Vector Analysis, Math 550, Section 01

Instructor: George Androulakis, giorgis@math.sc.edu
Lectures: MWF 9:40-10:30 @ LeConte 422
Office Hours: MWF 12-1, or by appt @ LeConte 402

Overview: Many physical and natural phenomena depend on more than one single variable. The physicist who studies the trajectory of a particle or the astronomer who studies the motion of a planet needs to understand geometry in two or three dimensions. In Vector Analysis we study curves in two and three dimensions as well as we discuss the multidimensional versions of the Derivative, the Integral and the Fundamental Theorems of Calculus. These ideas are very important in Geometry, Physics and Astronomy.
Expected Learning Outcomes: The students are expected to master the following concepts (and demonstrate that by being able to solve related problems):

1. Vector fields.

2. Line and path integrals.

3. Orientation and parametrization of lines and surfaces.

4. Change of variables and Jacobians.

5. Oriented surface integrals.

6. Theorems of Green, Gauss, and Stokes.

7. Introduction to tensor analysis.

Text: Achieve for Vector Calculus by Marsden and Tromba 6th Edition. ISBN: 9781319584962. This is not a physical copy of the book but a one-semester access to an online grading system which includes e-book access. The University bookstore has already received copies of this.

Prerequisites: Completion of Math 241 with a grade of C or better.

Grading: Your grade in this course will be based on your performance on homework, quizzes, two midterms exams and a final exam. The weights assigned to each of these components will be:

These weights assume that we will have a grader for grading the quizzes. I have requested a grader from the math department for grading the quizzes. If a grader will not be assigned to us, then there will be no quizzes and the weights will be 25 % in each of the remaining four components. Course grades will be determined according to the scale: [0, 60) $\Rightarrow$ F, [60, 65) $\Rightarrow$ D, [65, 70) $\Rightarrow$ D+, [70, 75) $\Rightarrow$ C, [75, 80) $\Rightarrow$ C+, [80, 85) $\Rightarrow$ B, [85, 90) $\Rightarrow$ B+, [90,100] $\Rightarrow$ A.
Homework: It will be assigned regularly and graded via the Achieve. In order for me to receive your grades in Achieve, you will to you will need to register the first time that you use Achieve using the following link, (you will still need to purchase the access to the Achieve which is included in the above ISBN). In order to access the Achieve in the subsequent times please click the following link, (you may want to bookmark it). The lowest homework grade will be dropped. The homework deadlines will be strictly observed, and they will not be changed, so make sure that you start working on your homework as soon as they are assigned.
Quizzes: Every Wednesday except the first two Wednesdays and the last Wednesday of the semester, and the Wednesday of the Thanksgiving recess, we will have an in class quiz. The approximate time allowed for the quizzes will be 5-10 minutes. The quizzes will be based on the recent homework assignments. Calculators, cellphones, computers, books or notes will not be allowed during quizzes. If you must miss a quiz day, then you may try to excuse your missed quiz by filling out the form which is provided by the Office of Student Advocacy. If their office approves your excuse, then they will send me to both of us an official excuse letter and your absence will be excused. If the Office of Student Advocacy will not approve your excuse, then your absence will not be excused and your grade for the unexcused missed quiz will be a zero. For each excused missed quiz you can take a make-up quiz. Friday November 20th is the designated make-up quiz/exam day, (for all students who have excused quizzes/exams). The lowest quiz grade will be dropped. Unexcused missed quizzes will count for zeros. Therefore, the lowest quiz grade will be a zero if there is an unexcused missed quiz. Your Quiz Grade will be the average of all your quiz grades not counting the lowest quiz grade.
Exams: There will be two midterm exams whose tentative dates are listed below. If you miss a midterm exam because of a documented reason of a University approved excuse, then please upload your documentation as soon as possible here, (Office of Student Advocacy). If the Office of Student Advocacy approves your excuse, they will send to both you and me an email, and you can take a make-up exam on the make-up exam day, (Friday November 20). Otherwise, your absence will not be excused and your grade for the unexcused missed exam will be a zero.
Important dates:

• Monday September 7: Labor Day Holiday , (no classes).

• Friday October 2: tentative date for the first midterm exam.

• Thursday October 15 - Friday October 16: Fall Break, (no classes).

• Wednesday November 4: last day to drop a course or withdraw without a grade of “WF” being recorded.

• Friday November 13: tentative date for the second midterm exam.

• Friday November 20: Make-up quiz/exam day for the excused quizzes/exams (if no students need to take make-ups, then we will have a normal class day).

• Sunday November 22- Sunday November 29: Thanksgiving recess (no classes).

• Friday November 27: Make-up day for excused quizzes and exams.

• Friday December 4: last day of classes.

• Wednesday, December 9, 9:00 a.m–12 noon: Final exam.

Academic Integrity: The Honor Code applies to all students and all work for this course. Please review the Honor Code here. Students found violating the Honor Code will be subject to discipline.
On the use of AI for the Homework: Usually when people learn new concepts they initially have some misconceptions and misunderstandings. Because of these misconceptions and misunderstandings, the first few attempts in solving problems may not be successful. That is why Achieve will give you five opportunities for each problem. This will allow you to clear your misconceptions and misunderstandings by being pardoned up to four times for each problem. If you use AI to solve the homework, then you loose your opportunity to clear your misconceptions and misunderstandings and to be pardoned by Achieve, so the first time that your misconceptions and misunderstanding may show up will be during quizzes or exams where you do not have the four pardoned allowances. Thus, I recommend that you work on the homework on your own rather than using AI in order to understand the materials better and maximize your performance in the quizzes and exams.
Disability Services: Any student with a documented disability should contact the Office of Student Disability Services at 777-6142 to make arrangements for appropriate accommodations. Please let me know anything that I need to know in order to properly provide accommodations.