**Course Description: **

1- Solution of Hermite equation by general power series and the proof of orthogonality of Hermite polynomials and recurrence relations for Hermite polynomials using the generating function and rodrigues formula

2- Solution of Legendre equation by general power series and the proof of orthogonality of Lagedre polynomials and recurrence relations for Lagedre polynomials using the generating function and rodrigues formula

3-Solution of Laguerre equation

4-Fourier Series, properties of Fourier Series ,summation of Fourier series , the complex form of Fourier series

5-Fourier transforms and Laplace transforms

6-Solution of differential equations by Fourier transforms and Laplace transforms