Advanced Engineering Mathematics, 7th Edition

1.1 Definitions and Terminology

INTRODUCTION

The words differential and equation certainly suggest solving some kind of equation that contains derivatives. But before you start solving anything, you must learn some of the basic definitions and terminology of the subject.

A Definition

The derivative dy/dx of a function y = ϕ(x) is itself another function ϕ′(x) found by an appropriate rule. For example, the function is differentiable on the interval (−∞, ∞), and its derivative is dy/dx = . If we replace in the last equation by the symbol y