Introduction. First-order ordinary differential equations. Separable equations. Exact equations, integrating factors. Linear equations. Solution via substitution. Higher-order ordinary differential equations. Linear equations with constant coefficients. Order reduction. Solution of inhomogeneous differential equations. Laplace transform and its use for solving differential equations. Series solution of differential equations, ordinary and singular points. Systems of differential equations, solution with the matrix method. Complex numbers. Complex functions. Differentiation of complex functions. Integration of complex functions.

Upon successful completion of this course, students will be able:

• to recognize the mathematical models for certain physical problems,
• to identify the general form of differential equations,
• to apply appropriate methods for determining partial and general solutions,
• to solve initial value problems,
• to determine solutions in the form of power series,
• to exploit the Laplace transform,
• to solve systems of differential equations,
• to graphically solve certain types of differential equations,
• to deal with fundamental problems of complex analysis.

Elements of the following courses are required: 
Mathematical Analysis Ι
Mathematical Analysis ΙΙ
Linear Algebra

Summative mid-term written assessment (25%) and
summative final written assessment (75%) in Greek. The
adequacy of theoretical knowledge, the ability to apply
specific methodologies and the ability to solve problems
under specific time constraints are tested. The evaluation
criteria refer to the validity of the answers, as well as to the
degree of their clarity and completeness. Oral exams are
provided for students with learning difficulties. The criteria
can be accessed by students via the platform
eclass.uowm.gr.

1. W. E. Boyce R. C. Diprima, Στοιχειώδεις Διαφορικές Εξισώ-
σεις & Προβλήματα Συνοριακών Τιμών, ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ
ΠΟΛΥΤΕΧΝΕΙΟ, Έκδοση: 2η/2015.
2. Θ. Ρασσιάς, Μαθηματικά ΙΙ β έκδοση, ΤΣΟΤΡΑΣ ΑΝ ΑΘΑΝΑ-
ΣΙΟΣ, Έκδοση: 2η/2017.
3. Τραχανάς Στέφανος, Συνήθεις Διαφορικές Εξισώσεις, ΠΑ-
ΝΕΠΙΣΤΗΜΙΑΚΕΣ ΕΚΔΟΣΕΙΣ ΚΡΗΤΗΣ, 2008.
4. Κάρολος Σεραφειμίδης, Διαφορικές Εξισώσεις, Εκδόσεις
"σοφία", 2010.
5. ΝΙΚΟΛΑΟΣ M. ΣΤΑΥΡΑΚΑΚΗΣ, Διαφορικές Εξισώσεις: Συνή-
θεις και Μερικές. Θεωρία και Εφαρμογές από τη Φύση και
τη Ζωή, ΤΣΟΤΡΑΣ ΑΝ ΑΘΑΝΑΣΙΟΣ, Έκδοση: 2η/2017.
6. Μυλωνάς Νίκος, Σχοινάς Χρήστος, Διαφορικές Εξισώσεις,
Μετασχηματισμοί και Μιγαδικές Συναρτήσεις, ΕΚΔΟΣΕΙΣ Α.
ΤΖΙΟΛΑ & ΥΙΟΙ, Έκδοση: 1η/2015.
7. Κραββαρίτης Δ., Εισαγωγή στις Διαφορικές εξισώσεις,
ΤΣΟΤΡΑΣ ΑΝ ΑΘΑΝΑΣΙΟΣ, Έκδοση: 1η/2014.
8. David Logan, J., A First Course in Differential Equations
[electronic resource], Heal-Link/Σύνδεσμος Ελληνικών
Ακαδημαϊκών Βιβλιοθηκών.
9. Soare, Mircea V. Teodorescu, Petre P. Toma, Ileana,
Ordinary Differential Equations with Applications to
Mechanics [electronic resource], Heal Link/Σύνδεσμος Ελ-
ληνικών Ακαδημαϊκών Βιβλιοθηκών.