Calculus is one of the most difficult courses in college mathematics department.
Calculus involves how to solve the integrals and derivatives of various functions, which requires a deep understanding of the concepts, extreme values and curve approximation of continuous functions and discontinuous functions. Because of the abstraction of calculus, students usually spend a lot of energy to understand these concepts.
Calculus is a branch of mathematics, which studies the differentiation of functions, division of products 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.
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 orange number of the function. Therefore, the derivative is also called WeChat business.
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.
Calculus is widely used in science, economy, engineering and other fields to solve problems that cannot be effectively solved by algebra alone. Calculus is based on algebra, trigonometry and analytic geometry, including differential calculus and integral calculus. Differential calculus, including the calculation of derivatives, is a set of theories about the rate of change.
It enables functions, velocities, accelerations and slope of curves to be derived from 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 theorem of calculus points out that differential and integral are inverse operations, which is why the two theories are unified into calculus.
We can discuss calculus with either of them as the starting point, but we usually introduce differential calculus into teaching first. In the deeper field of mathematics, calculus is usually called analysis and is defined as the science of studying functions.