Submitted by: Khaled Omran
Linear algebra is the branch of science that deals with linear equations, vectors, vector spaces, linear transformations, and systems of vector matrix. It has many applications not only in science and engineering but in the natural and social sciences as well.
Analytical geometry can not express more than a three dimensional space i.e. a graph can not have more than three dimensions. However, with linear algebra a multiple dimension space to any level can be expressed and represented as data sets. This way one can use computer simulations using it’s techniques to represent and manipulate multidimensional systems without the need to visually represent data.
It’s applications in science and engineering are not only restricted to modeling but extend much further than that. It has many applications for example the analysis of rotation in space, curve fitting techniques and the solution of differential equations. It has more advanced applications like the engineering modeling of satellite and airplane engines. This is just a small example for it’s applications in science and engineering. There are many books written only on the engineering applications of linear algebra.
In arts and social sciences, on the other hand, it has a saying. Imagine a musician playing on an instrument or a singer tuning his or her voice to make a nice sound that appeals to the audience. Sound is all about wave frequencies. The sound that appeals to the ear is because it is in a specific 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 for the ear.
Frequencies and their effect has many interesting applications in our every day lives. There is a very interesting story I heard about that I would like to share. In the nineteenth century in Manchester soldiers were marching on a bridge and the bridge suddenly started to collapse. The reason for this was because the frequency of the waves produced by the soldiers marching was equal to the natural resonance frequency of the bridge this caused the bridge oscillate and thus collapse. This is why in our day today soldiers are required to cut the rhythm of their march while crossing bridges.
For the many diverse applications of this branch of mathematics the engineering student regardless of his specialty should study it. One might argue that the student should study only the applications that are relevant to his specialization whether electrical, mechanical, etc. I disagree with this point and I think he should cover as diverse applications as possible Because this will give the engineer the sense of the reflection of the mathematical principles on real physical life. When he sees the equations and laws he will see its physical manifestation in real life. This will give him enough insight to be able to even create new applications from the mathematical laws and formulae.
My suggestion is that there should be two courses in linear algebra. The first one at the 300 level and introduces all it’s mathematics and just touches the subject of it’s 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 it’s techniques to solve or explain some real life problems. The second course should be optional but compulsory only to students of the school of mathematical modeling in engineering or the school of engineering mathematics
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