Abstract World VS Real World - 2

Mark Misin
A free video tutorial from Mark Misin
Aerospace & Robotics Engineer
4.6 instructor rating • 2 courses • 2,769 students

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INTUITION MATTERS! - Applied Calculus for Engineers-Complete

Calculus + Engineering + PID: Functions, Limits, Derivatives, Vectors, differential equations, integrals: BEST CALCULUS

34:53:37 of on-demand video • Updated October 2020

  • You will develop very strong intuition & understanding in Calculus
  • You will learn how to apply Calculus in real life to the level not seen in other courses
English [Auto] So this is what mathematics does. It does not care about specific situations it's signs of numbers and variables and how they relate to each other. It explores the relationships between them and creates tools that other engineers and scientists can use for their own specific situations. So for example in our airplane example in the last lecture we we would take this linear function which is this one and we would apply it to that specific example. On the other hand if you're a civil engineer and your task is to design a tank then then you would apply this function to your specific situation but you would only do that if you believe that this function accurately represents the physical situation. So in other words it has to at least very closely approximate to what's really going on. So you can't have something like this that let's say the airplane. So again that time distance graph that the airplane that the relationship between time and distance is this. But you choose this function so it doesn't make sense. So once you choose a tool from mathematics for your situation it needs to represent the physical situation. Now of course it never represents the physical situation. 100 percent because you can have a situation like this. I mean it just show it to you very quickly. So let's say you have time and distance and the real physical situation is something like this. So completely a straight line. Then you you would have a straight line here and there is a small error right between the physical situation and and your function. But then the engineer might think something like this. OK sure. Fair enough. It doesn't completely represent my physical situation but should I should I create should I choose a function that is super complicated or extremely precisely represent my function or I can just take an easy function that is easy to work with. And since the error is so small it simply doesn't matter. And in many cases they're just going to say yeah I'm too lazy and there's so small. I'm just going to take the easy way which you should do because you would save a lot of time by doing that which is also a big issue in the world of engineering. In fact you can have really bizarre functions that only exist in mathematics but never in the physical world. For example we have this function y equals 1 over x. If I graph it and I put X here and Y here is the pause. These are the positive signs. And these are the negative sites. So out my graph would look something like this. And these lines they would go to infinity. So they would go to plus infinity here and minus infinity here plus infinity here and minus infinity here. Now I don't know what in real world is infinity. Maybe you can approximate something with infinity if something is very big. Let's say universe is very big. And then you can approximate it within function with a function that goes to infinity. But an even more bizarre concept is mine is infinity. I don't know what can be minus infinity in real life. But again mathematics doesn't care about it and it's not the job. It just investigates how variables relate to each other. And then you as an engineer or as a scientist you choose and you have to be skillful enough to choose what you take from this immense bag of knowledge. So there again the goal of this lecture was to create some kind of bridge between realistic examples and the abstract world. So in the next lecture we're going to start manipulating those functions. And we're going to be more abstract. Just working with why is an axis. But remember always remember they just represent relationships. And and if you feel that they are too abstract just try to think of an example all those functions that can be used for specific situations. I hope you'll stick around. See.