Multivariable Calculus
MAT 2228 Spring 2009
Instructor: Dr. Brian Gill Office: OMH 209 E-mail: bgill@spu.edu
Phone: 281-2954 Web page: http://myhome.spu.edu/bgill
Prerequisites: Mastery of the material from MAT 1225 and 1226 (Calculus I and II) is essential. Some of the
content from MAT 2401 (Linear Algebra) is also required. Some basic familiarity with Maple will also be
expected.
Course Materials:
Textbook: Calculus, 5th edition, by James Stewart. See the attached schedule for details of the material to be
covered. A variety of valuable supplements for the textbook are also available for purchase, including a student
solutions manual and a study guide, but they are not required.
Computer Software: The class will meet in a computer classroom equipped with one PC for every two students.
In this class, we will make substantial use of Maple, a computer algebraic system. Maple is available for use on
computers in labs throughout the campus. You are also encouraged to purchase a copy of the software for use on
your own computer since many homework assignments may require the use of the software. It will be available
for purchase at a substantial discount for students using a discount code provided by your instructor.
Most of your homework for the course will also be submitted online through WebAssign, so you will need to have
access to a computer with an internet connection when working on homework. Please plan accordingly.
University and Departmental Mission: Seattle Pacific University seeks to be a premier Christian university
fully committed to engaging the culture and changing the world by graduating people of competence and character,
becoming people of wisdom, and modeling grace-filled community. The mathematics department at Seattle Pacific
University seeks to provide excellent instruction to enable our students to be competent in the mathematics required
for their chosen fields, and to share our expertise with the community through service and leadership. Hence,
common goals for students in mathematics courses include 1) becoming competent in the topics covered in the
course, 2) demonstrating skills and attitudes which contribute to professional, ethical behavior, 3) the ability to
communicate mathematically, in both written and verbal form, and 4) learning to appreciate the beauty and utility of
mathematics.
Course Objectives: This course provides an introduction to multivariable and vector calculus. The course covers
vectors and analytic geometry in three dimensions, partial differentiation, multiple integration, and an introduction
to line integrals. The primary aims of the course are to help students develop new problem solving and critical
reasoning skills and to prepare them for further study in mathematics, the physical sciences, or engineering. By the
end of the course, students should be able to
recognize and sketch surfaces in three-dimensional space;
recognize and apply the algebraic and geometric properties of vectors and vector functions in two and three
dimensions;
compute dot products and cross products and interpret their geometric meaning;
compute derivatives and integrals of vector functions;
compute partial derivatives of functions of several variables and explain their meaning;
compute directional derivatives and gradients of scalar functions and explain their meaning;
solve multiple variable maximum and minimum value problems;
set up and evaluate double and triple integrals using a variety of coordinate systems;
evaluate line integrals through scalar or vector fields and explain some physical interpretations of these
integrals;
apply Green’s theorem;
use Maple effectively to explore and solve problems;
analyze and solve complex problems;
write short proofs using the ideas and techniques listed above; and
provide clear written explanations of the ideas behind key concepts from the course.
Students should also gain an increased appreciation of mathematics as part of the language of science and as a study
in itself. Finally, I hope that you will have fun accomplishing all of these objectives, even if the material is difficult
and the course takes a lot of time and effort.
