SECS-S/06 - 9 CFU - 1° Semester

- KNOWLEDGE AND UNDERSTANDING: The student will receive the basic tools allowing to deal with the modern formal approaches to economics and business management. The focus will be on the basic principles of mathematics applied to economics rather than on a sterile technicality. The course will give also an idea of the possible applications of the introduced tools. More generally, the course will try to educate students to a rigorous approach to the analysis of economic and management business phenomena. The accuracy of the mathematical treatment will allow the student to acquire a mindset that will be beneficial for all the other subjects of the university courses and, more generally, for all the professional issues that have to be handled.
- APPLYING KNOWLEDGE AND UNDERSTANDING: The student will be given the opportunity to analyze rigorously a mathematical problem and to use the basic concepts in order to draw appropriate conclusions. The student will be able to solve simple but not trivial mathematical problems. The student will be able to conduct a mathematical reasoning through the introduction of rigorous definitions and the proofs of some theorems particularly significant. The student will also be able to apply the knowledge, learned during the course, to the formalization of some basic economic and management business issues such as profit maximization and utility maximization.
- MAKING JUDGMENTS: Students will be educated to elaborate by themselves the most appropriate approach to the proposed problems avoiding sterile applications of repetitive patterns. The student will be educated to judge the considered mathematical formalization by different points of view such as the elegance of the model, the power of the mathematical tools, the computational burden and so on.
- COMMUNICATION SKILLS: Students will be able to use the technical terms and they will learn how properly express the mathematical formalization of the problem and the results obtained with it. Students will be able to give a formal presentation of economic phenomena and management business. The student will critically discuss quantitative models related to economic and management business phenomena.
- LEARNING SKILLS: Taking into account the ever increasing use of mathematical formalization in economics and management business, the course will enable to access the more qualified literature in these areas, giving an essential basis for future learning in both educational and professional level.

Classrooom-taught lessons including also exercising sessions during which it will be shown how to apply the theoretical concepts introduced during the course.

**1 ^{st} PART**

ELEMENTS OF MATHEMATICAL LOGIC: languages and propositions; connectives; quantifiers.

SET THEORY: properties, subsets, operations. Functions. Binary relations. Real numbers and inequalities. Basics of trigonometry.

COMBINATORICS: dispositions, combinations and permutations. Binomial theorem, binomial coefficients.

MATRICES AND DETERMINANTS: definitions and classifications. Sum and product between matrices. Inverse matrix. Determinant and its property. Rank of matrix.

LINEAR SYSTEMS: linear forms. Definitions and properties. Normal linear systems: Cramer’s rule. Rouché-Capelli Theorem. Solution of parameterized systems.

**2 ^{nd} PART**

ANALYTICAL GEOMETRY: Cartesian coordinate system. Straight line equation in the plane.

REAL FUNCTIONS OF REAL VARIABLE: definitions, classifications, geometrical representation. Composite functions and inverse functions. Limits: definitions and theorems. Continuous functions. Infinitesimals and infinities.

DERIVATIVES AND DIFFERENTIALS: definitions, properties and their geometric interpretation. Derivatives of elementary functions. Derivatives and differentials of sum, product and quotient of functions. Derivatives of composite and inverse functions. Derivatives and differentials of n-th order. Main theorems on differentiable functions.

APPLICATIONS OF DIFFERENTIAL CALCULUS: Taylor’s and Mac Laurin’s formulas. Indeterminate forms. Monotonic functions, convex functions, local and global extrema, inflection points, asymptotes. Study of function. Elasticity of a function.

**3 ^{rd} PART**

INTEGRALS: indefinite integral and primitives. Definite integral and its geometric interpretation. Main methods of integration.

- S. Corrente, S. Greco, B. Matarazzo, S. Milici, "Matematica Generale", Giappichelli Editore, Torino, 2021.
- B. Matarazzo, M. Gionfriddo, S. Milici, “Esercitazioni di Matematica” ed. Tringale, Catania,1990.
- A. Giarlotta, S. Angilella, “Matematica generale. Teoria e pratica con quesiti a scelta multipla. VOLUME 1. Logica – Insiemistica – Combinatorica - Insiemi numerici”. Giappichelli Editore, 2013.