Study of differential equations. Qualitative theory and basic methods of solving differential equations and systems. Applications to modeling physical problems.
# | Title | Description | Hours |
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1 | Introduction | Derivation - mathematical models, concept of a differential equation, classification, concept of solution, initial boundary value problems, well-posed problems | 2 |
2 | First-order Differential Equations | Linear equations of separated variables, exact differential equation and integrating factors, homogeneous, formulation of the theory of existence and uniqueness, modeling of physical problems. | 8 |
3 | Linear Differential Equations | Theory of homogeneous differential equation, linear independence of functions or solutions and Wronskian determinant, Abel's theorem, reduction of the order - d'Alembert's method, non-homogeneous differential equation and the method of varying coefficients - Lagrange method, equations with constant coefficients, characteristic polynomial-simple, multiple, complex roots, method of determining coefficients. | 8 |
4 | Laplace Transform | Definition, solving initial value problems, Heaviside and Dirac functions, equations with discontinuous non-homogeneous term, convolution theorem, Volterra equations | 6 |
5 | First Order Systems Differential Equation | Homogeneous linear with constant coefficients, complex, multiple eigenvalues, phase portrait, autonomous systems and stability, non-homogeneous linear systems | 6 |
6 | Solving Linear Second Order using Power Series | Solution in a regular point, Legendre equation, Legendre polynomials, Euler equation, solutions near a regular singular point, Bessel equation | 6 |
7 | Trigonometric Fourier Series | Fourier-Euler coefficients, convergence theorem, even and odd functions -cos and sin expansions, complex form of Fourier series | 4 |
8 | BoundaryValue Problems | Homogeneous Sturm-Liouville problems, eigenvalues and eigenfunctions | 4 |
9 | Separation of Variables | Wave equation-vibrations of an elastic string, D'Alebert's solution. The method of separation of variables in two and three dimensions. Modeling of physical problems | 8 |
Upon successful completion of the course, students will be able to:
Teaching methods | Lectures in class. Solving simple examples and problems in the classroom. |
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Teaching media | Blackboard. Programming with Matlab. |
Laboratories | Yes. |
Computer and software use | Students solve in the class with the help of tutors simple exercises using mainly Matlab in PC. |
Problems - Applications | Exercises |
Student presentations | Νο |
1 W.BOYCE - R.DIPRIMA, ΣΤΟΙΧΕΙΩΔΕΙΣ ΔΙΑΦΟΡΙΚΕΣ ΕΞΙΣΩΣΕΙΣ ΚΑΙ ΠΡΟΒΛΗΜΑΤΑ ΣΥΝΟΡΙΑΚΩΝ ΤΙΜΩΝ, ΠΑΝ. ΕΚΔΟΣΕΙΣ ΕΜΠ, 2015 2 Ν.Δ.ΑΛΙΚΑΚΟΣ, ΚΑΛΟΓΕΡΟΠΟΥ-ΛΟΣ Γ.Η., ΣΥΝΗΘΕΙΣ ΔΙΑΦΟΡΙΚΕΣ ΕΞΙΣΩΣΕΙΣ, ΣΥΓΧΡΟΝΗ ΕΚΔΟΤΙΚΗ, 2003. 3 Ι. ΠΟΛΥΡΑΚΗΣ, ΣΥΝΗΘΕΙΣ ΔΙΑΦΟΡΙΚΕΣ ΕΞΙΣΩΣΕΙΣ, Ι. ΠΟΛΥΡΑΚΗΣ, 1998 4 Γ.Παντελίδης, Δ.Κραββαρίτης, Ν.Χατζησάββας, Συνήθεις Διαφορικές Εξισώσεις, Ζήτη, 1990