Ebook: Lineära system

The content of the course Linear Systems has remained largely unchanged since it was first given in the fall of 1981. During this time the development of personal computers has meant a revolution in the possibilities for the engineer to use mathematics. With numerical and symbolic programs such as Matlab and Maple, you can now easily perform calculations on your desk that were almost unthinkable in 1981. However, the theoretical background is still the same, and is becoming more and more important the more calculations are handed over to computers. This means that the course has not lost any of its relevance. Nor does the possibility of having computers do the calculations make the solution of simple exercises by hand superfluous. In this, as in many other higher level mathematics courses, the exercises are more likely to help you understand the theory and concepts than the other way around. However, the reader is encouraged to try Matlab and Maple (which are available on school computers for those taking the course at LTH) and see how powerful tools such programs are.

The course is taken after a total of one semester (20 credits) of mathematical studies at the university. The areas covered are in many cases in higher mathematics, and it is clear that one cannot expect a deep and complete treatment of the problems. Moreover, the readers do not have the background in technical subjects that would be needed to get a full understanding of the problems. The author has therefore used a lot of space to discuss the relationships between the mathematics and the applications. However, it should be noted that the course is not a textbook in circuit theory or systems engineering, but the application examples should be seen as samples of what mathematics can be used for. It is also the case that all the methods described are used just as much in classical and modern physics as in control engineering and signal theory.