The aim of the course is to provide the ability to use quantitative models in economics, with a special focus on the use of mathematical tools in economic analysis.
Course Prerequisites
The contents of the course Matematica Generale are considered as preliminary notions
Teaching Methods
Lectures and tutorials, 66 hours.
Assessment Methods
Written exam with exercises (90 minutes)
Texts
Carl P. Simon, Lawrence E. Blume, Matematica per le scienze economiche, 2015 Egea, Milano. Giorgio Giorgi, Matematica per l'Analisi Economica e Finanziaria, 2017 Giappichelli, Torino. K. Sydsaeter, P. Hammond, A. Seierstad, A. Strom. Further Mathematics for Economic Analysis. Prentice Hall, Pearson Education, 2008.
Contents
1) Linear algebra Review of Basic Linear Algebra. Linear Independence. Rank of a Matrix. Main Results on Linear Systems. Eigenvalues. Diagonalization. Quadratic Forms. Quadratic Forms with Linear Constraints. Partitioned Matrices and Their Inverses. 2) Multivariable calculus Gradients and Directional Derivatives. Convex Sets. Concave and Convex Functions. Quasi-concave and Quasi-convex Functions. Taylor's Formula. Implicit and Inverse Function Theorems. Degrees of Freedom and Functional Dependence. Differentiability. Existence and Uniqueness of Solutions of Systems of Equations. 3) Static Optimization. Extreme Points. Local Extreme Points. Equality Constraints: The Lagrange Problem. Local Second-Order Conditions. Inequality Constraints: Nonlinear Programming. Sufficient Conditions. Nonnegativity Constraints. 4) Differential equations. Introduction. Separable Equations. First-Order Linear Equations. Transformation of Variables. Qualitative Theory and Stability. Existence and Uniqueness. Second-order and higher-order equations. 5) Difference equations. First-Order Difference Equations. Economic Applications. Second-Order Difference Equations. Linear Equations with Constant Coefficients. Higher-Order Equations. Systems of Difference Equations.
