1
$\begingroup$

What is the difference between a normal equation such as $f(t) = t^2$ and a differential equation such as: $d/dt f(t) = t*f(t)$. I mean what is physical intuition of the difference between the two? thanks

  • 0
    The unknown is a *number* in the first case, a *function* in the second case. – 2017-01-18
  • 0
    Could you explain in terms of time evolution, like we are looking for how the function changes as time in the case of differential? – 2017-01-18
  • 0
    It would be more or less as @Robert Israel answer: the ordinary equation gives you the value of a physical quantity (depending on time) at any time, and the differential equation gives its rate of variation as a function of time and of the physical quantity. – 2017-01-18

1 Answers 1

2

A "normal" equation gives you global information: it determines directly what the function $f(t)$ is for every $t$ in the domain of the function. Thus if $f(t)$ represents your position, the equation is like a timetable telling you where to be at any time.

A differential equation, on the other hand, gives only local information: the rate of change of $f(t)$ at any time $t$, possibly depending on $f(t)$ itself. In the example, it tells you what your velocity (speed and direction of movement) should be at any given time and place.

  • 0
    Great answer... I have a differential equation(the first one) in section Propagation on page, subsection 'Continuous-Time System Modelling'. Here I have values of w, with initial value q(0) = 0. Could you tell how the equation changes if I have the value of q itself at every t. Here is the link – 2017-01-18
  • 0
    the link is: http://www.ee.ucr.edu/~mourikis/tech_reports/TR_MSCKF.pdf – 2017-01-18
  • 0
    I would be grateful if you take some precious time of you. thanks – 2017-01-18
  • 0
    That would be appropriate for an entirely new question – 2017-01-18
  • 0
    If you have the value of $q$ itself at every $t$, you have a solution of the differential equation with this initial value. – 2017-01-18