## MATHEMATICS MATEMATICA GENERALE

A.Y. Credits
2023/2024 8
Lecturer Email Office hours for students
Laerte Sorini To be defined in class during the first lessons
Teaching in foreign languages
Course with optional materials in a foreign language English
This course is entirely taught in Italian. Study materials can be provided in the foreign language and the final exam can be taken in the foreign language.

### Assigned to the Degree Course

Economics and Management (L-18 / L-33)
Curriculum: generico
Date Time Classroom / Location
Date Time Classroom / Location

### Learning Objectives

The course aims to provide the student with the basic knowledge of the tools of Mathematics that are widely used in the study and applications of Economics, Statistics and Finance.
In particular, through the study of the classical tools of General Mathematics, the student will be able to understand the fundamental formalizations of the problems of the Economy and Modern Finance, moreover, he will have acquired the indispensable knowledge for an effective study, attentive also to logical aspects and formal, of many other disciplines included in their curriculum of studies.

### Program

The course is divided into four parts and treats in a unified way the topics related to differential calculus for the functions of one and more variables and of the matrix calculation, giving priority to the application aspects, without however renouncing the presentation of the elements and instruments of a formal nature.

Part I. (Introductory Elements)

1. Numerical sets.
The sets N, Z, Q and their algebraic properties. The field of real numbers R and its properties: algebraic and order structure. Q density in R. Equations and inequalities in R.

2. Elementary functions.
Straight line, parabola, ellipse and circumference. Fractional polynomial and rational functions. Exponential and logarithmic functions. Circular functions and their inverse. Even and odd functions. Monotonicity of functions. Representation of elementary functions of one and more real variables.

Part II. (Differential and integral calculus)

3. Function limits
Topology elements of R. Accumulation points. Open and closed sets. Limited and compact sets. Limits of functions of a real variable. Operations on the limits of converging functions. Right and left limit. Local convergence and limitations. Comparison theorems. Sign permanence theorem. Limits to infinity. Indeterminate forms. Vertical, horizontal and oblique asymptotes. Continuous functions. Local properties (sign, boundedness) and global (Weierstrass theorem, existence of zeros, intermediate values). Inverse function.

5. Derivatives of functions
Derivatives of functions of a real variable: definition, geometric meaning and interpretation. Left and right derivatives, derivatives of higher order. Rules of derivation. Fundamental theorems of differential calculus: Rolle, Lagrange, Cauchy and De l'Hôpital. Differentiability and its meanings. Taylor polynomial and formula. Conditions of the first and second order, necessary and / or sufficient for the study of critical points (maxima, minima, inflections). Concavity and convexity of functions over an interval. Convexity and sign of the second derivative. Qualitative study of the graph of a function.

6. Primitive and integral functions
Definition of integral of continuous functions and fundamental properties. Primitive functions and properties.

Part III (Elements of Linear Algebra)

7. Linear algebra.
N-dimensional real space structure. Vectors, operations and properties. Operations with matrices and properties. Transposed matrix. Diagonal and triangular matrices. Determinant and ownership. The rules of Laplace and Sarrus. Inverse matrix and properties. Rank of a matrix and properties. Cramer's theorem. Rouchè Capelli theorem. Resolution of systems of linear equations. Homogeneous systems.

Part IV (Elements of functions of several variables)

8. Real functions of several variables.
Limits of functions of several real variables and continuity. Partial derivatives of functions of several variables. Gradient and tangent plane. Hessian matrix. Critical points and their classification (maximum and minimum, saddle points).

Parallel to the course there will be exercises in the classroom, assisted by the teacher, both to illustrate the topics presented in the lesson and to carry out guided exercises on the applications.

None.

### Learning Achievements (Dublin Descriptors)

At the end of the course the student should be able to:
- Know the mathematical language through the basic concepts and the tools presented in the course to use them to formalize the main problems of Economics and Finance.
- Understand the operational meaning of the mathematical tools used in the applications.
- To elaborate simple mathematical or formal models or graphs to illustrate and study relations between variables, even in the multidimensional case.

