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Facoltà di Scienze Agrarie e Alimentari Università degli Studi di Milano
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Code: K070D-
Teacher:  Giovanni Naldi
Year: 
Term: 
CFU: 
CFU subdivision: Lectures: 5
Practices in classroom: 1
Basic aims:  The aim of the course is to provide basic mathematical methods for solving a wide range of applications in economics.
Main topics of the course are: Linear Algebra, Functions of Several Variables and Optimization Problems.
Acquired skills:  Basic mathematical methods and tools required to read and understand contemporary literature and modelling in economics.
Course contents:  The aim of the course is to provide mathematical methods for
solving a wide range of real applications in economics.

The topics of the course are: Linear Algebra, Functions of Several
Variables and Optimization Problems.
Program:  System of Linear equations: examples. General form, Matrix
and Vector representation, basic techniques for solving linear
system. Rank of matrix and Rouché-Capelli Theorem. Matrix
algebra: basic operations, scalar and matrix multiplication.
Transpose Matrix. Square Matrix. Determinant. Inverse Matrix.
Special kind of matrices. Quadratic Form. Eigenvalues and
Eigenvector.

Real vector spaces. Linear combination, dependence and linear
independence. Basis and dimension in R^n. Algebra of vectors,
inner product and Norm. Linear Transformation and Linear
subspaces. Basic Calculus functions of one variable. Functions
of several variables: graphs of functions of Two Variables, Level
Curves. Special Kinds of functions: linear functions, quadratic
functions. Domain, continuity and partial derivatives.
Differentiability. Directional
derivatives. Gradients. Second order Derivatives. Hessian
matrix. Concave and convex functions.

Optimization problems: Definition of local and global
minimum/maximum. First and Second order conditions for
unconstrained problems. Constrained optimization: equality
constraints and Lagrange Multipliers. Inequality constraints and
Kuhn–Tucker conditions. Linear programming (Basic)
Prerequisites:  Basic Calculus: Functions of one variables and their properties.
Continuity and differentiability. Single-variable optimization.
Integration. Matrix and vector algebra.
Preparatory instructions:  none
Learning materials:  Readings: Simon, C.P. and Blume, L.E. (1994): “Mathematics for
Economists”, Norton, W. W. & Company, Inc.
Other info:  The exam is in English. The exam consists of a written test and a
possible oral test . The oral part is compulsory if the score of the
written exam is between 15 and 17.
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