Learning Outcomes
After the successful completion of the course, students will be able to know the required basic Mathematical Tools (Univariate Differential Calculus, Linear Algebra, Multivariate Differential Calculus) in order to be able to effectively continue their studies in Economics. More specifically, they will be able to solve Mathematics exercises using the above tools, as well as to model and solve Economic Problems using the above mathematical tools successfully.
Course Content (Syllabus)
MATHEMATICS I
I. UNIVARIATE CALCULUS
The derivate and differential for functions of one variable.
Higher order derivatives.
Exponential and logarithmic functions. Cobb-Douglas functions.
Marginal Revenue Product. The elasticity concept.
Necessary conditions for unconstrained maxima and minima.
Second-order conditions.
Definition of a tangent line.
Taylor Series Formula.
II. LINEAR ALGEBRA.
Matrices. Determinants.
Solving systems of linear equations. (Cramer’s rule).
III. MULTIVARIATE CALCULUS
Functions of n-variables.
Partial differentiation.
More properties of functions with economic application.
Partial elasticity.
Second-order (and higher order) partial derivatives.
Chain rule.
Implicit differentiation.
Hessian matrix. Total differential.
Quadratic forms. Definiteness of quadratic form.
Optimization of functions of n-variables. First and second-order conditions.
Constrained optimization.
Comparative Statics.