Mathematics for economics
A.A. 2023/2024
Obiettivi formativi
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.
Main topics of the course are: Linear Algebra, Functions of Several Variables and Optimization Problems.
Risultati apprendimento attesi
Basic mathematical methods and tools required to read and understand contemporary literature and modelling in economics.
Periodo: Primo semestre
Modalità di valutazione: Esame
Giudizio di valutazione: voto verbalizzato in trentesimi
Corso singolo
Questo insegnamento può essere seguito come corso singolo.
Programma e organizzazione didattica
Edizione unica
Responsabile
Periodo
Primo semestre
Programma
Linear Algebra: vector, vector operations, matrices, matrices operations. Linear systems: matrix representation. Rank of a matrix. Linear independency. Inverse of a matrix. Gaussian elimination method (linear system solution, determinant and inverse matrix computation). Symmetric matrices. Norm of a vector. Basis and dimension in R^n. Geometry of the 3D space.
Multivariable functions. Special case: graphs of functions of two variables. Level curves. Quadratic forms. Continuity and differentiability of multivariable functions. Partial derivatives, gradient and Hessian matrix. Two variable functions: tangent plane and gradient vector. Convex and concave functions. Optimization problems: first and second orderd conditions for unconstrained problems. Constrained optimization: equality constraints and method of the Lagrangian multipliers. Constrained optimization: inequality constraints and Karush-Khun-Tucker conditions. Linear programming (basic concepts).
Multivariable functions. Special case: graphs of functions of two variables. Level curves. Quadratic forms. Continuity and differentiability of multivariable functions. Partial derivatives, gradient and Hessian matrix. Two variable functions: tangent plane and gradient vector. Convex and concave functions. Optimization problems: first and second orderd conditions for unconstrained problems. Constrained optimization: equality constraints and method of the Lagrangian multipliers. Constrained optimization: inequality constraints and Karush-Khun-Tucker conditions. Linear programming (basic concepts).
Prerequisiti
Numerical sets. Intervals of the real line. Monomials, polynomials, power function with rational exponent, power function with negative exponent. Elementary functions: sine, cosine, exponential functions, logarithms, natural logarithms. Functions composition. Real functions and their properties. Plot of real functions. Limits of real functions. Continuity and differentiability. Derivatives of elementary functions. Maxima and minima of real functions. Solution of 2x2 and 3x3 linear systems. Geometry: circumference, ellipse, parabola, hyperbola.
Metodi didattici
Lecture-style instruction, integrated with slides created by the teacher. Usage of multimedia (video) and advanced software for improving the learning experience. Use of theoretical and real--life examples to show how the topics addressed in class can be directly applied in an economic framework.
Materiale di riferimento
K. Sydsæter, P. Hammond with A. StrØm; Essential Mathematics for Economic Analysis; Pearson.
R. A. Adams, C. Essex; Calculus: a complete course; Pearson
M. P. Deisenroth, A. A. Faisal, C.S. Ong, Mathematics for Machine Learning
Teacher's notes.
R. A. Adams, C. Essex; Calculus: a complete course; Pearson
M. P. Deisenroth, A. A. Faisal, C.S. Ong, Mathematics for Machine Learning
Teacher's notes.
Modalità di verifica dell’apprendimento e criteri di valutazione
The exam consists of a written test.
The test consists of theoretical questions (both open and mutiple choice questions) aimed to verify the comprehension of the topics studied in class. The test includes also exercises devoted to check the ability of applying independently the methodologies studied in class. The duration of the test depends on the number and on the structure of the questions, but it will not exceed 3 hours.
Results will be communicated via personal e-mail and on the UNIMIA web portal.
The test consists of theoretical questions (both open and mutiple choice questions) aimed to verify the comprehension of the topics studied in class. The test includes also exercises devoted to check the ability of applying independently the methodologies studied in class. The duration of the test depends on the number and on the structure of the questions, but it will not exceed 3 hours.
Results will be communicated via personal e-mail and on the UNIMIA web portal.
MAT/06 - PROBABILITA E STATISTICA MATEMATICA - CFU: 6
Esercitazioni: 16 ore
Lezioni: 40 ore
Lezioni: 40 ore
Docenti:
Benfenati Alessandro, Marta Alessio
Siti didattici
Docente/i