Introduction to calculus:
Calculus, a mathematical concept, is a branch of higher mathematics that studies the differential and integral of functions and related concepts and applications. It is a basic subject of mathematics, including 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.
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, you know that it refers to calculus.
Geometric significance of folding:
Let Δ x be the increment of point m on the curve on the abscissa y=f(x), Δ y be the increment of the curve on point m corresponding to Δ x on the ordinate, and dy be the increment of the tangent of the curve on point m corresponding to Δ x on the ordinate. When | Δ x | is very small, |Δy-dy | is much smaller than |δx | (high-order infinitesimal), so we can use a tangent line segment to approximate the curve segment near point M.
Definite integral and indefinite integral:
Integration is the inverse operation of differentiation, that is, knowing the derivative function of a function and finding the original function in reverse. In application, definite integral is not only that, but also widely used for summation, that is, to find the area of curved triangle. This ingenious solution is determined by the special properties of integral. The indefinite integral of a function (also known as the original function) refers to another set of functions, and the derivative function of this set of functions is just the previous function.