Question

(calc discussion question) Calculus can be defined as the study of the rate of change many regarded as the most important branch of mathematics why might the study of the rate of change be so important in math in what ways is it important in real world situations

Answer 1

Basically, because all phenomenological problems are described in the form of differential equations, for example Newton's law of cooling states that the rate of heat loss of a body is directly proportional to the difference in the temperatures between the body and its environment. The equation is given by:

$\begin{gathered} \frac{dT(t)}{dt}=-r(T-Tm) \\ \end{gathered}$

A more basic example is velocity, which is defined as the change in position with respect to time:

$v(t)=\frac{dx}{dt}$

As we can see, all the physical phenomena that surround us can be described as a variable that changes depending on another.