Mathematical concept

*** 13 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.

Calculus mainly includes limit, differential calculus, integral calculus and its application, and has become an important part of modern university education.

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.

Main idea

Tangent line, function

research contents

Tangent, function, limit, integral, differential

subject

Mathematics, physics

Differential invention

Leibniz, isaac newton

bale

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 [1].

Unary differential

Folding definition

Set the function? There is a definition in a certain interval. And then what? +δ x is in this interval. If the increment of the function δδy = f (? +δx)–f(？ ) 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 called at point? Is differentiable, a Δ x is called the differential of the function corresponding to the increment of the independent variable Δ x at point x0, and it is denoted as dy, that is, dy = a Δ x. ..

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.