Calculus problem - Education and Training Encyclopedia

Calculus problem

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Take you to calculus.

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calculus

Mathematical concept

*** 14 meaning

Calculus is a branch of mathematics, which studies the differential and integral of functions and related concepts and applications in higher mathematics. It is the basic subject of mathematics. The content mainly includes limit, differential calculus, integral calculus and its application. Differential calculus, including the calculation of derivatives, is a set of theories about the rate of change. It makes the function, velocity, acceleration and curve slope can be discussed with a set of universal symbols. Integral calculus, including the calculation of integral, provides a set of general methods for defining and calculating area and volume [1].

Chinese name

calculus

Foreign name

calculus

Differential and integral relation

Reciprocal operation

Integral invention

Leibniz, isaac newton

Subject characteristics

The theory is rigorous and widely used.

brief Introduction of the content

The basic concepts and contents of calculus include differential calculus and integral calculus.

The main contents of differential calculus include: limit theory, derivative, differential and so on.

The main contents of integral include definite integral, indefinite integral and so on.

Generalized mathematical analysis includes calculus, function theory and many other branches, but now it is generally customary to equate mathematical analysis with calculus, and mathematical analysis has become synonymous with calculus. When it comes to mathematical analysis, known refers to calculus [2].

Unary differential

Folding definition

Let the function be defined in an interval, and +δ x is in this interval. If the increment Δ y = f (+Δ x)–f () of a function can be expressed as Δ y = a Δ x+o (Δ x) (where a is a constant independent of Δ x), and o (Δ x) is infinitely less than Δ x, then the function f o(δx) is said to be differentiable at one point, and Δ x is called the function corresponding to the increment Δ x of the independent variable at one point x0.

Usually, the increment Δ x of the independent variable X is called the differential of the independent variable, which is denoted as dx, that is, dx = Δ x. Then the differential of the function y = f(x) can be written as dy = f'(x)dx. The quotient of the differential of the function and the differential of the independent variable is equal to the derivative of the function. So derivative is also called WeChat business [3].

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reference data

[1] foreign languages press, major discoveries and inventions in the world, edited by Yang Jianfeng 20 13-94.