Mathematics
A.A. 2024/2025
Obiettivi formativi
The aim of the course is to enable students to apply mathematics as a useful and precise tool in economics and statistics. Starting with a revision of basic mathematics and developing new theory using practical examples, the course will also foster students' ability in using graphs to simplify and check the resolution of problems.
Risultati apprendimento attesi
Students should be able to formalize practical situations using mathematical methods. They should become competent at creating graphs to represent functions and convey information. Students should be able to develop an effective study method in the subject for further independent learning and to critically analyze relations between mathematical theory and its practical applications.
Periodo: Secondo trimestre
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
Secondo trimestre
Programma
Analytic Geometry: Cartesian Plane and Reference Systems, Euclidean Distance and Pythagorean Theorem, The Equation of a Circle. The Equation of a Parabola and a Straight Line.
Matrix and Matrix Algebra: Matrix definition, addition and subtraction between matrices, matrix multiplication. Multiplication by scalars. Application of Matrix Algebra, example of Rotation Matrix and compact representation of a system of linear equations. Solutions of a two dimensional linear systems, algebraically and geometrically.
Introduction to MATLAB: Desktop interface, variables and assignments, matrices and vectors and relative algebraic operation.
Functions of one Variable: Introductions, Domain and Range, Graph of Functions; Linear functions, Slope, Point-Slope and Point-Point formulas, intuitive definition of limits to infinity; Quadratic Functions, Concavity intercepts with the axes. Cubic Functions, Rational Functions, Power Functions. Exponentials and Logarithms and their properties. Inverse Functions.
Differentiations: slope of curves, tangents and derivatives. Increasing and Decreasing Functions, A Brief Introduction to Limits, Simple Rules for Differentiation, Sums, Products and Quotients, The Chain Rule. Higher Order Derivatives. Linear and Quadratic Approximation.
Concave and Convex Functions: first and second derivative test.
Optimization: critical points, necessary and sufficient conditions, inflection points.
Integrations: Integrals as antiderivative and Integrals as areas.
Matrix and Matrix Algebra: Matrix definition, addition and subtraction between matrices, matrix multiplication. Multiplication by scalars. Application of Matrix Algebra, example of Rotation Matrix and compact representation of a system of linear equations. Solutions of a two dimensional linear systems, algebraically and geometrically.
Introduction to MATLAB: Desktop interface, variables and assignments, matrices and vectors and relative algebraic operation.
Functions of one Variable: Introductions, Domain and Range, Graph of Functions; Linear functions, Slope, Point-Slope and Point-Point formulas, intuitive definition of limits to infinity; Quadratic Functions, Concavity intercepts with the axes. Cubic Functions, Rational Functions, Power Functions. Exponentials and Logarithms and their properties. Inverse Functions.
Differentiations: slope of curves, tangents and derivatives. Increasing and Decreasing Functions, A Brief Introduction to Limits, Simple Rules for Differentiation, Sums, Products and Quotients, The Chain Rule. Higher Order Derivatives. Linear and Quadratic Approximation.
Concave and Convex Functions: first and second derivative test.
Optimization: critical points, necessary and sufficient conditions, inflection points.
Integrations: Integrals as antiderivative and Integrals as areas.
Prerequisiti
High school algebra, in particular students should be able to solve algebraic equations involving exponential, logarithms, square roots, ratio.
Metodi didattici
Lectures with many examples performed both with paper and pencil and with the help of Matlab. Notes of the lectures will be made available to students, together with detailed coding sections, in notebooks format.
Materiale di riferimento
Suggested Book: Essential Mathematics for Economic Analysis -- Knut Sydsaeter, Peter Hammond, Arne Strom, Andrés Carvajal -- 6th Edition 2022, Pearson.
Modalità di verifica dell’apprendimento e criteri di valutazione
The final evaluation will be a written exam with two or three exercises
SECS-S/06 - METODI MATEMATICI DELL'ECONOMIA E DELLE SCIENZE ATTUARIALI E FINANZIARIE - CFU: 6
Lezioni: 40 ore
Docente:
Liuzzi Danilo
Docente/i
Ricevimento:
Monday 10:30-13:30
Stanza 32, Via Conservatorio 7, DEMM, 3rd floor