Independently of each other, around the same time, Sir Isaac Newton
and Gottfried Leibniz
discovered the Fundamental Theorem of Calculus. This theorem states the inverses relationship between integration and differentiation. Some of these questions will be part of your final exam.
1. Give an appropriate definition of the term "The Calculus".
2. Define the term derivative formally.
3. Define the term indefinite integral (antiderivative)formally.
4. Define the term definite integral formally.
5. State the First and Second Fundamental Theorems of Calculus
6. Describe how the integral symbol developed. It is now applied to both the definite and indefinite integral. To which was it applied to first -- why does this make sense?
7. Why is the Fundamental Theorem of Calculus important. What does it allow us to do?
8. Research contributions to calculus by Leibniz and Newton and the historic feud between the two over credit for the development of the calculus. What was Newton's contribution to the development of calculus and the relationship between integration and differentiation. What was Leibniz's approach? How did the feud between Newton and Leibniz play out? (Summarize -- one page handwritten.)