MATHEMATICS I

Compulsory Course - 1st Semester (Autumn 1st year) | Course ID: 0005 | E-Class

Lecturers

Iraklis Kollias

Stelios Kotsios

Language of instruction

Greek and English

Course contents

The set Rn
Vectors in Rn
Matrices-Determinants
Eigenvalues Eigenvectors
Multivariate functions
Partial Derivatives
Geometric meaning of the partial derivative
Complex Derivation
Elasticities
Total Differential
Higher-order differentials
Del operators
Jacobian Hessian
Derivative by direction
Tangent planes
Taylor multivariate theorem
Implicit differentiation
Inverse Function Theorem
Implicit Derivation Theorem (with Jacobian)
Theory of Contour Lines
Contour Lines in Economics
Homogeneous Functions Basics
Derivation of Homogeneous Functions
Euler's Theorem
Economic Applications of Homogeneous Functions
Homothetic Functions
Convex Concave Functions
Quasi-Convex
Pseudo-convexPseudo-concave
Positive and Negative Definite Matrices
Optimisation of multivariate functions Economic applications
Envelope Theorem
Least Squares Method
Lagrange method Economic applications
Interpretation of the Lagrange Method
Kuhn-Tucker method Economic applications

Bibliography

Strang, Gilbert (2006). Linear Algebra and Its Applications, Cengage [4^th edn]. Greek edition Crete UP [2016].
Sydsaeter, Knut, and Peter Hammond (2008), Essential Mathematics for Economic Analysis, Prentice-Hall, 3^rd edition.
Κατσίκης, Βασίλης Ν., και Στέλιος Κώτσιος (2021). Γενικά Μαθηματικά για την Οικονομία και τη Διοίκηση. Τόμος ΙΙ, Εκδόσεις Τσιόρτας, 3^η έκδοση.

Assessment

The course is assessed by written examinations at the end of the semester. Students are assessed on their understanding of key concepts, critical thinking and analysis and their ability to research, analyse and solve problems. Assessment criteria are communicated to students via the course outline posted on the course website in e-class.

PROGRAMME OF POSTGRADUATE STUDIES MPHIL “ECONOMICS”