What have you benefited from studying calculus?

Learned about a unique language that describes the rules by which the world works. It is so concise and elegant, and at the same time guarantees the rigor and reliability of the entire narrative. Although, the world described by mathematics may not be exactly the real world, it does offer us a unique alternative.

As the most important and valuable cornerstone of the modern mathematical system, calculus contains the most indispensable factors for enlightenment. ‍‍

Personally, I think that calculus provides a new statistical and computational solution that allows people to subdivide complex problems into regular problems through simulation, and then summarize the research results to express or explain the overall laws, which is opposed to probability theory and chaos science (the view that the world is discontinuous and discrete and irregular), which believes that the world is continuous and has laws to follow. ‍‍

I have learned the basic idea of solving problems, of course, if you are engaged in science and engineering, calculus is a must, and if you don't learn calculus, it is difficult to reach a higher level! ‍‍

Calculus is the best tool for analyzing and studying nonlinear problems. If it weren't for the complexity of the nonlinear problem and the fact that calculus would not have been introduced at all, the general algebraic methods would have been sufficiently applicable. ‍‍

First of all, I realized that although the difference in talent between people can be so great and so unequal, after centuries of development and refinement, I only need to spend a relatively short time and very little effort to see the world as seen by those who are extraordinarily intelligent, and the world is ultimately fair. ‍‍

Differentiation is the study of small changes in infinity and microscopic differences. Integration is its reverse process, which studies the macro. It is the foundation of modern physics, economics and other sciences. Don't look at the difficulty of mastering at the beginning, just like driving, you don't have to understand the transmission principle first, and you will be able to do it slowly. ‍‍

Workers engaged in basic engineering research and experiments, in the construction industry, aviation industry, etc., calculus is used in many places, such as design institutes, aviation experiments, and so on. ‍‍

The harvest is that the essence of mathematics is the needs of life, it is a kind of summary and combing, and the general method is extracted, and the more you learn the principle, the easier it is.

Rationality, seriousness, clarity, and not so-so.

Exercising your brain cells helps to develop, and it is still very helpful for teenagers.

It is simply useless in everyday life and daily work!

I think it's a basic tool for electronic and mechanical design.

I've scratched the surface of math.

By studying the parts, we can understand the whole.

I wonder what real-life problems it solves?

During his university studies, he learned about functions, limits, and continuities through the calculus course; Derivatives and Differentiation; applications of the small value theorem and derivatives; Antiderivative; definite integrals and their applications; differential calculus of multivariate functions; double integrals; infinite series; Differential Equations vs. Difference Equations.

Relevant highlights of Calculus at the University.

The textbook is based on the basic principles of application, practicality and application, with theory downplayed and practice highlighted. In the process of compiling this textbook, the editors combined the characteristics of application-oriented undergraduates and higher vocational colleges, and only gave results or simple and intuitive geometric explanations for the derivation and proof of relatively cumbersome theorems and formulas as much as possible. The selection of example questions is from shallow to deep, and the narration is as simple as possible, and strives to have a certain degree of inspiration and application.

When I was studying in college, I learned some of the ideas of differentiation through calculus and then solved engineering problems, and the idea of calculus is very important.

The premise of learning calculus is to learn functions and integrals first.

Integral is the branch of mathematics in advanced mathematics that studies the differentiation and integration of functions, as well as related concepts and applications. It is a basic discipline of mathematics, which mainly includes limits, differential calculus, integral science and its applications. Differential calculus consists of the operation of finding derivatives and is a set of theories about the rate of change.

It makes it possible to discuss functions, velocities, accelerations, and slopes of curves in a common set of notations. Integralism, including the operation of finding integrals, provides a general set of methods for defining and calculating area, volume, etc.

The premise of learning calculus is to first learn the derivative knowledge of functions in high school.

The derivative is an important basic concept in calculus, when the independent variable x of the function y=f(x) produces an incremental δx at a point x0, the ratio of the incremental δy of the output value of the function to the incremental δx of the independent variable is the limit a when δx approaches 0 If it exists, a is the derivative at x0, denoted as f'(x0) or df(x0) dx.

If both the independent variables and the value of a function are real, the derivative of the function at a certain point is the tangent slope of the curve represented by the function at that point.

Since the seventeenth century, the concepts and techniques of calculus have been continuously expanded and widely used to solve various practical problems in astronomy and physics, and great achievements have been made. However, until the nineteenth century, the problem of the rigor of mathematical analysis of calculus was not solved during its development.

In the eighteenth century, many great mathematicians, including Newton and Leibniz, were aware of this problem and made efforts to solve it, but they did not succeed in solving it.

Throughout the eighteenth century, the foundations of calculus were confusing and unclear, and many English mathematicians, perhaps because they were still bound by the geometry of ancient Greece, doubted the full extent of calculus' work.

It was not until the second half of the nineteenth century that this problem was completely solved by the French mathematician Cauchy, whose criterion of limit existence injected rigor into calculus, which was the creation of the limit theory. The creation of the limit theory allowed calculus to be based on rigorous analysis, and it also laid the foundation for the development of mathematics in the 20th century.

1 All calculus is developed in connection with practical application, and it has more and more extensive applications in astronomy, mechanics, chemistry, biology, engineering, economics and other natural sciences, social sciences and applied sciences. In particular, the invention of the computer has contributed to the continuous development of these applications.

Everything in the objective world, from the smallest particles to the largest universe, is always in motion and changing. Therefore, after the introduction of the concept of variables in mathematics, it is possible to describe the phenomenon of motion mathematically.

Due to the deepening of the concept of functions and the deepening of their application, as well as the needs of the development of science and technology, a new branch of mathematics was born after analytic geometry, which is calculus. Calculus is a very important discipline in the development of mathematics, and it can be said that it is the largest creation of all mathematics after Euclidean geometry.

Calculus is the branch of mathematics that studies the differentiation and integration of functions, as well as concepts and applications. Calculus is based on real numbers, functions, and limits. Calculus is ubiquitous in real life and can be said to be closely related to our lives.

The application of calculus can manifest itself in many different aspects of life. Calculus is developed in connection with practical application, and it has become more and more widely used in astronomy, mechanics, chemistry, biology, engineering, economics and other branches of natural science, social science and applied science. In particular, the invention of the computer has contributed to the continuous development of these applications.

For example, the application of calculus in investment decision-making: elementary mathematics is widely used in economic life, for example, in investment decision-making, if the deposit method is in an even flow, that is, the funds are deposited in the bank on a regular basis in the same way as a flow, then the calculation of the median value after 1 year can be calculated by way of definite integral. For example, an enterprise invests 200 million yuan in a project at one time, and completes it one year after the top, and obtains economic returns.

If you ignore the time value of the money, it will pay for itself in 5 years, but if you take the time value of the money into account, the situation may change. Therefore, the application of calculus makes investment more rational, which can take risks and increase returns.

For example, if you want to do something that you think is quite different from your current abilities; You might as well divide it into a number or many steps according to a certain law, your first step should be within your current ability, and then the second step is close to the requirements of the first step ability, so that step by step, you can reach the final goal. Explained in the social sciences, it is the principle of gradual and gradual improvement, but as a direct operation, we can learn from the idea of differentiation.

For example, for an object with irregular density, the mass can be found ...... and so onBasically, anything can be studied with it.