Mathematics III (ordinary differential equations)

Mathematics III is the course which includes the study of:

1. First Order Differential Equations (solve first order differential equations which are exact, separable, homogeneous, linear, Bernoulli or Riccati, understand the existence and uniqueness theorem),
2. Higher Order Linear Differential Equations (understand the general theory, solve higher order differential equations with constant coefficients, apply the methods of undetermined coefficients and variation of parameters, solve higher order differential equations with series),
3. Laplace transforms (solve higher order differential equations with constant coefficients especially in the case where the inhomogeneous part is expressed as a Heaviside of a Dirac function, understand and apply convolution theorem),
4. First Order System of Linear Ordinary Differential Equations (understand the general theory, solve a system using the eigenvalues and the eigenvectors of a matrix, apply the methods of undetermined coefficients and variation of parameters),
5. Fourier series.