Mathematics
A.Y. 2024/2025
Learning objectives
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.
Expected learning outcomes
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.
Lesson period: Second trimester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
Second trimester
Course syllabus
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.
Prerequisites for admission
High school algebra, in particular students should be able to solve algebraic equations involving exponential, logarithms, square roots, ratio.
Teaching methods
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.
Teaching Resources
Suggested Book: Essential Mathematics for Economic Analysis -- Knut Sydsaeter, Peter Hammond, Arne Strom, Andrés Carvajal -- 6th Edition 2022, Pearson.
Assessment methods and Criteria
The final evaluation will be a written exam with two or three exercises
SECS-S/06 - MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES - University credits: 6
Lessons: 40 hours
Professor:
Liuzzi Danilo
Professor(s)
Reception:
Wednesday 10:30-13:30 am
Room 32, Via Conservatorio 7, DEMM, 3rd floor