Math 2A03 is a basic course on vector calculus for students in physics, chemistry, and mathematical sciences. It continues the subjects of Calculus I and II but addresses functions of several variables in two-dimensional and three-dimensional geometry. Topics of particular importance in terms of physical applications are gradient vectors, optimization problems, curves, integration along paths, integration over surfaces, and the classical integration theorems. Note that if you are interested in taking the upper-level mathematics courses (such as real and complex analysis, differential geometry, differential equations), you should take the full-year vector calculus (Math 2X03 and 2XX3) instead of this course, which teaches the same material in one term. Math 2A03 is not a sufficient prerequisite for Math 2XX3.

Functions of several variables, chain rule, Taylor's formula, extremal problems, Lagrange multipliers; multiple integrals, change of variables formula, line and surface integrals, Green's, Gauss's and Stokes' theorems.

Lecturer: Dr. Martin Bays mbays@math.mcmaster.ca

Lectures: Mondays, Wednesdays, Thursdays; 10:30, T13/127.

Tutorials:

- Mondays 15:30-16:20, HH/305
- Tuesdays 08:30-09:20, HH/305

Lecturer office hours: Mondays, Wednesdays, Thursdays; 11:30-12:30, HH/409

TA office hours: TBA

*Vector Calculus* by M. Lovric (John Wiley & Sons, 2007), ISBN 978-0-471-72569-5

- Assignments (10%): Five home assignments will be posted on the course webpage with specific deadlines. The four best grades will be counted towards the final mark. The numbers "five" and "four" in this paragraph should be considered tentative estimates, subject to change.
- Midterms (40%): There will be two midterms, each worth 20% of the course total mark, tentatively scheduled for the 6th of October and the 4th of November respectively, taking place during the usual lecture hour in the usual room. Textbooks, lecture notes, and McMaster calculators will be allowed on the tests.
- Final exam (50%): There will be a final exam, testing the entirety of the course, around three hours in duration. The date and location of the final exam will be announced by the registrar's office at some point during the term.

Contact Dr. Bays as soon as possible. Failing that, contact the Associate Dean's Office.

You are expected to exhibit honesty and use ethical behaviour in all aspects of the learning process. Academic credentials you earn are rooted in principles of honesty and academic integrity.

Academic dishonesty is to knowingly act or fail to act in a way that results or could result in unearned academic credit or advantage. This behaviour can result in serious consequences, e.g. the grade of zero on an assignment, loss of credit with a notation on the transcript (notation reads: "Grade of F assigned for academic dishonesty"), tutting, and/or suspension or expulsion from the university.

It is your responsibility to understand what constitutes academic dishonesty. For information on the various types of academic dishonesty please refer to the Academic Integrity Policy, located at www.mcmaster.ca/academicintegrity.

The following illustrates but three forms of academic dishonesty:

- Plagiarism, e.g. the submission of work that is not one's own or for which other credit has been obtained;
- Improper collaboration in group work;
- Copying or using unauthorised aids in tests and examinations.

In this course, we may be using such wonders of the modern age as electronic mail, IRC, wikis, and anything else which looks fun and useful. Students should be aware that, when they make use of the electronic components of this course, private information such as first and last names, usernames for email accounts, and program affiliation may become apparent to all other students in the same course. The available information is dependent on the technology used. If you have any questions or concerns about such disclosure, please discuss this with the course instructor, who will be happy to discuss possible technical workarounds.

The instructor and university reserve the right to modify elements of the course during the term. The university may change the dates and deadlines for any or all courses in extreme circumstances. If either type of modification becomes necessary, reasonable notice and communication with the students will be given with explanation and the opportunity to comment on changes. It is the responsibility of the student to check their McMaster email and course websites weekly during the term and to note any changes.

Requests for Relief for Missed Academic Term Work for absences from classes lasting up to 5 days: Using the McMaster student absence form (MSAF) on-line, self-reporting tool, https://www.mcmaster.ca/msaf/index.html, undergraduate students may report absences lasting up to 5 days and may also request relief for missed academic work. The submission of medical or other types of supporting documentation is normally not required. See http://academiccalendars.romcmaster.ca/content.php?catoid=7&navoid=559#Requests_for_Relief_for_Missed_Academic_Term_Work for full details; the following is a summary.

Students may use this tool to submit a maximum of one request for relief of missed academic work per term. Students must immediately follow up with their course instructors regarding the nature of the relief. Failure to do so may negate the opportunity for relief. It is the prerogative of the instructor of the course to determine the appropriate relief for missed term work in his/her course.

For absences from classes lasting more than five days: Students who are absent more than five days cannot use the on-line, self-reporting tool to request relief. They MUST report to their Faculty Office to discuss their situation and may be required to provide appropriate supporting documentation. If warranted, students will be approved to use a discretionary version of the MSAF on-line, self-reporting tool.

Usually, relief for missed work will take the form of a transferral of its weight to the final exam.