This is an undergraduate course on ordinary differential equations (ODEs) and associated initial value problems. Special emphasisis placed on fundamental concepts, solution methods and applications of ODEs to problems in Mechanical Engineering and Physics more generally.  

Introduction: the concepts of the ordinary differential equation and of the initial value problem, applications of differential equations.

First‐order equations: integral curves, existence and uniqueness of solutions; analytical methods for solving linear, separable, exact, homogeneous, autonomous, and Bernoulli equations; numerical methods; applications. Second‐order linear equations: existence and uniqueness of solutions,  homogeneous and non‐homogeneous equations, equations with constant coefficients, applications to the problem of free and forced vibration.

Third‐  or higher‐order linear equations. The method of the power series: introduction to power series, ordinary and singular points, regular and irregular singular points, solutions about ordinary points, the Legendre equation, solutions about regular singular points, the Bessel equation.

The Laplace transform: solving differential equations, step functions and applications, impulse functions and applications, the convolution theorem and applications.

Suggested Literature:

• Boyce, W.E. & DiPrima, R.C., Elementary Differential Equations and Boundary Value Problems, Wiley, 2012.
• Μυλωνάς, Ν. & Σχοινάς, Χ., Διαφορικές Εξισώσεις, Μετασχηματισμοί και Μιγαδικές Συναρτήσεις, Εκδόσεις Τζιόλα, 2015.
• Σταυρακάκης, Ν., Διαφορικές Εξισώσεις: Συνήθεις και Μερικές, Εκδόσεις Σταυρακάκης, 2015.
• Τραχανάς, Σ., Συνήθεις Διαφορικές Εξισώσεις, Πανεπιστημιακές Εκδόσεις Κρήτης, 2013.
• Cengel, Y. A. & Palm III, W. J., Differential Equations for Engineers and Scientists, McGraw‐Hill, 2012.
• Σούρλας, Δ., Συνήθεις Διαφορικές Εξισώσεις, Εκδόσεις Συμμετρία, 2010.

Related Academic Journal:

• Journal of Engineering Mathematics
• SIAM Journal on Applied Mathematics

Greek

Lectures