This main goal of the course is to gain an understanding and appreciation of the basic ideas underlying a remarkable achievement of the human intellect: the differential calculus of single-variable functions.
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:
- Intervals and absolute values
- Functions and graphs
- Trigonometric functions
- Limits and continuity
- Derivatives of functions
- Rules of differentiation
- Tangents and tangent lines
- Maxima and minima of functions
- Related rates
- Applications of derivatives
See the the course outline for more details.