Math 212 — Multivariable Calculus (Fall 2025)
Duke University
Overview
- Class Meetings
- Days & Time: TuTh 8:30AM-9:45AM; Room: Physics 259
- Instructor
- Shuchen Zhu (shuchen.zhu@duke.edu)
- Office Hours
- After class (or by appointment)
- Graders
- Ben Mei-Dan (ben.mei-dan@duke.edu) and Kevin Zheng (kevin.zheng@duke.edu)
- Help Room Hours
- Link
- Textbook
-
- Multivariable Calculus 6th edition by Edwards and Penney
- Description
- Partial differentiation, multiple integrals, and topics in differential and integral vector calculus, including Green's theorem, the divergence theorem, and Stokes's theorem.
- Grading
-
- Weekly Homework: 40%
- Midterm I: 15% (Sep 30 class time)
- Midterm II: 15% (Nov 11 class time)
- Final Exam: 30% (Dec 15 9:00AM - 12:00PM at Foreign Languages 211). Please Note the final is NOT in the usual classroom!
Schedule
| Week | Date | Topic | Reading | Homework |
|---|---|---|---|---|
| 1 | Aug 26, Aug 28 | Vectors, dot product, determinant | 12.1, 12.2, 12.3 | HW1 Due Sep 4: p777/1, 7, 13, 17, 23, 31, 35, 40, 52, 55; p786/5, 18, 23 ,25, 31, 33, 39, 42, 43, 47, 53, 62, 67-70; p845/1 |
| 2 | Sep 2, Sep 4 | Cross product, lines and planes, curves, surfaces | 12.3, 12.4, 12.5, 12.7 | HW2 Due Sep 11: p794/3, 5, 7, 11, 15, 17, 19, 21, 23, 29, 30, 36; p845/5; p801/3, 7, 13, 14, 15, 17, 25, 27, 29, 30, 32, 33, 37, 40, 51, 53, 56, 57, 59; p813/2, 4, 11, 21, 31, 33, 45, 46, 49, 54, 55, 56, 64; p845/16 |
| 3 | Sep 9, Sep 11 | Multivariable functions, limit and continuity, partial derivatives | 12.7, 13.2, 13.3, 13.4 | HW3 Due Sep 18: p837/1, 3, 7, 9, 13, 15, 21, 25, 29, 30, 43, 51; p857/7, 11, 15, 25, 27, 29, 34, 37, 39, 41, 43, 53-58; p875/3, 7, 13, 19, 22, 35, 41, 43, 53, 55, 57(a,c), 58(a,c), 60, 71; p896/43 |
| 4 | Sep 16, Sep 18 | Increment and differentials, chain rule, directional derivative | 13.6, 13.7, 13.8 | HW4 Due Sep 25: p895/5, 7, 17, 18, 26, 34, 42; p904/3, 7, 9, 19, 28, 37, 40, 43, 45, 51; p915/6, 8, 14, 19, 26, 28, 30, 33, 34, 36, 40, 48, 50, 51, 56, 57 |
| 5 | Sep 23, Sep 25 | Double integrals, midterm I review | 14.1, 14.2 | No homework, midterm I will be on Sep 30. [Sample 1], [Sample 1 solution], [Sample 2], [Sample 2 solution]. |
| 6 | Sep 30, Oct 2 | Double integrals, general regions, area and volume | 14.3 | HW5 Due Oct 9: p945/3, 15, 17, 32, 34, 40; p953/1, 12, 18, 22, 23, 30, 31, 41, 42; p959/3, 7, 18, 22, 24, 28, 30, 37. [Midterm I stats]. |
| 7 | Oct 7, Oct 9 | Applications, triple integrals | 14.5, 14.6 | HW6 Due Oct 16: p975/8, 15, 42, 44, 46; p985/2, 6, 8, 10, 12, 14, 22, 28, 33 |
| 8 | Oct 16 | Change of variables, polar coordinates | 14.9, 10.2 | HW7 Due Oct 23: p1007/1, 3, 4, 6, 7, 8, 10, 12, 14, 17; p635/1(a,b,c), 2(d), 6, 11, 24, 25, 39, 41, 42, 53, 56 |
| 9 | Oct 21, Oct 23 | Spherical coordinates, integrals in polar coordinate, integrals in spherical coordinate | 12.8, 14.4, 14.7 | HW8 Due Oct 30: p843/1, 9, 15, 17, 23, 26, 27, 29, 30, 31, 33, 39, 55; p966/2, 5, 10, 12, 14, 23, 28, 29, 34, 38; p959/33, 34, 42; p993/1, 3, 4, 5, 15, 20, 22, 26, 30, 38 |
| 10 | Oct 28, Oct 30 | Surface integral, vector fields, line integrals | 14.8, 15.1, 15.2 | HW9 Due Nov 6: p1000/2, 3, 7, 13, 15, 17, 18; p1010/49; p1018/1, 6, 9, 11, 12, 20, 21, 28, 32, 35, 36, 37, 38, 39, 40. p1028/2-5, 6, 10, 11, 12, 14, 16, 21, 22, 36; p1072/9. Midterm II date announced. |
| 11 | Nov 4, Nov 6 | midterm II review | Midterm II will be on Nov 11. [Sample 1], [Sample 1 solution], [Sample 2], [Sample 2 solution]. |
![[Midterm I stats]](midterm_1.png){kind=link}
Course Policies
Academic Integrity
Academic honesty is taken very seriously, in line with Duke University's Honor System. For problem sets, you may discuss ideas with others or use outside resources, but you must write your own solutions as if you were taking an exam. For each problem, list all collaborators and all references or online tools you used (including ChatGPT or other AIs). Do not submit work you do not understand. I may ask you to explain any part of your submission; if you cannot show understanding, you will receive no credit and may be reported to the Honor Council.
Grading
Course grades will be determined by participation, problem sets, and exams. There will be weekly homeworks and they are due at the beginning of class. Late work will not be accepted. It is important that you understand and agree with the grades you receive on assignments and exams. If a score is unclear, please contact me to discuss how it was determined. To protect your privacy, these discussions will take place during office hours or by appointment.
Given the pace of the course, it is essential that you review the material on your own soon after we cover it in class, using both your notes and the textbook. Begin problem sets as soon as they are posted. You may need multiple sessions to complete them, so do not wait until the last minute.