Differential Equations

Prerequisite Knowledge

Analysis I, Analysis II (Basic concepts for the last unit), Linear Algebra Εφαρμογές

Course Units

#	Title	Description	Hours
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

Learning Objectives

Upon successful completion of the course, students will be able to:

1. Know the important role of differential equations.
2. To have the ability to model using ordinary and partial differential equations.
3. Understand the importance of analytical and theoretical methods of problem solving

Teaching Methods

Teaching methods	Lectures in class. Solving simple examples and problems in the classroom.
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

Student Assessment

• Final written exam: 70%
• Assignments (projects, reports): 30%

Textbooks - Bibliography

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

Lecture Time - Place:

• Tuesday, 12:45 – 14:30,
  Rooms:
  • Αμφ. 1/2
• Friday, 10:45 – 13:30,
  Rooms:
  • Αμφ. 1/2