online]. Available: https://www.hep.com.cn/book/show/3c03343f-fa8a-4fbc-94aa-15ff4e23b964
  3. [8]
    T. M. Apostol, CALCULUS, 2nd ed., vol. 1, 2 vols. US: John Wiley & Sons, Inc., 1967. Accessed: Apr. 03, 2026. [Online]. Available: https://www.wiley.com/en-us/Calculus%2C+Volume+1%2C+2nd+Edition-p-9781119496731
  4. [9]
    T. M. Apostol, CALCULUS, 2nd ed., vol. 2, 2 vols. US: John Wiley & Sons, Inc., 1969. Accessed: Apr. 03, 2026. [Online]. Available: https://www.wiley.com/en-us/Calculus%2C+Volume+2%2C+2nd+Edition-p-9781119496762
  5. [10]
    J. R. Hass, C. E. Heil, M. D. Weir, and P. Bogacki, Thomas Calculus, 15th ed. US: Pearson, 2022. Accessed: Apr. 03, 2026. [Online]. Available: https://www.pearson.com/en-us/subject-catalog/p/thomas-calculus/P200000007103/9780137616077?format=eTextbook_lifetime
  6. [11]
    J. R. Hass, C. E. Heil, M. D. Weir, and P. Bogacki, Thomas Calculus: Early Transcendentals, 15th ed. US: Pearson, 2022. Accessed: Apr. 03, 2026. [Online]. Available: https://www.pearson.com/en-us/subject-catalog/p/thomas-calculus-early-transcendentals/P200000007104/9780137559824?format=eTextbook_lifetime
  7. [12]
    W. G. Strang, Calculus, 3rd ed. Wellesley, MA: WELLESLEY-CAMBRIDGE PRESS, 2017. Accessed: Apr. 03, 2026. [Online]. Available: https://ocw.mit.edu/courses/res-18-001-calculus-fall-2023/pages/about/
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说明

Section titled “说明”
  • 个人认为，同济高数[6][7]大问题基本没有，但总体缺乏出彩的地方，只能说中规中矩，可以凑合用。
  • 注意到有观点称 Thomas 微积分[10][11]的难度总体低于同济高数，但差别不大。
  • T. M. Apostol 著《微积分》两卷[8][9]主要面向数学系；内容相对较旧（1960 年代出版）；线性代数部分可以跳过。

院校开课情况选讲

Section titled “院校开课情况选讲”

一般而言，《微积分》开设 2 个学期（semester）/学段（period），主要内容分别是单变量微积分与多变量微积分。部分院校可能会拆成 3 个学期/学段，矢量微积分等内容常安排在第 3 学期/学段。