6004 Differential Equations

The differential equations describe a broad range of phenomena and processes in technological, physical, biological, and financial sciences. The aim of this course is to provide the basic knowledge for the comprehension of the differential equations as well as their basic solution methods and techniques. Skills: Upon successfully completion of the course, the student should be in position to • formulate a mathematical model for simple mechanical systems, i.e., to account for the right ordinary differential equation as well as for the appropriate initial conditions that accompany it. • apply the taught solution methods to linear and non-linear ordinary differential equations of first order. • apply the solution methods to homogeneous and non-homogeneous ordinary differential equations of second order with constant coefficients and to apply them to the solution of mechanical and electrical vibration problems. • solve linear systems of differential equations with constant coefficients. • solve initial value problems for second order differential equations using the Laplace transform method. • apprehend the fundamental notions of partial differential equations and to apply the variables’ separation method to the three basic partial differential equations of mathematical physics.
ECTS : 4
Language : el
Learning Outcomes : Upon successful completion of the course, the student will be able to: • know the process of modeling simple mechanical systems for formulating an ordinary differential equation and initial conditions. • know and apply solution methods for linear and nonlinear ordinary differential equations of 1st order of various types. • know solution methods for homogeneous and non-homogeneous ordinary linear differential equations of 2nd order with constant coefficients and apply these to solving mechanical-electrical oscillation problems. • solve ordinary linear differential equations of 2nd order with non-constant coefficients using the power series method. Recognize Bessel and Legendre differential equations and recall their solutions. solve linear systems with constant coefficients. • solve initial value problems of 2nd order ordinary differential equations using the Laplace transform method. • understand the introductory basic concepts of partial differential equations and apply the method of separation of variables to the three basic partial differential equations.