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 and integral 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:
- Functions, limits, and continuity
- Inverse Functions
- Logarithms and exponential functions
- Trigonometric and Inverse trigonometric functions
- Derivatives of functions
- Rules of differentiation
- Tangents and tangent lines
- Applications of derivatives
- The definite integral
- Antiderivatives and the indefinite integral
- The Fundamental Theorem of Calculus
- Integration techiques
- Applications of integrals
- Improper integrals
See the the course outline for more details.