Matlab like every other programming language is a medium via which we pass instructions to the computer to get things done. At the heart of its activity is computation. But programming languages do more than just run calculations. You can send an email with matlab, you can play music, write video, analyze data and predict the future.
Mathematics can be a boring subject when we spend most of our time doing the calculations or derivation and less time on analysis of what we are actually doing. Deriving physical intuitions from what we computed can make the the whole exercise more fun. It fun to solve wave equation and actually see the wave. If you solve a simple pendulum problem and you can not visualize the pendulum in motion, the motivation for such to study the pendulum, might not receive the required spark.
The hype around visualization is mostly about plotting data, like the velocity and acceleration of the pendulum over time. What if you can actually see the pendulum accelerating? It turns out the same tools we use to just plot the velocity can be used to make a digital copy of the object and give it that velocity and acceleration so we can see it move .
That umbrella in the picture above is a complete mathematical object, every line and surface is from a mathematical expression. Would it not be cool if you can do that? Well, here is a video of it being done. Mathematics is the tool that enables science. And Matlab enables math.
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