The main goal of the course is to extend the ideas of the differential calculus of a single variable to the relm of multi-variable functions. The concept of a vector will play an important role in this, and we will find it very convenient to consider our functions to be defined on vectors and to return a vector value. Along the way, we will present some key ideas from linear algebra.
Notice that the goal is not to provide the student with a set of computational techniques and procedures for solving a set of predefined problems. Rather, the emphasis is on the fundamental concepts and how they relate to each other. Computation is an important part of this process, but it is not the only one, nor is it the primary one. Students who approach this course assuming that "the answer" is the only thing that counts will find it frustrating and are not likely to do well.
The material to be covered includes:
See the the course outline for more details.
- vectors and vector operations,
- multi-variable function,
- vector-valued functions,
- equations of lines and planes in space,
- partial derivatives,
- tangent and normal vectors,
- tangent planes,
- systems of linear equations, and
- matrix operations.