In this masters thesis, we first present the basic theory of systems of linear differential equations of first order. We mostly focus on solving the appropriate homogeneous system, introduce the fundamental matrix and show how to solve a diagonalizable system and how to solve a general system using the exponential function on matrices. We apply the theory on the problem of modeling the concentration of a solvent in a solution that flows inside a system of tanks connected by pipes. We will look at star arrangements, linear arrangements and circular arrangements of tanks.
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