Math 20E

Math 20E

Vector
Calculus

Winter 2020

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
Email: dstapleton@ucsd.edu
Office Hours: Mondays 10am-12pm
Office: AP&M 6432

TA: Jebin Moses
Sections: 1 and 2
Email: jmoses@ucsd.edu
Office Hours: Fridays 9:30am-11:30am
Office: Mayer Hall Addition 5722

TA: Shan Jiang
Sections: 3 and 4
Email: shj043@ucsd.edu
Office Hours: Tuesdays 12pm-2pm
Office: AP&M 2313

TA: Srivatsa Srinivas
Sections: 5 and 6
Email: scsriniv@ucsd.edu
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!):

Monday Wednesday Friday

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.
HW1 due.

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.
HW2 due.

1/20. MLK day. No class. 1/22. §6.2 Change of variables theorem. 1/24. §6.2 Change of variables theorem.
HW3 due.

1/27. §4.3 Vector fields. 1/29. Midterm 1. Practice Midterm.
Midterm 1 Solutions. 1/31. §7.1 Path integrals.
HW4 due.

2/3. §7.2 Line integrals. 2/5. §7.3 Parametrized surfaces. 2/7. §7.3 and §7.4.
HW5 due.

2/10. §7.4 Area of a surface. 2/12. §7.5 Integrating functions over surfaces. 2/14. §7.5 and §7.6.
HW6 due.

2/17. Presidents' Day. No class. 2/19. §7.6 Surface integrals of vector fields. 2/21. §8.1 Green's theorem.
HW7 due.

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.
HW8 due.

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.
HW9 due.

3/9. § 8.3. Conservative vector fields. 3/11. TBD. 3/13. Final Review.
HW10 due.
Practice Final.
Final Exam.

Monday	Wednesday	Friday
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. HW1 due.
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. HW2 due.
1/20. MLK day. No class.	1/22. §6.2 Change of variables theorem.	1/24. §6.2 Change of variables theorem. HW3 due.
1/27. §4.3 Vector fields.	1/29. Midterm 1. Practice Midterm. Midterm 1 Solutions.	1/31. §7.1 Path integrals. HW4 due.
2/3. §7.2 Line integrals.	2/5. §7.3 Parametrized surfaces.	2/7. §7.3 and §7.4. HW5 due.
2/10. §7.4 Area of a surface.	2/12. §7.5 Integrating functions over surfaces.	2/14. §7.5 and §7.6. HW6 due.
2/17. Presidents' Day. No class.	2/19. §7.6 Surface integrals of vector fields.	2/21. §8.1 Green's theorem. HW7 due.
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. HW8 due.
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. HW9 due.
3/9. § 8.3. Conservative vector fields.	3/11. TBD.	3/13. Final Review. HW10 due. Practice Final. Final Exam.

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 ~~two~~three 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.

Course Policies:

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.