Elective Course - 4th Semester (Spring 2nd year) | Course ID: Q207 | E-Class
According to the curriculum, students must choose three elective courses during the fourth semester

Lecturers

Elias Camouzis

Stelios Kotsios

Language of instruction

Greek and English

Course description

Introduction to difference equations, “Famous equations”. Linear first, second and higher order. Solution. Casorati determinant. Fundamental set of solutions. Equilibrium points, periodic solutions, stability, phase diagrams, bounded solutions, unbounded solutions, economic applications, Samuelson model. Systems of linear equations, Cournot model. Nonlinear difference equations, Riccati's equations, periodic solutions, nonperiodic solutions, chaotic solutions, Li & Yorke's theorem.  Qualitative analysis of nonlinear equations, logistic equation, period doubling route to chaos.

Course contents

Lectures

1. Introduction to D equations

2-4. First order linear equations. Economic applications.

5-7. Higher order linear equations. Economic applications.

8-10. Systems of first order difference equations. Economic applications.

11-13. Non-linear difference equations. Accounting equations. Riccati equations. Periodic solutions. Chaotic solutions.

Bibliography

• Camouzis, Elias and Gerry Ladas. Rational Difference Equations with Open Problems and Conjectures, Taylor and Francis, 2007.
• Elaydi, Saber. An Introduction to Difference Equations, 3^rd edition, Springer, 2005
• Devaney, Robert. An Introduction to Chaotic Dynamical Systems, 3^rd edition, Chapman & Hall/CRC, 2021.
• Li, Tien-Yien, and James A. Yorke. “Period Three Implies Chaos”, American Mathematical Monthly 82, no. 10 (1975): 985–92.

Assessment

Το μάθημα αξιολογείται στην βάση εξαμηνιαίας εργασίας-αναφοράς  100% στην οποία οι φοιτητές παρουσιάζουν τις λύσεις των ασκήσεων που αναφέρονται σε ολόκληρο το υλικό των εξισώσεων διαφορών που παρουσιάζεται και διδάσκεται κατά την χρονική περίοδο του εξαμήνου.