In many problems of the everyday life we deal with the change of a quantity, of our interest, in relation to time (rate of change). Differential equations are the proper tool used for (mathematical) modeling and solving these problems. The aim of the course is to introduce (i) basic concepts of differential equations and (ii) techniques for solving o.d.e.’s (iii) some of their applications in basic problems of Engineering, electromagnetism, the Environment, etc.

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

• Recognizes the different types of differential equations
• Solve differential equations.
• Interprets the solutions of differential equations.
• Uses differential equations to model natural phenomena.

• Work autonomously
• work in teams
•  Retrieve, analyze and synthesize data and information, with the use of proper technologies.
• advance free, creative and causative thinking.

1. Introduction to Ordinary Differential Equations (definition of an O.D.E, order, degree, solution of an O.D.E. e.t.c.)
2. Ordinary Differential Equations of 1st order: separation of variables, homogenous.
3. Ordinary Differential Equations of 1st order: Bernoulli, Riccati, Euler, exact o.d.e’s.
4. Method of integrating factor. 1st order linear differential equations.
5. Applications of 1st order o.d.e.’s to problems in Chemical and Environmental Engineering.
6. Linear dependence/ independence condition, Wroskian, the y = gY transformation.
7. Linear differential equations of higher order with constant coefficients: homogenous.
8. Linear differential equations of higher order with constant coefficients: non homogenous.
9. Linear differential equations of higher order with non constant coefficients.
10. Laplace’ s transformation method.
11. Applications of higher order O.D.E in Engineering and electricity.
12. Power series method.
13. Systems of differential equations with constant coefficients.

Assessment Method

• Theoretical problems to be resolved.

OR

I. Midterm exams (100%=50%+50%)

II. Problems/Exercises during the semester (Bonus 10%).

• W. E. Boyce - R. C. Diprima, Elementary differential equations and boundary value problems,  1999, Ed. E.M.P. (in Greek)
• Trahanas S., elementary differential equations,  2008, Ed C.U.P.. (in Greek)
• Y.A.Cengel, W.J.Palm III, Differential equations for engineers and scientists, 2017,Ed Tziola. (in Greek)
• E-class notes