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What are the applications of linear algebra in mechanical engineering?
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A, mechanical engineering services:

All departments that use machinery and tools, as well as energy and material production, need mechanical engineering services. Modern mechanical engineering has five service fields: ① developing and providing energy conversion machinery, including various power machinery that converts thermal energy, chemical energy, atomic energy, electric energy, fluid pressure energy and natural mechanical energy into mechanical energy suitable for application, and energy conversion machinery that converts mechanical energy into other required energy. (2) develop and provide machinery for producing various products, including agriculture, forestry, animal husbandry, fishery machinery and mining machinery, as well as various heavy industry machinery and light industry machinery. (3) Develop and provide machinery engaged in various services, such as material handling machinery, transportation machinery, medical machinery, office machinery, ventilation, heating and air conditioning equipment and environmental protection equipment such as dust removal, purification and noise elimination. (4) Develop and provide machinery for family and personal life, such as washing machines, refrigerators, clocks, cameras, sports equipment and entertainment equipment. ⑤ Develop and supply all kinds of mechanical weapons.

Second, the course content of linear algebra:

Linear algebra serves to cultivate high-quality professionals needed by China's socialist modernization. Through the study of this course, linear algebra can be roughly divided into two parts, one is the theory of determinant, linear equation and matrix, and the other is the theory of space, which mainly includes linear space, linear transformation, canonical form, Euclidean space and so on.

The numerical solution of complex linear equations is a common problem in the field of mechanical engineering, and some multi-solution problems in mechanical engineering, such as mechanism configuration, tree-like solution of robot mechanism and multi-solution of design scheme, often need some theoretical solutions of linear equations in linear algebra. The formulas in linear algebra are generally applicable to all kinds of carbon steel and alloy steel that can be quenched and hardened. In fact, these equations can be regarded as a quantitative scale, which is widely used in designing or selecting steel grades, formulating or revising standards, controlling melting components and so on. In addition, it is also helpful to establish a complete calculation system of composition, microstructure and properties. This has made great contributions to the field of mechanical engineering.

The application of determinant in mathematical analysis, geometry, linear equations theory, quadratic theory and many other aspects has laid the foundation for us to learn linear equations in the future.

Matrix theory includes: linear space, linear transformation, inner product space, orthogonal projection, Jordan canonical form, norm theory and so on.

In matrix theory, there is a matrix diagram method. Matrix method is widely used in engineering management. ① When there are many undesirable phenomena in the production process and they have several common causes, find out the relationship between these undesirable phenomena and their causes, and then eliminate them in one fell swoop.

Except ... (2) it is helpful to develop new products or improve the starting point of old products, ensure the quality characteristics of products and improve production efficiency.

According to the current international standards, linear algebra is expressed by axiomatization. It is the second generation mathematical model, and its roots come from Euclidean geometry, analytic geometry and the theory of linear equations. Personally, I have a plan, that is, I will take the postgraduate entrance examination after finishing college. Look up information on the Internet. There is a course of linear algebra in postgraduate courses, so we should learn linear algebra well. And because I study mechanical engineering, if I am not familiar with the concepts of linear algebra, such as linear properties, vectors, linear spaces, matrices and so on. It is basically difficult to learn natural science and study new products, and linear algebra is involved. Although not all, it is necessary to study hard, which will lay a good foundation for your major and future.