Specific Meaning of Calculus 20, Specific Meaning of Calculus

Calculus is the branch of mathematics in advanced mathematics that studies the differentiation and integration of functions, as well as related concepts and applications. It is a fundamental subject of mathematics. The content mainly includes limits, differential calculus, integral science and their applications.

Differential calculus consists of the operation of finding derivatives and is a set of theories about the rate of change. It makes it possible to discuss functions, velocities, accelerations, and slopes of curves in a common set of notations. Integralism, including the operation of finding integrals, provides a general set of methods for defining and calculating area, volume, etc.

Dividing a thing into infinitesimal parts, and taking one of them is called differential.

Conversely, adding infinitesimal equal parts to get a whole thing is called an integral.

For example, if you have a circle, its differentiation is its circumference, and its integral is a sphere.

The sum of the infinitesimal circumferences is the area of the circle; The sum of the infinitesimal circles is the sphere.

Calculus, unthinkable, is to divide a concrete and non-concrete into several parts, those small parts can be regarded as a specific entity, can be calculated, and some of the companies that need to be used in the object are permutated and combined to find the desired answer, which is my understanding, for ......reference only

Calculus is the branch of mathematics in advanced mathematics that studies the differentiation and integration of functions, as well as related concepts and applications. It is a basic discipline of mathematics, and the content mainly includes limits, differential calculus, integral science and its applications.

Calculus is a general term for differentiation and integralization. It is a mathematical idea, 'infinite subdivision' is differentiation, 'infinite sum' is integration, algebra is a concept that people are already familiar with, however, algebra cannot deal with the concept of "infinite". Therefore, it is necessary to use algebraic processing to represent infinite quantities, and the concept of "limit" is carefully constructed.

The history of calculusIt shows that human cognition starts from vivid intuition, and then reaches abstract thinking, that is, the process of realizing from perceptual to rational cognition. Human beings' understanding of the regularity of the objective world is relative and limited by the times. With the deepening of human understanding, understanding will develop step by step from low to high level and from incomplete to relatively comprehensive.

There is never an end to man's quest for nature.

Refer to the above content at: Encyclopedia - Calculus.

Calculus isAdvanced mathematics and old learningstudies the differentiation and integration of functions, as well as the branches of mathematics related to concepts and applications. It is a fundamental subject of mathematics.

The content mainly includes limits, differential calculus, integral science and their applications. Differential calculus consists of the operation of finding derivatives and is a set of theories about the rate of change. It makes functions, velocities, accelerations.

and the slope of curves, etc., can be discussed with a common set of symbols. Integralism, including the operation of finding integrals, provides a set of general methods for defining and calculating area, volume, etc.

Folding geometric meaning.

Let δx be the increment of the curve y = f(x) at the point m on the abscissa, δy is the increment of the curve at the point m corresponding to δx on the ordinate, and dy is the tangent of the curve at the point m.

Corresponds to the delta of δx on the ordinate.

When|δx|Very small, |δy－dy|than |δx|much smaller (infinitesimal of higher order, so near the point m, we can approximate instead of curve segments with tangent segments.

The significance of calculus is as follows:

Calculus is a mathematical idea that includes two main concepts, "infinite subdivision" and "infinite summation". Calculus can be used to describe phenomena in nature, such as the motion of objects, the motion of planets, fluid flow, etc. It is able to express complex laws of motion in simple language, making research in fields such as physics and engineering more convenient.

Calculus is a precise mathematical tool capable of describing the amount of change, including velocity, acceleration, curves, and more. It plays an important role in understanding the law of change, solving complex problems, and deriving formulas.

Calculus also occupies an important place in the field of mathematics, and it is the foundation of mathematical analysis, differential equations, real analysis, and other disciplines. The study of calculus has contributed to the development of mathematics and has also provided important mathematical tools for other disciplines. Calculus is a mathematical tool with wide application significance, and its existence and development provide strong support for the progress of human civilization.

Calculus can also solve problems in the actual production process, such as in industry, construction, machinery and other fields.

Features of calculus percolation:

1. Continuity.

Calculus emphasizes the study of continuous variables, which can describe the change of variables at a certain point, and can also describe the tendency of variables to change over a continuous interval. This description of continuity allows calculus to solve many practical problems, such as the distance traveled by an object, the relationship between speed and time, or the law of conservation of energy in physics.

2. Unlimited segmentation.

"Infinite subdivision" in calculus is the idea of infinite subdivision, that is, dividing a continuous interval into infinitely small intervals, and analyzing the small changes in each interval. This idea of infinite subdivision enables calculus to solve problems that cannot be solved in finite intervals, such as acceleration and impulse in physics.

3. Infinite summing.

The "infinite summation" in calculus is the idea of accumulating infinitely small quantities, that is, by summing up the small changes in each interval through Sun judgment, the total amount of change is obtained. This idea of infinite summation allows calculus to deal with some problems that cannot be solved in finite summation, such as kinetic energy, potential energy, etc. in physics.