微积分

学习材料

教科书

英文

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

中文

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

• 《Calculus: A Complete Course》[1]为首选，此书为多所院校数学系或数学要求较高的理工类专业采用。
  • Single Variable Calculus (XB_41007) @ VU
  • Multivariable Calculus (XB_41008) @ VU
  • Calculus Variant 2 (2WBB0) @ TU/e
  • Calculus Variant 3 (2WCB0) @ TU/e
• 龚昇《简明微积分》[2]对于基础相对薄弱的同学可能较难。

未选书目

英文

3. [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/
4. [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/
5. [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

• 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

教科书

中文

6. [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
7. [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

英文

8. [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
9. [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
10. [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
11. [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
12. [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/
    免费资源：

    • Calculus Open Textbook
13. [13]
    J. Feldman, A. Rechnitzer, and E. Yeager, CLP-1 Differential Calculus. 2024. Accessed: Oct. 03, 2026. [PDF]. Available: https://personal.math.ubc.ca/~CLP/CLP1/
    免费资源：

    • PDF (CC-BY-NC-SA-4.0)
    • clp_1_dc_problems.pdf (CC-BY-NC-SA-4.0)
    • HTML (CC-BY-NC-SA-4.0)
14. [14]
    J. Feldman, A. Rechnitzer, and E. Yeager, CLP-2 Integral Calculus. 2024. Accessed: Oct. 03, 2026. [PDF]. Available: https://personal.math.ubc.ca/~CLP/CLP2/
    免费资源：

    • PDF (CC-BY-NC-SA-4.0)
    • clp_2_ic_problems.pdf (CC-BY-NC-SA-4.0)
    • HTML (CC-BY-NC-SA-4.0)
15. [15]
    J. Feldman, A. Rechnitzer, and E. Yeager, CLP-3 Multivariable Calculus. 2024. Accessed: Oct. 03, 2026. [PDF]. Available: https://personal.math.ubc.ca/~CLP/CLP3/
    免费资源：

    • PDF (CC-BY-NC-SA-4.0)
    • clp_3_mc_problems.pdf (CC-BY-NC-SA-4.0)
    • HTML (CC-BY-NC-SA-4.0)
16. [16]
    J. Feldman, A. Rechnitzer, and E. Yeager, CLP-4 Vector Calculus. 2024. Accessed: Oct. 03, 2026. [PDF]. Available: https://personal.math.ubc.ca/~CLP/CLP4/
    免费资源：

    • PDF (CC-BY-NC-SA-4.0)
    • clp_4_vc_problems.pdf (CC-BY-NC-SA-4.0)
    • HTML (CC-BY-NC-SA-4.0)
17. [17]
    J. E. Marsden and A. Weinstein, Calculus, 2nd ed., vol. 1, 3 vols. in Undergraduate Texts in Mathematics. New York, NY: Springer-Verlag, 2012. doi: 10.1007/978-1-4612-5024-1.
    免费资源：

    • CaltechAUTHORS
18. [18]
    J. E. Marsden and A. Weinstein, Calculus, 2nd ed., vol. 2, 3 vols. in Undergraduate Texts in Mathematics. New York, NY: Springer-Verlag, 2012. doi: 10.1007/978-1-4612-5026-5.
    免费资源：

    • CaltechAUTHORS
19. [19]
    J. E. Marsden and A. Weinstein, Calculus, 2nd ed., vol. 3, 3 vols. in Undergraduate Texts in Mathematics. New York, NY: Springer-Verlag, 2012. doi: 10.1007/978-1-4612-5028-9.
    免费资源：

    • CaltechAUTHORS
20. [20]
    M. Corral, Elementary Calculus. Michael Corral, 2022. Accessed: Oct. 03, 2026. [PDF]. Available: https://www.mecmath.net/calculus/index.html
    免费资源：

    • PDF (GFDL-1.3-or-later)
21. [21]
    M. Corral, Vector Calculus. Michael Corral, 2022. Accessed: Oct. 03, 2026. [PDF]. Available: https://www.mecmath.net/
    免费资源：

    • PDF (GFDL-1.2-or-later)

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。

视频

英文

22. [22]
    G. Sanderson, Essence of Calculus, (Apr. 28, 2017). Accessed: Oct. 10, 2026. [Online video]. Available: https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr

    主讲：Grant Sanderson

    免费资源：

    • Bilibili
    • 3Blue1Brown

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。