What is Calculus

You will find that you are on a small airplane and you can read altimeter only 100 feet above ground! Do you need to worry?

On the other hand, what happens if the altimeter shows 100 feet above the ground and the height is decreasing? Is this reason enough to worry?

maybe. Even though the altitude of the aircraft is declining, it probably fell at a slow speed. Perhaps the pilot is preparing to land. do not worry

The important thing is that the height of the aircraft alone is not enough to judge whether there is a problem. But what is this related to calculus?

Calculus is to measure and describe the change. In the above scenario, knowing the altitude of the aircraft at a particular moment is the same as knowing a single point in the functional diagram.

But this is not all. What will happen next? Will the function increase? Is it still decreasing? Still, will growth (or decline) occur slowly? Still very fast? Does this function last forever in this direction, or will it change direction? (See Figure 1)

Figure 1: The story is more than just functional value. I care about the direction and how the function moves in this direction.

Algebra alone can not deal with these problems. We need a set of more powerful tools bundled in the package called Calculus.

In addition, each part of the calculus has two main explanations. One is geometric and the other is physical. (See below)

I know the slope of the line well. Regardless of which two points you use, the rate change is always the same.

Calculus is part of modern mathematics education. Calculus course is the entrance to other more sophisticated mathematics courses specializing in functions and restrictions and is widely known as mathematical analysis. Historically, the calculus has been called "infinitely small calculus" or "infinitely small calculus". The term calculus (complex calculation) is used not only for several theories such as propositional calculations, rich calculations, mutation calculations, lambda calculations, process calculations, but also for specific calculation methods or symbolic methods.

Tensor calculus was developed by Gregorio Ricci-Curbastro around 1890, called Absolute Calculus, originally proposed by Ricci in 1892. Published by Rich and Tullio Levi-Civita's 1900 classic text Méthodesdecalculdifférentiel, many mathematicians can use it. Absolu et al. Learn application (absolute calculation method and its application). In the 20th century, this theme was called tensor analysis and Einstein's general relativity theory was introduced around 1915. General relativity is completely expressed in tensor language. It is difficult for Einstein to learn from geometry Marcel Grossmann. Levi-Civita started communication with Einstein in order to correct errors in tensor analysis with Einstein. Communication lasted 1915 - 17 years and was characterized by mutual respect: