Math 275
Class
Policies
Mike O’Leary Autumn
2001
Office: 301C Stephens Hall MW: 2:00-3:15 p.m., Stephens Hall 201
Office Phone: 410-704-3896 Tu: 2:00-2:50 p.m., Stephens Hall 210
Email: moleary@towson.edu Th: 2:00-2:50 p.m., Stephens Hall 206
Office Hours: M,Tu: 9:00-10:00, Th: 10:00-11:00 Section: 001
Prerequisites: MATH 274 or MATH 284.
Catalog Description: Vectors in two and three dimensions,
differential and integral calculus of functions of several variables. Not open
to those who have successfully completed MATH 373.
Learning Objectives:
1.
The student
will understand the calculus of functions defined parametrically and functions
defined using polar coordinates.
2.
The student
will understand vectors and the geometry of space. This includes understanding
the algebra of lines and planes in space; it also includes the notion of a
vector, including the dot product and the cross product, as well as their
applications. Students shall also understand quadric surfaces, and cylindrical
and spherical coordinates for points in space.
3.
Students will
understand the basic calculus of vector-valued functions. This includes
differentiation and integration of vector-valued functions, as well as the
tangent and normal vectors. Students will also be able to calculate the arc
length of a space curve.
4.
Students will
understand the calculus of a single function of several variables. Students
will understand various methods for graphing such functions, and will
understand the basic notions of limits and continuity of these functions. The
students will know how to take the partial derivatives of functions of several
variables, including the use of the chain rule. Students will understand the
gradient and the directional derivative of a function, and shall be able to
find tangent planes and linear approximations to functions of several
variables. Students will also be able to find extrema of functions of several
variables, with and without constraints, including the use of Lagrange
multipliers.
5.
Students will
understand the techniques of multiple integration, including polar coordinates,
cylindrical coordinates, spherical coordinates and the Jacobian change of
variables. Students will also be able to apply these ideas to problems like the
center of mass, moment of inertia, and surface area calculations.
6.
Students will
understand elementary vector analysis. In particular, students will understand
the notion of a vector field, including conservative vector fields. Students
will also understand line integrals and Green’s theorem.
Academic Integrity: The nature of higher mathematics requires
that students adhere to accepted standards of academic integrity. Violations of
academic integrity include cheating, plagiarism, falsification and fabrication,
complicity in academic dishonesty, personal misrepresentation and proxy,
bribes, favors and threats. Cheating is a serious offense that will have grave
consequences for your academic life.
Students
who violate these standards will either fail the course outright or, at the
instructor’s discretion, may merely receive a zero on any assignment for which
the student receives inappropriate assistance. Particularly serious violations
of these standards will be referred to the administration for possible
additional action.
Instructional Material: The primary required text is Calculus, Early Transcendental Functions, by
Larson, Hostetler and Edwards. Also required is Laboratory Explorations for
Multivariable Calculus using Mathematica, second edition, by Boules,
Goodson, Kim and O’Leary.
Other Required Material: A graphing calculator is required.
Methods of Instruction: We shall use lectures, class discussion,
group work, and laboratory work.
Attendance: Attendance is expected; you should only
miss a class for a compelling reason. If you do miss a class, you are
responsible for any material that you miss, including any homework assignments
given in that class.
Homework: The only way to learn mathematics is by
doing problems, problems, and more problems. In addition to the labs, homework
will be assigned on a regular basis, and will form a substantial portion
of your final grade. Expect to spend a substantial amount of time studying and
working on homework. The general rule is two to three hours outside class for
each hour inside; this translates to about 10-15 hours of homework and personal
study per week.
Quizzes: Occasional unannounced quizzes may be given.
For purposes of determining the final grade, they shall be treated as a
homework assignment.
Computer
Laboratory: There will be
weekly computer based laboratory exercises. Laboratory assignments are due,
unless otherwise specified, at the beginning of class one week after the
assignment is given.
Although the computer room in Stephens 310 is
available for student use, do not wait until the last minute to complete your
assignments because computer resources are limited. Accordingly, you are
encouraged not to fall behind in your lab work.
Laboratory
assignments will be graded based on the following criteria:
a. Content (approx. 40%)
b. Accuracy (approx. 40%)
c. Format, appearance (approx. 20%)
Each lab report
shall be well written and conform to the usual rules for English composition.
Merely listing the obtained answers is unacceptable. The report may be in the
form of a Mathematica notebook.
Guidelines for
Homework and Laboratory Reports:
(1) Late work will not be accepted
without a compelling reason.
(2) Assignments are required to be
neat, clean, and paper-clipped or stapled.
(3) Assignments must include the
author’s name, and a brief description of the assignment.
(4) Students are allowed to discuss
homework problems with their classmates, however all work that is turned in
must be the student’s own work.
Any assignment that does not meet
these criteria may receive a deduction in score, or more generally will simply
be rejected.
Midterms: There shall be four midterm examinations,
tentatively scheduled for September 26, October 15, November 5, and December 3.
Attendance is expected. Make-up exams shall only be given for compelling
reasons; all excuses are subject to verification.
Final Exam: The Final Exam is scheduled for Tuesday, December 18, from 12:30-2:30. The final exam will not be rescheduled.
Attendance is expected; a make-up exam will not be given without an extremely
compelling reason. The final exam shall be comprehensive.
Final Grade: Final grades shall be determined by the
following method:
Midterms 30% Final
30%
Labs 15% Homework/Quizzes 25%
Note the weight of
the final. A student who does not complete 70% of the laboratory assignments
may not receive a grade of C or better.
The last day to withdraw from the
course with a grade of “W” is November 7.
Help: If you have difficulty completing a homework assignment, do not
hesitate to ask for help, either from your friends, or from me. You are welcome
to stop by my office, for whatever reason, and at whatever time, even if there
are no office hours scheduled then. If you wish, you may also simply send an
e-mail message.
Web Page: My web page at http://www.towson.edu/~moleary has a
page devoted to this course, which contains the syllabus, and copies of exams
once they are given. Also archived on that site are copies of all of the old
exams that I have given while at Towson.