Basic definition:
Let the unknown function f(x)=0 have a solution in [a, b], and arbitrarily insert several points in [a, b], where a = x0.
Interval is also called extension, because when it runs out of allocated intervals, it needs to allocate new intervals when inserting new records (that is, expand some blocks); Once an interval is assigned to one object (table, index and cluster), it cannot be assigned to other objects. Divide it into the product f(ξi)△xi of the length of closed interval, open interval and semi-open and semi-closed interval, and sum them.
If no matter how [a, b] is divided, and no matter how the point ξi between cells is taken, as long as the length of the interval tends to zero, S always tends to a certain limit I, then we call this limit I the definite integral of the function f(x) on the interval [a, b] k.
The content of calculus:
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.
Univariate calculus and multivariate calculus;
Unary calculus:
Let the function y=f(x) be defined in an interval, and both x0 and x0+δ x are in this interval. If the increment of the function δ y = f(x0+δx)–f (x0) can be expressed as δy = aδx+o(δx) (where a is a constant independent of δx), and o(δx) is infinitely less than δ x, then the function f (x) is said to be differentiable at point x0.
And aΔ x is called the differential of the function corresponding to the increment of the independent variable Δ x at the x0 point, which is denoted as dy, that is, dy = aδx x. Usually, the increment 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. Therefore, the derivative is also called WeChat business.
Multivariate calculus:
Multivariate differential, also called total differential, is expressed by the increment of one-variable differential corresponding to the partial derivatives of two independent variables. Δ z = a×Δx+b×Δy+ο (ρ) is the full increment of function z at point (x, y), (where a and b have nothing to do with Δ x and Δ y, but only with x and y, ρ=[(x? +y∧2)]∧( 1\2), A×δX+B×δY is the total differential of z at this point.