The Students will be able to
1. solve first order differential equations using an appropriate method.
2. model simple physical models and study their evolution by using differential equations
3. solve special equations of higher order Differential equations which are related with particular physical models.
4. solve Linear equations/systems.
5. to understand the notion of solution of a partial differential equation and solve 1st order linear equations and some particular linear equations of higher order.
Course Content (Syllabus)
1 Introduction and solution existence theorems
2 Ordinary Differential equations (ODEs) of 1st order (separable,homogeneous, linear, exact, special cases
3 Problems with differential equations of 1st order
4 Special forms of higher order ODEs
5 Linear ODEs, theory of solutions. Linear ODEs with constant coefficients
6 Linear Oscillators - problems
7 Linear systems (2x2) of ODEs with constant coefficients
8 Problems with Linear systems (2x2). Systems with higher dimensions
9 Introductionary concepts of nonlinear systems of ODEs
10 Introduction to partial differential equations (PDEs)
11 Solutions of PDEs of 1st order
12 Linear PDEs of higher order with constant coefficients
Course Bibliography (Eudoxus)
ΔΙΑΦΟΡΙΚΕΣ ΕΞΙΣΩΣΕΙΣ ΚΑΙ ΕΦΑΡΜΟΓΕΣ, Βουγιατζής Γεώργιος Β., Μπόζης Γεώργιος Δ.,Παπαδόπουλος Δημήτριος Β. ΕΚΔΟΣΕΙΣ ΚΛΕΙΔΑΡΙΘΜΟΣ 2012
ΔΙΑΦΟΡΙΚΕΣ ΕΞΙΣΩΣΕΙΣ, ΘΩΜΑΣ ΚΥΒΕΝΤΙΔΗΣ, ΕΚΔΟΣΕΙΣ ΚΥΒΕΝΤΙΔΗ 2007
ΣΥΝΗΘΕΙΣ ΔΙΑΦΟΡΙΚΕΣ ΕΞΙΣΩΣΕΙΣ, ΤΡΑΧΑΝΑΣ ΣΤΕΦΑΝΟΣ, ΠΑΝΕΠΙΣΤΗΜΙΑΚΕΣ ΕΚΔΟΣΕΙΣ ΚΡΗΤΗΣ, 2008