Mathematics II

    Course Code: 
    4104
    Semester: 
    2nd
    Compulsory Courses
    Professor: 

    ROUMANIAS KONSTANTINOS

    Number of credits allocated: 6 ECTS Credits

    Objective of the course (expected learning outcomes and competences to be acquired)

    The goal of the course is to introduce the students to methods of dynamic analysis which are useful to economists. Through this course students will learn to:

    • solve first and second order linear differential and difference equations
    • to solve linear systems of differential equations systems
    • understand the concept of stability and the stability properties of steady states in dynamical systems.

    The course includes economic examples to assist students in understanding mathematical tools in the context of economics, as well as solving problems using scientific software (Mathematica). The course is supported by a tutorial during which related exercises are solved and explained.

    Prerequisites

    It is recommended that students have successfully followed Mathematics I.

    Course contents:

    • Integrals: Indefinite integrals, Methods of integration, Definite integrals, Improper integrals, Applications to economics.
    • Differential equations: Terminology and basic concepts, Differential equations with constant coefficients, Dynamic stability, First and second order differential equations, Solution and stability, Higher order linear differential equations, Qualitative analysis, Applications to economics.
    • Dynamical systems: Terminology and basic concepts, Linear dynamical systems, Stability analysis of two dimensional systems, Stable, unstable and saddle point stability, Applications to economics.
    • Difference equations: Terminology and basic concepts, First and second order difference  equations, Dynamic stability, Linear systems Applications to economics.

    Recommended reading

    • Chiang, A. Mathematical Methods of Economic Analysis, Kritiki Publishing, 2001 (in Greek)
    • Boyce and DiPrima, Στοιχειώδεις διαφορικές εξισώσεις και προβλήματα συνοριακών τιμών, Πανεπιστημιακές Εκδόσεις Πολυτεχνειου.

    Teaching methods

    Lectures, Tutorials, Internet-based communication with students.

    Assessment methods: Final written exam

    Language of instruction: Greek