Linear algebra is the branch of science that deals with linear equations, vectors, vector spaces, linear transformations, and systems of vectors. It has many applications that spread from science and engineering to the natural and social sciences.
Analytical geometry can express three dimensional space i.e. a graphs can not have more than three dimensions. Nevertheless, with linear algebra one can express a space with more than three dimensions and represent it in the form of data sets then computer simulations can be used that use certain techniques to represent and manipulate multidimensional systems without the need to represent data visually.
This subject's applications in science and engineering are not only restricted to modeling but extend a lot further than that. This subject has many other applications for example the analysis of rotation in space, curve fitting techniques and the differential equations solutions. It has more advanced applications like the engineering modeling of satellite and airplane engines. This is just a small example of linear algebra applications in science and engineering. There are many books written only on its engineering applications.
In arts, humanities, and social sciences, on the other hand, linear algebra has a saying. Imagine a musician or an artist playing on an instrument or a singer tuning his or her voice to make a pleasant sound that is appealing to the ear. Sound is all about wave frequencies. When a sound appeals to the ear this is because it is tuned in a certain frequency range and it has specific wave characteristics. By analyzing the frequency domain of the sound that appeals to the ear one can produce the desired tones at will and become in control of making the sound desirable to the ear. The knowledge of the frequency spectrum is used in the tuning of musical instruments.
Frequencies have many interesting applications in our every day lives. There is a very interesting story I heard about and I would like to share. In the nineteenth century in Manchester soldiers were marching on a bridge and the bridge suddenly collapsed. The reason for this was because the frequency of the waves produced by the soldiers as they marched across the bridge was equal to the natural resonance frequency of the bridge this caused the bridge to oscillate and collapse. In our day today soldiers are required to cut the rhythm of their march while crossing bridges.
For the diversity of applications of linear algebra the engineering student, regardless of his specialty, should study it. Some might say that the student should study only the applications that are of relevance to his specialization whether electrical, mechanical... etc. I disagree with them and I think the student should cover as diverse applications as possible because this will give him the sense of reflecting these mathematical principles on real physical life. When he sees the equations and laws he will see its physical manifestation in real world. This will give him enough insight to be able to even create new applications from the mathematical laws.
I suggest that engineering students should study two courses in linear algebra. The first one at the 300 level undergraduate and introduces all the relevant mathematics and just touches the subject of applications. This course should be compulsory for all engineering students. The second course should be a 400 level course dedicated to applications and the student should do a project of applying linear algebra techniques to solve or explain a real life problem. This second course should be optional but compulsory only to students of the school of mathematical modeling in engineering or the school of engineering mathematics
Article Source: http://EzineArticles.com/?expert=Khaled_Omran
No comments:
Post a Comment