Introduction to Differential Equations (definitions, the notion of the solution, Initial and
boundary value problems, Well-posed problems), Separable equations, Linear equations of
1st order, Homogeneous equations, Exact equations and integrating factors, Linear equations
of n-order, General theory, Linear independence and Wronskian, Method of reduction of
order, Homogeneous equations with constant coefficients, Method of variation of parameters,
Method of undetermined coefficients, Euler equation, Series solutions of second order linear
equations, Series solutions near an ordinary point, Legendre equation, Series solutions near a
regular singular point, The Laplace transform, Definition and properties, The step function,
Solution of linear equations with discontinuous forcing function, Convolution and Laplace
transform, Solution of integral equations of special type, Systems of 1st order linear equations,
Solution of homogeneous and nonhomogeneous systems with constant coefficients, Real,
complex, repeated eigenvalues, The phase plane for linear systems, Autonomous systems and
stability, Fourier series, the convergence theorem, Sine and cosine series, Sturm-Liouville
boundary value problems, Derivation of diffusion equation via Fick’s law, Solution of initialboundary value problems for the heat conduction equation using separation of variables with
homogeneous and nonhomogeneous boundary conditions.
- Teacher: Βασίλειος Καλπακίδης
- Teacher: Ελευθέριος Πρωτοπαπάς
ECTS : 5
Language : el
Learning Outcomes : Not provided.