The goal of this chapter is to provide the opportunity for the reader to develop a fundamental understanding of the key concept of differential calculus. Chapter 1 introduces the concept of the difference equation, which gives the response in one variable to a change in another. The difference equation is the bridge between the normal equation and the differential equation that provides a conceptual stepping stone from one to the other.
The difference equation is introduced using relationships that are well known and fundamentally understood; for example, the relationship between the length of a side of a square and its perimeter. The “normal” or “ordinary” equation relates the perimeter to the length of a side. The difference equation gives the change in the perimeter in response to a change in the length of a side.
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