- Docente: Maria Letizia Guerra
- Credits: 10
- SSD: SECS-S/06
- Language: Italian
- Moduli: Maria Letizia Guerra (Modulo 1) Maria Letizia Guerra (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Rimini
- Corso: First cycle degree programme (L) in Finance, Insurance and Business (cod. 8872)
Learning outcomes
At the end of Mathematics course, the student will be able to apply all the basic elements of Calculus in one variable and some relevant topics in several variables.
Course contents
The numerical sets N, Z, Q, R and their structures.
The real function of a real variable: basic definitions, elementary functions and examples of mathematical models in Finance.
The discrete Mathematics: sequences, limits and series.
Limits for real functions: properties and theorems related to the continuous property, local and global.
The concept of derivatoive and its geometric meaning. Derivatives properties, computation rules and theorems: Rolle, Lagrange and Cauchy.
Unconstrained optimization in one variable. Convexity and concavity Taylor formula and Taylor-MacLaurin formula.
The concept of anti-derivative and its properties. Integrability methods and theorems. Generalized integrals.
N-dimensional vector spaces; matrices, determinat and rank.
Linear systems, Cramer and Rouchè-Capelli theorems.
Eigenvalues, eigenvectors and their meaning.
Introductory elements of several variables unconstrained optimization. Gradient vector and Hessian matrix.
Readings/Bibliography
K. Sydsaeter, P. Hammond, A. Strom (a cura di D. La Torre), Metodi Matematici per l'Analisi Economica e Finanziaria, Pearson.
Teaching methods
Students are involved in traditional lectures through the individual solution of examples; at the end of each lecture, homework is assigned and solved at the beginning of the next lecture.
Assessment methods
The written exam is organized into two partial examinations, the final mark is the mean value between them and the student passes the exam when the mean is greater or equal to 18.
An elective oral examination can be required by the students and the final mark is the mean between the written and the oral part.
Teaching tools
The attendance of the crash course is strongly recommended, together with the attendance of the exercises based course.
A booklet based on solved exam exercises will be downloadable from the present page.
Office hours
See the website of Maria Letizia Guerra
SDGs
This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.