Μαθηματικά IV (Διαφορικές Εξισώσεις)

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.