ABSTRACT
Calculus is a branch of mathematics involving or leading to calculations dealing with continuously varying functions such as velocity and acceleration, rates of change and maximum and minimum values of curves. Calculus has widespread applications in science and engineering and is used to solve complicated problems for which algebra alone is insufficient. Calculus is a subject that falls into two parts: (a) differential calculus (or differentiation), (b) integral calculus (or integration). This chapter provides an introduction to differentiation and applies differentiation to rates of change.Chapter 35 introduces integration and applies it to determine areas under curves. Further applications of differentiation and integration are explored in Engineering Mathematics (Bird, 2010).
In an equation such as y = 3x2 + 2x − 5, y is said to be a function of x and may be written as y = f (x). An equation written in the form f (x) = 3x2 + 2x − 5 is termed functional notation. The value of f (x) when x = 0 is denoted by f (0), and the value of f (x) when x = 2 is denoted by f (2), and so on. Thus, when f (x) = 3x2 + 2x − 5,
