Applied Mathematics III
Instructor: Petropoulou Eugenia
Course code: 5301
Semester: 3ο
Course content:

  1. Basic notions of ODEs. 1st  order ODEs (ODEs with separable variables, ODEs with homogeneous coefficients, linear ODEs, Bernoulli equations, exact ODEs, ODEs that can be reduced to exact), orthogonal trajectories.
  2. Linear ODEs of higher order, homogeneous and nonhomogeneous, with constant or nonconstant coefficients. Euler ODEs. Boundary value problems and eigenvalue problems.
  3. Systems of ODEs (Reduction to one ODE, diagonalization method).
  4. Fourier series.
  5. Basic notions of PDEs. General solutions for special classes of PDEs (D’Alembert's solution, the method of characteristic equation).
  6. Solution of PDEs using the separation of variables method.
  7. Laplace transform and its application to the solution of ODEs and PDEs.
  8. Fourier transform and its application to the solution of ODEs and PDEs
  9. Use of MuPad at the laboratories for the solution of problems regarding the above mentioned topics.

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