ABSTRACT
This chapter introduces the mathematical concept of dynamic systems, and then presents methods for their solutions. It discusses special linear methods and introduces decompositions to reduce specially structured high-dimensional problems to smaller dimensional ones. The term dynamic refers to phenomena that produce time-changing patterns and the characteristics of the pattern at one time being interrelated with those of other times. The chapter shows that by using appropriate matrix transformations, matrices can be transformed into special forms. It presents the methods based on the fundamental matrix. Because the solution is obtained directly using the state vector, this methodology is called the state-space approach. The other method is based on Laplace transforms, and it is called the transfer function approach, because it is based on a special relation between the Laplace transforms of the input and output functions, which is known as the transfer function.
