Mathematics for Electrical Engineering and Computing

6

Differentiation

6.1 Introduction

We have used functions to express relationships between variables. For instance, in an electrical circuit the current and the voltage through a resistor can be related by V =IR. Here, one physical relationship can be found by simply substituting in the formula the known value of the other. Another common relationship between physical quantities is that one quantity is the rate of change of another: for instance, speed is defined as rate of change of distance with respect to time. It is simple to find the average speed of a moving object if we know how far it has travelled in a certain length of time, which is given by

$\frac{\text{Distance}?\text{travelled}}{\text{Time}?\text{taken}}$

This does not give an idea of the speed at any particular instant. ...