What is Calculus? A brief overview, what exactly calculus is

What is Calculus? Meaning of Calculus:

Calculus is the branch of mathematics that studies the differentiation and integration of functions, as well as 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.

To be easy to understand, you need to go back to the concept"The original intention"。

The original meaning of calculus in English is:"Algorithms", translated as"Calculus"。So, first of all, calculus is all about"Addition, subtraction, multiplication, and division --- the same"Calculation method:"。

Secondly,"Calculus"The translation of the original English text is more reflective of its algorithmic nature.

Calculus"Divided into:"Differentiation"with"Credits"Two parts. Generally speaking, the former is to find the micro trend of the known macro law, and the latter is the opposite.

Calculus"What's even greater is that differentiation and integration are inverse operations. This also made Newton Leibniz famous in history. At the same time, we can see how exquisitely calculus is translated (here we should pay tribute to the late Qing mathematician, astronomer, mechanic, botanist, --- Li Shanlan).

The early days of calculus were indeed done"Algorithms"exists, lacks rigorous logical proof, and gave rise to the famous one that lasted nearly three hundred years"The Second Mathematical Crisis"。It was the great Cauchy who solved this problem and made calculus based on rigour"Limits"Theoretically.

Mathematics is the language of science, and calculus greatly enriches the language base of science. But again, calculus is conditional, and calculus is only one part of mathematics.

Off topic--- our mathematics and natural science education, lacking"What exactly"Historical and philosophical inquiry. so that it can be in the discipline"Interior"Skillfully logic, but possible"I don't know what I'm doing"。

That's probably why"Separation of Arts and Sciences Liberal arts and sciences are opposed"Modern education is separated from traditional education, and creativity is not proportional to learning ability.

Calculus is an accumulation, which can be thought of as slices of bread, stacked on top of each other.

Calculus includes differentiation and integration, and the operations of differentiation and integration are opposite, and the two are inverse operations of each other.

Integrals include definite and indefinite integrals.

A definite integral means that there is a fixed integral interval and its integral value is determined.

An indefinite integral does not have a fixed integration interval, and its integral value is indefinite.

Applications of Calculus:

1) The problem of finding each other between velocity and distance in motion.

2) Find the tangent of the curve.

3) Find the length, area, volume, and center of gravity problems.

4) Finding the maximum and minimum values of the problem (quadratic functions, belonging to a class of calculus) Application of definite integrals:

1. Solve the problem of finding the area of curved edge figures.

Example: Find the area s. of a plane figure d surrounded by a parabola and a straight line

2. Find the distance of linear motion at variable speed.

The distance s traveled by an object in linear motion with variable speed is equal to the definite integral of its velocity function v=v(t) (v(t) 0) over the time interval [a,b].

3. Change force to do work.

Calculus refers to differentiation and integrals. It is an important part of advanced mathematics and mathematical analysis. Its object of study is functions.

Calculus includes differentiation and integration, and the operation of differentiation and integration is just the opposite, and the two are reversed to each other.

Integrals include definite and indefinite integrals.

A definite integral means that there is a fixed integral interval, and its integral draft high value is determined.

An indefinite integral does not have a fixed integration interval, and its integral value is indefinite.

Applications of Calculus:

1) The problem of finding each other between velocity and distance in motion.

2) Find the tangent of the curve.

3) Find the length, area, volume, and center of gravity problems.

4) Finding the maximum and minimum values of the problem (quadratic functions, belonging to a class of calculus) Application of definite integrals:

1. Solve the problem of finding the area of curved edge figures.

Example: Find the area s. of a plane figure d surrounded by a parabola and a straight line

2. Find the distance of linear motion at variable speed.

The distance s traveled by an object in linear motion with variable speed is equal to the definite integral of its velocity function v=v(t) (v(t) 0) over the time interval [a,b].

3. Change force to do work.

Calculus includes differential and code comma integration operations, and their main content is the derivation and product of functions, as well as the problem of finding the limit, determining the normal equation of the curve, and the late selling area of the curve.