There are two fundamental questions that the Calculus tries to answer. The first question deals with the rate of change of a function at a point. This rate of change is also the slope of the tangent line to the function at the point. In trying to answer this question we will encounter the concepts of a limit and the derivative. Mathematicians stuggled with this question for centuries until Newton and Leibniz developed, independently, a rigorous method for its answer.
The second question deals with calculating the area of an irregular region. Ancient cultures had developed formulas for the areas of regular regions such as triangles, rectangles, and circles. The connection between these shapes is their simple boundaries. The problem is to find a method to calculate the area of a region whose boundary can be described but that is more complex than straight lines and arcs. The study of this problem lead to the development of the definite integral.
The striking fact of the Calculus is that the answers to these two questions are related. The relationship between the derivative and definite integral is stated in the Fundamental Theorem of Calculus and will be the culmination of our study of these two questions. We will then try to answer a slightly more difficult question, “How can we calculate the volume of a sphere without using the formula?”
We will use James Stewart's Calculus 5th edition as the text for this course. Students are encouraged to study in groups as long as solutions are written up independently. A graphing calculator is not required for the course as we will learn how to use the Maple software package. However, you may use your graphing calculator if you wish.
To start off the semester students should take the review quiz. Anyone who gets below 70% should come and see me. Students should check out the Homework section for the latest assignments. The syllabus and course schedule are provided for future reference.
