Department of Information & Communication Systems Engineering
University of the Aegean
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.
 
Additional References
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.
 
Assessment/Grading Methods
One final written exam.
 
Language of Instruction
Greek, English (for Erasmus students)
 
Μode of delivery
Face-to-face.

Notes
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