Mathematics is everywhere.
If you open your eyes,
you will start to see numbers and equations
and functions absolutely everywhere.
We looked at how it applies
to different areas
and these are just some of the
main areas we spoke about.
engineering, and radioactivity.
But now, we’ll focus
completely on medicine.
When you look at the growth
and decay of any model,
so look at a tumor or bacteria,
you will have to use differential equations
to model how they change over time.
In medical imaging, mathematics
is used extensively.
In our ever changing world of medicine
where things are becoming more technical,
things are becoming more complex,
the background behind it
all is just mathematics.
You see things like
which is a complicated integral equation
combined together with
in things like MRI scans
and in ultrasounds.
You see Maxwell’s equation in things
like cancer therapy of hyperthermia.
And the Navier Stokes equation
is just one other example of the
kind of equations that we use.
This describes the flow of fluid through
pipes, narrow or widened pipes.
You’ll start to notice that these equations
build the foundations of our medical study,
and in fact, of any field
in the modern world.
You’ll also see that in these equations,
there are quite a few familiar notations.
You can see the integral signs,
you can see the differentials,
although these are fairly
complicated at this point in time,
but you understand
what is happening,
you understand whether
you’re looking the gradients
or whether you’re looking at
the areas of these equations.
So let’s just look at some
and see if we can apply differential
equation to some real life medical problems.
Have a look at these examples
and they’re very simple, basic examples
and they’re very specific
cases that we’re looking at.
But it does require some use of calculus.
So have a little read of them and see if
you can figure these out for yourselves.
We’ll do them in a minute together,
but remember you will need a calculator
for some of these calculations.