As mentioned above, the establishment of a discipline is not the achievement of one person, but the achievement of one person or several people after the efforts of many people and the accumulation of a large number of achievements. The same is true of calculus.
Everything in the objective world, from particles to the universe, is always moving and changing. Therefore, after introducing the concept of variables into mathematics, it is possible to describe the movement phenomenon in mathematics.
Due to the emergence and application of the concept of function and the needs of the development of science and technology, a new branch of mathematics has emerged after analytic geometry, which is calculus. Calculus plays a very important role in the development of mathematics. It can be said that it is the greatest creation in all mathematics after Euclidean geometry.
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Early application of calculus
1, the mutual solution of velocity and distance in motion. Find the velocity and acceleration of an object at any time; Conversely, it is known that the accelerometer of an object is a function formula with time as a variable, and the speed and distance are obtained. This kind of problem appears directly when studying sports. The difficulty is that the speed and acceleration studied are constantly changing.
However, according to physics, there is no doubt that every moving object must have a speed at every moment of its movement. The problem of finding the moving distance with the known speed formula also encounters the same difficulty. Because the speed changes all the time, we can't get the moving distance of an object by multiplying the moving time by the speed at any moment? .
2. Find the tangent of the curve.
The problem itself is pure geometry, which is of great significance to scientific application. Because of the need of studying astronomy, optics is an important scientific research in the17th century. In order to study the light passing through the lens, the designer of the lens must know the angle at which the light enters the lens in order to apply the reflection law.
What matters here is the angle between the light and the normal of the curve, which is perpendicular to the tangent, so it is always to find the normal or tangent; Another scientific problem involving the tangent of a curve appears in the study of motion, that is, to find the direction of motion of a moving object at any point on its trajectory, that is, the tangent direction of the trajectory.
3, length, area, volume and center of gravity, etc.
These problems include finding the length of the curve, the area enclosed by the curve, the volume enclosed by the surface, the center of gravity of the object, and the attraction of a relatively large object (such as a planet) to another object. In fact, the problem of calculating the length of an ellipse puzzles mathematicians, so that for a period of time, mathematicians failed in their further work on this issue, and new results were not obtained until the next century.
When Archimedes' work became famous in Europe, his interest in finding length, area, volume and center of gravity revived. The exhaustive method was first revised gradually, and then it was fundamentally revised because of the creation of calculus.
4. The problem of finding the maximum and minimum (quadratic function, a kind of calculus)
For example, when a shell is fired in a barrel, its horizontal distance, that is, its range, depends on the tilt angle of the barrel to the ground, that is, the firing angle. A "practical" problem is to find the launching angle that can shoot the maximum range.
Baidu encyclopedia-calculus
Baidu encyclopedia-calculus