Many people say that learning engineering mechanics well means learning mathematics well, what do yo

I feel like I'm only partially right. For engineering mechanics, the establishment of a reasonable mechanical model is far more important than learning mathematics. After the mechanical model is established and the methods and mathematical tools are used to solve it, it is more necessary to have a broad horizon and an in-depth understanding and application ability of mathematics.

There are many people who have a very good mathematical foundation, but they can't even get a proper mechanical model for practical problems, let alone solve them.

Disagree. This idea is similar to "soccer players have to run fast" or "basketball players have to be taller". Mechanics requires a lot of mathematical knowledge, there's no doubt about that.

But mechanics requires more understanding of physical problems, and mathematics is only a tool used to abstract mechanical problems. In many mechanical work, the most critical step is to find the key physical phenomenon or governing physical law of the problem, and then, if necessary, to find the appropriate mathematical tools to describe and solve the mechanical problem.

I think, first of all, mathematics plays a very important role in the learning process of mechanics majors, but it should be noted that the mathematics required by mechanics majors and the mathematics studied by mathematics majors are not the same thing! Secondly, compared with the foundation of mathematics, the mechanics major needs more cultivation in mechanics. To put it simply, this kind of cultivation is to write mathematics in your hand and think about mechanics in your heart.

In fact, the essence of mechanics is mathematics, which is the medium of mathematics application in the engineering community, civil engineering, electrical engineering, mechanical engineering, etc. contain a lot of mathematical knowledge, and these knowledge is transmitted through engineering mechanics. My undergraduate teachers also repeatedly emphasized that mathematics is the foundation of learning mechanics well, and when we reached graduate school, we still regarded mathematics as the main subject, including advanced numerical analysis, applied mathematical statistics, matrix theory, and so on.

Many problems in mechanics revolve around differential equations and partial differential equations about displacement fields and strain fields, and the solution of these equations includes numerical solutions, that is, the finite element method, precise analytical solutions (simple analysis problems of structural forms and loads can be found, such as static and dynamic analysis of beams and plates), and perturbation methods that tend to analytic solutions (with limitations), in fact, they are all playing with mathematics.

I can't agree, I think engineering mechanics is easier to learn than mathematics, and the two fields are not the same. However, I have to admit that one of the reasons why many engineering students (including me) struggle to learn later is that they don't learn the mathematical foundation well.

Our professor in the Department of Mechanics said that if possible, he would like to study mathematics as an undergraduate. If the mathematical tools are well mastered, it will be easier to understand the physical nature of the derivation and proof of mechanical equations without being trapped in the details.

For mechanics, mathematics is just a tool. Since mechanics makes more use of mathematics and its way of thinking, it will prompt you to learn mathematics well, in theoretical research, the requirements of mathematics in the Department of Mechanics are similar to those of the Department of Mathematics fifty years ago. As for the computational simulations that are more popular now, whether they are solid or liquid, the requirements for numerical methods are basically not much different from those of the mathematics department.

It is the existence of these basic theories that ensures the existence and uniqueness of the solutions to mechanical equations (the most typical embodiment is the famous Lax-Milgram Lemma); It is also the foundation of these theoretical foundations that enables the construction of numerical solutions. Functional analysis, Sobolev space theory, etc., are the conventional tools used in modern mechanics research. <>

It takes time to learn well, and that's how it is in college, it's easy to mix enough credits, but it's hard to know why.

Continuum mechanics is complex and of course requires a lot of mathematical foundation, as individuals can see

Calculus (if you are a freshman, it is recommended to look at mathematical analysis), linear algebra (please see advanced algebra for more time), complex variable functions, ordinary differential equations, tensor analysis, mathematical physics methods, real functions and functional analysis, partial differential equations, etc., if it is required by the undergraduate, the first four subjects are enough, more mathematical knowledge will be supplemented in relevant books, but it is not guaranteed that you can understand it all.

In addition, there is an independent mind, and you have to study with a skeptical attitude like a science student, so that you can build a structure of knowledge, otherwise learning more is just fat in the brain.

Whatever you want, it's not necessarily true:

Calculus, linear algebra, tensor analysis.