Series solutions of differential equations

In the first part of the thesis, we evaluated the importance and application areas of differential equations. In the second chapter, we have been informed about the historical development of differential equations which are encountered in engineering, physics and mathematics branches and mostly encountered in applications. In the third chapter, we discussed some of the definitions and theories that we need to know in order to better understand the solution method of differential equations by serial method. In the fourth chapter, we have obtained the solutions of differential equations by using Fourier series, Frobenius and Adomian decomposition methods.