On the implementation of thefouriermethodfor the solution ofhyperbolicand parabolic equations

Learning the methods of solving limit value and initial value problems is one of the main problems for partial differential equations. One of the most used methods is Fourier method that is termed the separation of variables method. Non- trivial solve of limit value and initial value problems is searched for a solution according to functions product related to each variable in Fourier method. Ordinary differential equations are taken for these functions by writing this solution in equation. Suitable conditions for each equation are found by considering to the matter in problem's limit and initial condition. In this thesis, limit value and initial value problems' solutions were learned with examples of the application by the Fourier method for hyperbolic and parabolic type partial differential equations. Also, finding the solution was shown application of limit value and initial value problems' solutions by the Fourier method in various examples. When learning of the separation of variables method, resources that should be used was used to solution of hyperbolic and parabolic differential equations.