- Docente: Luca Guerrini
- Credits: 8
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Rimini
- Corso: First cycle degree programme (L) in Business Economics (cod. 0909)
Learning outcomes
At the end of the course the student is familiar with the mathematics foundations, in particular with basic linear algebra, fundamentals of functions and one variable differential calculus, in order to approach the economics, financial and corporate applications.
Course contents
Basic Elements
Elementary Theory of Real Numbers. Relations and functions. Intervals, upper and lower bounds. Maximum and minimum of intervals. Algebraic, logarithmic, exponential and radical equations and disequalities. Graphic solution of equations. Analytic geometry: equations of lines, parabolas, hyperbole, circumference.
Calculus
Real functions of one real variable: properties, composition, inverse. Increasing and decreasing functions. Polynomial, logarithmic, exponential, rational and radical functions.Limits in a real point and to infinite. Local and global continuity. Weierstrass theorem and theorem about the existence of roots for a continuous function. Derivatives: properties and rules. Geometric meaning of the first derivative. Non constrained optimization: existence of maximum and minimum. Concavity and convexity. Qualitative analysis of the graphs of simple functions.
Matrix and vector algebra
Introductory matrix theory and operations with matrixes. Sarrus and Laplace rules for the determinant computation of square matrixes. Properties of the determinant. Invertible matrix, necessary and sufficient conditions for invertibility. Inverse matrix and rank. Eigenvalues and eigenvectors of a square matrix. Systems of linear equations: Cramer and Rouchè-Capelli theorems. Homogeneous systems. Solutions of systems depending on a parameter.
Readings/Bibliography
L. Scaglianti, A. Torriero, Matematica. Metodi e applicazioni, Cedam
G. Repetti, R. Rossetto, Matematica di base. Esercizi e complementi, Utet
Teaching methods
Frontal lecturers and exercises in collaboration with students.
Assessment methods
The course has two mid-term exams reserved only to freshman students. The examination is a written exam with an optional oral part (written).
Teaching tools
Before the official beginning of the lecturers, students are strongly encouraged to attend the pre-course in basic mathematics. A positive outcome in the written exam at the end of the pre-course enables students to acquire three points representing a bonus for the official tests in first exam session.
Office hours
See the website of Luca Guerrini