PID controller, P is proportional, I is integral and D is differential. PID controller can simulate both circuits and digital systems, such as single chip microcomputer, but either method involves the parameter setting of the system. As the name implies, PID requires proportional parameters, integral parameters and differential parameters. The determination of these three parameters and subsequent operations are based on advanced mathematics.
Hydraulic servo valve, for the calculation of hydraulic pressure, in fact, the principle application is "fluid mechanics" For fluid mechanics, you will probably come into contact with the general formula in the future, and basically you need to deduce it on the basis of high numbers. Please go to the library to borrow fluid mechanics for details.
Second: linear algebra, this course, to be honest, is Niu B. I think you must have learned coordinate system transformation in high school, such as coordinate translation and polar coordinate transformation. Now you think of a problem and give you a two-joint manipulator. How do you control the movement of this manipulator? How do I control each servo motor to determine the motion position and force of these machines? These problems will be discussed in detail in robot kinematics and robot dynamics. If I tell you, the knowledge they have used can be said to be a "matrix". I think you should be familiar with him through the study of line generation. Matrix operations, such as finding the inverse matrix and finding the adjoint matrix, are needed. This is just a line generation application that I know in my field.
Third: probability and statistics, I don't think it's necessary to say much about this, nor does classical probability. There are many cases in life that he has been used, and some examples that I think should be involved in textbooks, such as using probability theory to judge whether a new drug is effective in medicine. What about statistics? good ..........................................................................................................................................................................
Fourth, geometry, for some classical geometric models, we actually use them every day, such as finding the circumference and area of a circle, finding the volume of some standard bodies and so on. However, we have classified these knowledge as common sense, and it is far from enough for modern civilization to only have these basic geometric knowledge, so we have to use a lot of advanced mathematical knowledge to solve some geometric problems, such as analytic geometry, an important branch of geometry. Pro/E three-dimensional software commonly used in engineering, as long as you build a geometric body, no matter how irregular it is, you only need to click the button to find the volume, and it can be calculated for you. How to achieve it? Computers are fast, but not intelligent, so you need to write algorithms and write them out with programs. These algorithms are actually analytic geometry in advanced mathematics. Of course, it won't be that simple. It will definitely use some advanced mathematics, such as some finite element algorithms. (I don't know much about the volume algorithm in Pro/E, please forgive me if there are any mistakes.)
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As @ Chen Ran said, the study of these courses can make you look at the world from a different perspective, and you will be surprised to find that the world is actually made up of mathematics. Art students will think that the world is made up of colors, literature students will think that the world is made up of ideas, and economics students will know that the world is made up of money. ) you can understand the world more abstractly and understand its cause and effect. Chen Ran's answer is great, and I agree with it, but I think it's best to add some "living" examples that can be seen in real life.
The reason why I give this answer here is to let you know that these things are not useless. Their functions are beyond our imagination. Without advanced mathematics, even an ordinary machine tool can't be made, let alone a numerical control system ~
In fact, with the deepening of your study, you will find that your advanced mathematics is not enough. If you want to do your own projects in the future, you must learn some Laplace transform, Fourier transform and Z transform. What's more, you have to learn some special fields to use "professional" mathematics, such as numerical analysis and system variation, but at that time, I think you have deeply understood the meaning of mathematics.