# Mathematics in Medicine: Introduction

by Batool Akmal

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00:01 Mathematics is everywhere.

00:04 If you open your eyes, you will start to see numbers and equations and functions absolutely everywhere.

00:11 We looked at how it applies to different areas and these are just some of the main areas we spoke about.

00:17 Demographics, medicine, engineering, and radioactivity.

00:20 But now, we’ll focus completely on medicine.

00:24 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.

00:34 In medical imaging, mathematics is used extensively.

00:38 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.

00:50 You see things like Radon transformation, which is a complicated integral equation combined together with Fourier transformations in things like MRI scans and in ultrasounds.

01:02 You see Maxwell’s equation in things like cancer therapy of hyperthermia.

01:08 And the Navier Stokes equation is just one other example of the kind of equations that we use.

01:14 This describes the flow of fluid through pipes, narrow or widened pipes.

01:20 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.

01:30 You’ll also see that in these equations, there are quite a few familiar notations.

01:34 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.

01:49 So let’s just look at some mathematical examples and see if we can apply differential equation to some real life medical problems.

02:02 Have a look at these examples and they’re very simple, basic examples and they’re very specific cases that we’re looking at.

02:09 But it does require some use of calculus.

02:12 So have a little read of them and see if you can figure these out for yourselves.

02:16 We’ll do them in a minute together, but remember you will need a calculator for some of these calculations.

The lecture Mathematics in Medicine: Introduction by Batool Akmal is from the course Calculation Methods: Exercises.

### Included Quiz Questions

1. Hyperthermia treatment
2. Modeling the flow of blood in blood vessels
3. Medicine treatment
4. Chemotherapy
5. Targeted therapy
1. Differential equations
2. Navier-Stokes equations
3. Linear equations
5. Maxwell's equations

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