Department of Information & Communication Systems Engineering
 SCHOOL OF ENGINEERING Department of Information & Communication Systems Engineering
 Information & Communication Systems Security Information Systems Artificial Intelligence Computer & Communication Systems Geometry, Dynamical Systems & Cosmology
Διαφορικές Εξισώσεις

 Title: Διαφορικές Εξισώσεις Lesson Code: 321-2254 Semester: 4 ECTS: 5 Theory Hours: 3 Lab Hours: 2 Faculty: Kofinas Georgios

Content outline
Examples of differential equations. The differential equation x'=f(t). The first order linear differential equation. Extension of the exponential function. Two dimensional linear systems with constant coefficients. Second order linear differential equations with constant coefficients. Solution of x' = A x + f. Solution of x'' + bx' + cx = f. Superposition principle. Linear oscillations x' = A x + f. Linear oscillations x'' + bx' + cx = f. Exact equations. Differential forms and line integrals. Integral curves. Sequences. Series. Improper integration. Fixed-point theorems and successive approximations. Existence-uniqueness theorem. Series solution of differential equations. Numerical solution of differential equations. Legendre polynomials. Fourier series. Fourier approximations.

Learning outcomes
Ability understand what a differential equation is and what is a solution of it. Ability to solve 1st and 2nd order equations and linear systems with constant coefficients. Basic existence theory, series solutions of differential equations, fourier approximation.

Prerequisites
Calculus II, Linear Algebra.

Basic Textbooks
1. W.E. Boyce and R. C. DiPrima, Elementary differential equations and boundary value problems.

1. R. Bronson, Differential equations.

Learning Activities and Teaching Methods
Systematic development and explanation of the theory, methods of solutions of exercises, use of Mathematica.