Generally speaking, the so-called differential calculus is caused by the problem of finding the speed of variable speed motion in physics and the problem of finding the tangent of curve in geometry, which was mainly founded by Fermat, Descartes, Newton, Leibniz and others in the17th century. The main concept of differential calculus is derivative. Generally speaking, the derivative is the rate of change, such as speed is the rate of change of distance relative to time, and acceleration is the rate of change of speed relative to time.

Integral calculus is mainly caused by the problem of finding the area and volume of complex figures in geometry and finding work in physics. Compared with the backward development of differential calculus, as early as the ancient Greek era, human beings had a considerable understanding of integral calculus. For details, please refer to Archimedes' works. Integral mainly involves two concepts: definite integral and indefinite integral. Roughly speaking, the so-called definite integral refers to the accumulation of values of a given function in a certain interval, and its geometric meaning is the area of a graph sandwiched between the function and the abscissa axis. Indefinite integral is the inverse problem of derivative problem, which has no geometric significance in itself.

The basic theorem of calculus (Newton-Leibniz formula) links differential and integral together, and gives a method of finding definite integral with indefinite integral, which links indefinite integral (thus derivative) with definite integral.

It is not difficult to develop high-dimensional correspondence theory on the basis of one-dimensional calculus.

Calculus is the beginning of modern mathematics, which is completely different from high school mathematics that has not surpassed the level of ancient Greece. If there is a connection, it is helpful to master the basic function properties (trigonometric function, exponential function, etc.). ) to calculate and understand.