Mike O’Leary                                                                       Spring 2000

Office: 300E Stephens Hall                                                 Tu: 7:00-9:40 p.m., Stephens Hall 210

Office Phone: 410-830-3896                                                Th: 7:00-8:40 p.m., Stephens Hall 206

Email: moleary@towson.edu                                             Section: 101

Office Hours: M 2:00-3:00, Tu 6:00-6:50, Th 2:00-3:00               

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 the Math 275 Laboratory Manual, Spring 2000 edition.

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 February 17, March 9, April 13 and May 11. 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 Thursday, May 18 from 7:00 p.m.-9:00 p.m.  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.

            The last day to withdraw from the course with a grade of “W” is March 17.

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.       

For questions and comments, please use the feedback page, or email  your comments to moleary@towson.edu .

Last Modified: January 16, 2001