 Department
 People
 Studies
Studies in DCEup
Graduate Studies
PhD Program
 New Admissions
 General Description
 Program Requirements
 Courses
 Class Schedule
 Oral presentation
 Research Work
 PhD Thesis Defense
 Previous PhD Theses
Master's Program
 Students
 Alumni
ChemEngUP Alumni
 Research
 News & Events
Module Notes
Undergraduate, 3rd Semester (2nd Year, Fall)
Module Category:
Compulsory Modules
Module Type:
Background Courses
Teaching Language:
Greek
Course Code:
CHM_300
Credits:
4
ECTS Credits:
6
Teaching Type:
Lectures (3h/W)
Τutorial (2h/W)
Project/Homework (10/Semester)
Module Availability on Erasmus Students:
No
Course URL:
EClass (CMNG2174)
Module Details
 Application of mathematics in the solution of engineering problems
 Formulation of mathematical models for the solution of engineering problems

In the end of the class the students should be able to:
 Find general and particular solutions of first order differential equations.
 Solve second order linear differential equations with constant coefficients
 Use the method of power series for the solution of linear differential equations
 Find and use appropriately the solutions of the Bessel and Legendre differential equations.
 Use the Laplace transform and its inverse for the solution of ordinary differential equations
 Solve linear systems of ordinary differential equations with constant coefficients
 Investigate the qualitative behavior of the solution of a nonlinear differential equation without solving it
None
Ordinary differential equations (ODEs) basic concept and ideas. First order ODEs. Separable ODEs. Exact ODEs. Linear ODEs and Bernoulli equation. Homogeneous ODEs. Special form first order ODEs. Integrating factors. Linear second order ODEs. Homogeneous linear second order equations. Second order homogeneous ODEs with constant coefficients.
Nonhomogeneous equations. Solution by undetermined coefficients. Solution by variation of parameters. Power series solution of differential equations. Legendre’s equation. Frobenious method. Bessel’s equation and functions. Laplace transforms and their properties. Transforms of step and delta functions. Solution of ODEs by Laplace transform. Systems of ODEs. Transformation of higher order ODEs to a system of first order ODEs. Linear systems and the Wronski determinant. Homogeneous systems with constant coefficients. Graphical representation of solutions and the phase plane. Critical points and their stability. Qualitative solution of nonlinear systems of ODEs.
LECTURES: 3 h/w
RECITATION: 2 h/w
PROJECT/HOMEWORK: 10/semester
Total Module Workload (ECTS Standards):
180 Hours
Written Examination
The results of the final written and/or oral examination are multiplied by a factor based on the performance of the student in the written tests given during the semester.
 Δάσιος Γ., Συνήθεις Διαφορικές Εξισώσεις, Πάτρα, 1991.
 Σταυρακάκης Ν., Συνήθεις Διαφορικές Εξισώσεις, Εκδ. Παπασωτηρίου, Αθήνα, 1997.
 Τραχανάς Σ., Συνήθεις Διαφορικές Εξισώσεις, Παν. Εκδόσεις Κρήτης, Ηράκλειο, 2005.
 Kreyszig E., Advanced Engineering Mathematics, 8^{th} edition, Wiley, 1998.
 Bronson R., Εισαγωγή στις Διαφορικές Εξισώσεις, McGraw Hill, ΕΣΠΙ, 1978.
 Κρόκος Ι., Διαφορικές Εξισώσεις, Αρνος, 2005.
 Greenberg M., Advanced Engineering Mathematics, 2^{nd} Edition, Prentice Hall, 1998.
 Zill, D. G., Advanced Engineering Mathematics, 3^{rd} Edition, Jones & Burtlett, 2006.
 Αλικάκος Ν. Δ. και Καλογερόπουλος Γ. Η., Συνήθεις διαφορικές εξισώσεις, Αθήνα Σύγχρονη Εκδοτική, 2003.
 O’Neil P. V., Advanced Engineering Mathematics, 4^{th} edition, Boston PWS, 1995.
 Wylie C. R. and Barrett L. C., Advanced Engineering Mathematics, 6^{th} edition, McGraw Hill, 1995.