Announcements: Here is the final exam (there has been a correction to #3).
Here is the practice final. The final exam will be given as a ``take home exam". It will be posted here and on gradescope at 8am on Tuesday, March 17th and it will be due at 10pm on Wednesday, March 18th.
Schedule: MWF 9:00-9:50am
Class Location: Center Hall 119
Instructor: David Stapleton
Office Hours: Mondays 10am-12pm
Office: AP&M 6432
TA: Jebin Moses
Sections: 1 and 2
Office Hours: Fridays 9:30am-11:30am
Office: Mayer Hall Addition 5722
TA: Shan Jiang
Sections: 3 and 4
Office Hours: Tuesdays 12pm-2pm
Office: AP&M 2313
TA: Srivatsa Srinivas
Sections: 5 and 6
Office Hours: Tuesdays 4pm-6pm
Office: AP&M 6446
Oasis Workshop Leader: Sophia Alm.
Time: Tuesday and Thursday: 12pm-1:50pm.
To attend: You need to register (and be accepted!) for the Oasis workshop before you attend (this can be done at any point during the quarter). To register go to this site and click the link under "Apply Online".
Calendar (HW links can be clicked!):
|1/6. §5.1, §5.2 The Double Integral.||1/8. §5.3 Integrating over general regions.||1/10. §5.4 Changing the order of integration.
|1/13. §5.5 The triple integral.||1/15. §6.1 The geometry of 2D→2D functions.||1/17. §1.4 Cylindrical and spherical coordinates.
|1/20. MLK day. No class.||1/22. §6.2 Change of variables theorem.||1/24. §6.2 Change of variables theorem.
|1/27. §4.3 Vector fields.||1/29. Midterm 1. Practice Midterm.
Midterm 1 Solutions.
|1/31. §7.1 Path integrals.
|2/3. §7.2 Line integrals.||2/5. §7.3 Parametrized surfaces.||2/7. §7.3 and §7.4.
|2/10. §7.4 Area of a surface.||2/12. §7.5 Integrating functions over surfaces.||2/14. §7.5 and §7.6.
|2/17. Presidents' Day. No class.||2/19. §7.6 Surface integrals of vector fields.||2/21. §8.1 Green's theorem.
|2/24. §8.1 Green's theorem.||2/26. Midterm 2 (solutions).
Practice Midterm (solutions).
|2/28. §4.4, §8.2 Curl and Stokes' theorem.
|3/2. §4.4, §8.2 Curl and Stokes' theorem.||3/4. §4.4, § 8.4. Divergence and Gauss's Theorem.||3/6. §4.4, § 8.4. Divergence and Gauss's Theorem.
|3/9. § 8.3. Conservative vector fields.||3/11. TBD.||3/13. Final Review.
Course Description: Change of variable in multiple integrals, Jacobian, Line integrals, Green's theorem. Vector fields, gradient fields, divergence, curl. Spherical/cylindrical coordinates. Taylor series in several variables. Surface integrals, Stoke's theorem. Conservative fields.
Prerequisites: Math 20C (or Math 21C) or equivalent with a grade of C- or better.
Textbook: Vector Calculus, sixth edition, by Jerrold E. Marsden and Anthony J. Tromba, published by W. H. Freeman and Company (2012).
We will use Chapters 4-8 of the text.
Homework: Homework is a very important part of the course, and in order to fully master the topics, it is essential that you work carefully on every assignment and try your best to complete every problem. Homework will be due on Fridays at 10pm and will be handed in on Gradescope. You can find the homework assignments on the calendar and on gradescope.
Reading: Reading the sections of the textbook corresponding to the assigned homework exercises is considered part of the homework. Lecture time is very limited and not every subject can be fully discussed in the time allotted for lecture. Thus, you must read the assigned sections of your textbook (and work through the examples) to fully understand the subject. You should expect questions on the exams that will test your understanding of concepts addressed in the reading and assigned homework exercises, whether or not they are discussed in the lecture.
Grades: There are
twothree methods to compute your grade. Your grade will be determined using each method, and then the best grade will be used.
• Method 1. (20% HW)+(20% Midterm 1)+(20% Midterm 2)+(40% Final Exam).
• Method 2. (20% HW)+(20% Best Midterm)+(60% Final Exam).
• Method 3 (COVID-19). (20% HW)+(40% Midterm 1)+(40% Midterm 2).
After your grade is calculated, your letter grade will be calculated, based on a scale. The following grades are guaranteed:
A ≥ 93%, B ≥ 83%, C ≥ 73%, D ≥ 63%.
However, it is possible that I will change the grading scale to be more lenient.
Exams: There will be 3 exams. Two midterms and one final.
First Midterm: The first midterm will be held on January 29th.
Second Midterm: The second midterm will be held on February 26th.
Final Exam: The
final will be held on Wednesday, March 18th from 8am-11am. final will be a take home exam posted on Tuesday, March 17th at 8am and due at 10pm on Wednesday, March 18th.
Homework Policy: Late homework will not be accepted. At the top of each assignment should appear:
(1) Your name,
(2) Either a list of sources consulted (other than the textbook, lectures, and things posted on this site), or the sentence "Sources consulted: none."
You are not expected to solve every single problem on your own, and you are encouraged to work in groups. However, your homework write-ups should be done independently. Office hours are a great time to ask questions about the homework assignments.
No make up exams will be given. A missed midterm will be scored a 0.
Accomodations for students with disabilities must be requested in accordance with the Mathematical Departmental Policies. In particular, any such request must be made sufficiently in advance.
Violations of UCSD's academic integrity policies will be addressed using internal measures (e.g., asking students to defend their work orally, zeroing out affected homework or exam scores) and/or UCSD administrative measures at the professor's discretion. If you suspect a violation of academic integrity, please bring it to the attention of the professor and/or TA immediately.