MATH 2654

Calculus III

Spring 2003


Instructor: Dr. Scott Gordon, 324 Boyd, 836-4354.

E-mail: Office:, home:

Time and Location: M, W, F 12:00-12:50, T 12:30-1:20,306 Boyd.

Office Hours:


1:00 4:00*


1:30 4:00


11:00 12:00, 1:00 3:30


11:00 12:00

(*1:30-3:30 in 302 Boyd)

If you would like to see me but cannot come during one of these times, please call first or make an appointment.

Textbook: Calculus, Early Transcendentals, by James Stewart, Fourth Edition. We will cover Chapters 12-16.

Course Description: Three-dimensional space, vectors, vector-valued functions, motion along a curve, functions of two or more variables, partial derivatives, max-min problems for functions of two or more variables, double and triple integrals, centroids and center of gravity, line integrals, conservative vector fields, Green's Theorem, surface integrals, Divergence Theorem, Stoke's Theorem. (See Learning Outcomes for more information.)

Attendance Policy: You are expected to attend class regularly. I will randomly select at least 10 days during the semester to award bonus points (2 points per day) for attendance.

Homework: I will assign homework exercises after each section. These problems will not be graded, but you may be quizzed on them. I will allow some time during class to discuss the problems and I encourage you to use my office hours if you have any questions about them.

Quizzes: Each week that there is not a test, there will be a 15-minute quiz consisting of problems from homework. The first quiz will be this Friday 1/10; after that, they will fall on Wednesdays. There will be 10 quizzes in all, worth 20 points each.

Tests: There will be a test every third Wednesday, four in all, worth 100 points each. Test dates: 1/22, 2/12,3/5,4/2.

Make-up Tests and Quizzes: The following requirements must be met in order for you to be permitted to make-up a missed test or quiz: (i) You must have a legitimate, verifiable reason for missing the test or quiz, (ii) you must notify me as soon as you are aware of your need for a make-up, and (iii) you must be able (except in extreme circumstances) to take the test or quiz on or before the day of the next class.

Grading Errors: In order to have a grade changed as a result of a grading error, you must bring the error to my attention within one week of the time you received the graded test.

Final: A cumulative final exam worth 200 points will be given Wednesday, 4/30, 11:00-1:00. Everyone must take the final exam. There will be no exemptions.

Grading Scale: A: 86-100, B: 72-85, C: 58-71, D: 44-57, F: 0-43.

Grading: Your final grade will be determined as follows: Quizzes- 25%, Tests- 50%, Final Exam -25%.

Withdrawal: February 27 is the last day to withdraw from the course with a grade of W.

First Homework Assignment: p.787 #3,11,13,15,17,21,29,33.

Academic Dishonesty Policy: Any student who engages in any form of academic dishonesty will receive an F for the course. The incident will also be reported to the Office of Student Affairs so that they can determine if further disciplinary action is warranted. Academic dishonesty is defined as one or more of the following:

1.        Use of unauthorized information during a test or exam.

2.        Copying material from another student's paper during a test or exam.

3.        Giving or receiving information during a test or exam.

4.        Giving information about the content of a test or exam to a student who will be taking the test at a later time.

5.        Obtaining unauthorized information about the content of a test or exam before taking it.

6.        Copying work done by another student on a problem set and presenting it as your own.

7.        Using information from an unauthorized source in working on a problem set without properly crediting that source.

8.        Allowing another student to copy your work on a problem set.


Learning Outcomes: The student will be able to:

1.        Perform basic vector operations such as addition, subtraction, scalar multiplication, dot product, cross product, norm, or projection onto another given vector. (L1)

2.        Use the dot product and/or the cross product to find the angle between two vectors. (L1)

3.        Determine the components of a given vector that are parallel and orthogonal to another given vector. (L1)

4.        Find equations of lines, planes, and spheres in 3-space given geometric information about them. (L1)

5.        Differentiate and integrate vector-valued functions. (L1)

6.        Find the length of a curve in 3-space. (L1)

7.        Find curvature, tangential acceleration, and normal acceleration for an object moving along a curve in 3-space. (L1)

8.        Find partial and directional derivatives of a function of several variables. (L1)

9.        Find and classify local and absolute extrema of a function of several variables. (L1)

10.     Use Lagrange multipliers to find extreme values of a function of several variables subject to a constraint. (L1)

11.     Evaluate an iterated integral of a function of several variables. (L1)

12.     Determine the limits of integration of a double or triple integral given the region of integration. (L1)

13.     Change variables in a double integral from rectangular coordinates to polar coordinates or in a triple integral from rectangular to cylindrical or spherical coordinates. (L1)

14.     Use double and triple integrals to find surface areas, volumes, and centroids of regions in two and three dimensions. (L1)

15.     Use double and triple integrals to find masses, centers of mass, and moments of inertia. (L1)

16.     Determine if a vector field is conservative. (L1)

17.     Evaluate a line integral directly and, in the case of a conservative vector field, using the Fundamental Theorem of Line Integrals. (L1)

18.     Evaluate a line integral over a closed curve using Green's Theorem. (L1)

19.     Evaluate a surface integral directly and using Stokes' Theorem. (L1)

20.   Evaluate a surface integral over a closed surface either directly or using the Divergence Theorem. (L1)