In many problems / systems of everyday life we ​care about  the change of a quantity (variable) of our interest w.r.t. time (rate of change). In order to model (mathematically) and solve these problems we use differential equations. The role of d.e. is therefore a protagonist in many scientific fields, especially in engineering. The purpose of this undergraduate course is to introduce basic concepts and techniques to students in order to be able to solve ordinary differential equations. Furthermore, applications of d.e. are being presented in basic problems/fields of Mechanics, Electromagnetism, Environment and so on.

The aim of the course is also, to give the students the ability to use differential equations to model natural phenomena / situations, to be able to solve such equations and to interpret the solutions of the equations.

• Work autonomously
• Review, analyse and synthesise data and information, with the use of necessary technologies)
• Team work

• Introduction.
• 1st  and 2nd order d.e.: separation of variables, homogenous, exact, Bernoulli, Ricati, Euler, integrating factors.
• Newton's differential equation and applications in engineering problems.
• Linear independence, Wronskian.
• Linear differential equations with constant coefficients.
• Laplace transform method.
• Applications in Engineering and Electricity
• 1st order systems with constant coefficients..
• Power series method

Assessment Method

• Questions of theoretical knowledge.
• Theoretical problems to be resolved.

OR

I. Midterm and final exam (100%=50%+50%)

II.“Bonus” exercises (10% in addition to the project grade).

• 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