Mathematics is not as difficult and complex as you might imagine.
Although single-variable functions are often used in math problems, multi-variable functions are also useful in solving problems related to everyday life.
Mathematics has brought many conveniences to human life, starting from the ancient final writing system.
You can see that interesting math problems are hidden everywhere in everyday life.
---p27, The owner of a copy shop who is proficient in multivariable functions

You can also discover here that math is fun.
Even though it is 'nothing', it is considered as a state or set.
Any set can be a state of nothing, or it can contain a state of nothing.
This is like adding 0 to a number and getting that number back.
Therefore, the empty set can be a subset of every set.

---p31, Stationery and Set Theory

How can we find the instantaneous speed of a train? Think of this process as calculating the distance the train has traveled at a given moment. Physicists say that for a very short period of time, no observable change in speed occurs.
Therefore, for a short period of time, we can think of the train as moving at a constant speed.

---p47, The Hidden Mathematics of Train Transportation

Mathematical models have many similarities to the scale models used in filmmaking.
For example, when filming a historical drama, sometimes it is filmed in an actual palace, but sometimes it is filmed in a fake palace set.
Although the palace is a replica, there is no significant difference in visual effect, so there is no problem in filming it.
Also, when filming dangerous scenes, stunt doubles are used instead of real actors, and when filming disaster scenes such as earthquakes or tsunamis, realistic scenes are created using scale models or computer graphics.

---p67, Mathematical Model

At first, the slope of the curve changes significantly, but it soon becomes gentler.
This means that when we first add flour to the dough, we can clearly see the dough getting bigger, but when the dough reaches a critical size, adding more flour does not clearly change the size, and it becomes difficult to tell the difference with the naked eye.
At this time, the slope approaches 0, but cannot be perfectly 0.

---p74, Model of wheat dough

Some people compare functions to cameras.
This is because it is similar to the process by which a camera records the appearance of the person being photographed.
The process of taking a photo is the thought, the original photo is the dependent variable, and the person being photographed is the independent variable.
If the camera doesn't move, there will be a certain range of positions where the person being photographed can stand, and if they stand too far to either side, the photo won't be taken properly.
This range can be called the domain of the function.
Of course, these days there are many high-performance cameras that can capture the scenery from any angle.
In this case, the domain is from minus infinity to infinity.

---p108, Discussing Functions

Let's talk about macro and micro perspectives.
What ?x and ?y represent is a macroscopic difference.
If the length can be clearly measured, even if it is very short, it is considered a macroscopic difference.
On the other hand, what Leibniz invented, dx and dy, represent is a very short interval in microscopic terms.
So, no matter how accurate a ruler is, it cannot measure length.

---p163, Direction of addition

It was explained that when calculating the circumference of a circle, you can subtract the area of ​​a slightly smaller circle from the area of ​​the circle and then divide it by the difference in radii.
Similarly, when calculating the surface area of ​​a sphere, subtract the volume of a slightly smaller sphere from the volume of the sphere and then divide by the difference in radii.
We have previously proven that finding the circumference of a circle using this method is equivalent to finding the derivative of its area.
Therefore, the surface area of ​​a sphere is the derivative of its volume.

---p193, Revisiting Surface Area

As mentioned earlier, before the advent of calculus, most scholars studied stationary states.
So, for things that change over time, we must study them through the concept of calculus.
A differential equation model is a simplified model of a changing object or phenomenon.
Research and differential equation models are inextricably linked in areas such as epidemiological studies, drug distribution in the body, and population forecasting.
Differential equation models have had a significant impact on the development of clinical medicine and pharmacology, and later gave rise to a new scientific field called 'pharmacokinetics'.

---From the text