The course covers basic notions of differential equations and methods for their solution. More precisely the course covers:
i. Basic notions of ODEs, 1st order ODEs, orthogonal trajectories.
ii. Linear ODEs of higher order, homogeneous and nonhomogeneous
iii. Systems of ODEs. Basic notions. Solution by means of eigenvalues and eigenvectors.
iv. Basic notions of PDEs.
v. Laplace transform and its application to the solution of ODEs and PDEs.
vi. Fourier transform and its application to the solution of ODEs and PDEs.
vii. Boundary value problems and eigenvalue problems. Fourier series.
viii. Solution of PDEs using the separation of variables method.
ix. Applications of ODES, systems of ODEs and PDEs to problems of Civil Engineering.
x. Use of a scientific package of symbolic computations at the laboratory for the solution of problems regarding the above mentioned topics.