### Teaching Material

The teaching material prepared by the lecturer in addition to recommended textbooks (such as for instance slides, lecture notes, exercises, bibliography) and communications from the lecturer specific to the course can be found inside the Moodle platform › blended.uniurb.it

### Supporting Activities

Course materials made available by the teacher can be found, together with other support activities, within the Moodle platform › http://blended.uniurb.it

### Teaching, Attendance, Course Books and Assessment

Teaching

The course includes the use of different didactic methods:

• Lectures;
• Exercises in class.
• Tutorials at home.
• Development of themes proposed by students
• Educational seminars on particular topics of interest
Attendance

None.

Course books

The student can choose one of the texts listed below.
The text 1., relatively simple but complete, is suitable for the student who does not regularly attend lessons.
The text 2. is the most complete and is particularly recommended for students who will not be able to attend classes. It is also suggested for students who intend to learn the subject reaching a fairly solid preparation also oriented to the continuation of economic and / or financial studies.

1.

Mathematics Title
Author Guerraggio Angelo
Data 2004, 432 p.

All the text.

2.

General Mathematics Title for Economic Sciences
Author G. C. Barozzi - C. Corradi
Third Edition, Il Mulino, 1999

All the manual, with the exception of the sections Appendix 1, section 1.2, section 1.4, Appendices 3 and 4, Appendices 6 and 7, section 3.2, section 3.3, section 3.6, section 5.9, Appendix 9, section 6.5, section 6.6, section 7.4, section 7.5, section 7.6, Appendix 10.

Assessment

The examination consists of a written evidence on questions which will be half on part of mathematical analysis (15 points) and half on the part of algebraic geometry (15 points).

If the written exam will be overtaken with score > = 15 you will be able to sustain the oral examination.

The duration of the written examination is two hours.

Disabilità e DSA

Le studentesse e gli studenti che hanno registrato la certificazione di disabilità o la certificazione di DSA presso l'Ufficio Inclusione e diritto allo studio, possono chiedere di utilizzare le mappe concettuali (per parole chiave) durante la prova di esame.

A tal fine, è necessario inviare le mappe, due settimane prima dell’appello di esame, alla o al docente del corso, che ne verificherà la coerenza con le indicazioni delle linee guida di ateneo e potrà chiederne la modifica.

### Additional Information for Non-Attending Students

Teaching

Course materials made available by the teacher can be found, together with other support activities, within the Moodle platform › http://blended.uniurb.it

Attendance

None.

Course books

The student can choose one of the texts listed below.
The text 1., relatively simple but complete, is suitable for the student who does not regularly attend lessons.
The text 2. is the most complete and is particularly recommended for students who will not be able to attend classes. It is also suggested for students who intend to learn the subject reaching a fairly solid preparation also oriented to the continuation of economic and / or financial studies.

1.

Mathematics Title
Author Guerraggio Angelo
Data 2004, 432 p.

All the text.

2.

General Mathematics Title for Economic Sciences
Author G. C. Barozzi - C. Corradi
Third Edition, Il Mulino, 1999

All the manual, with the exception of the sections Appendix 1, section 1.2, section 1.4, Appendices 3 and 4, Appendices 6 and 7, section 3.2, section 3.3, section 3.6, section 5.9, Appendix 9, section 6.5, section 6.6, section 7.4, section 7.5, section 7.6, Appendix 10.

Assessment

The examination consists of a written evidence on questions which will be half on part of mathematical analysis (15 points) and half on the part of algebraic geometry (15 points).
If the written exam will be overtaken with score > = 15 you will be able to sustain the oral examination.
The duration of the written examination is around two hours.

Disabilità e DSA

Le studentesse e gli studenti che hanno registrato la certificazione di disabilità o la certificazione di DSA presso l'Ufficio Inclusione e diritto allo studio, possono chiedere di utilizzare le mappe concettuali (per parole chiave) durante la prova di esame.

A tal fine, è necessario inviare le mappe, due settimane prima dell’appello di esame, alla o al docente del corso, che ne verificherà la coerenza con le indicazioni delle linee guida di ateneo e potrà chiederne la modifica.

### Notes

The examination will be in English at the request of the student.

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