Portale di Ateneo - En.Unibs.it

Borrowed courses

LINEAR ALGEBRA AND CALCULUS II

ECONOMIA E GESTIONE AZIENDALE

AMMINISTRAZIONE E CONTROLLO
LINEAR ALGEBRA AND CALCULUS II

ECONOMIA E GESTIONE AZIENDALE

BUSINESS
LINEAR ALGEBRA AND CALCULUS II

ECONOMIA E GESTIONE AZIENDALE

GESTIONE DELLE IMPRESE
LINEAR ALGEBRA AND CALCULUS II

ECONOMIA E GESTIONE AZIENDALE

GESTIONE DEL TURISMO
LINEAR ALGEBRA AND CALCULUS II

ECONOMIA

PERCORSO GENERALE IN ECONOMIA
LINEAR ALGEBRA AND CALCULUS II

BANCA E FINANZA

CORSO GENERICO

Other Courses of the Study Programme

Course year: 1

ACCOUNTING ESSENTIALS - 12 credits - Basic
ELEMENTARY ENGLISH: BASIC NOTIONS - Student's own choice
ELEMENTARY MATHEMATICS: BASIC NOTIONS - Student's own choice
INFORMATION TECHNOLOGY ELIGIBILITY - 2 credits
INTRODUCTION TO BUSINESS ADMINISTRATION - 6 credits - Characterising
LINEAR ALGEBRA AND CALCULUS I - 9 credits - Basic
MICROECONOMICS - 9 credits - Basic
PROBLEM SOLVING FOR COMPUTER SCIENCE - 6 credits - Related/Supplementary
PUBLIC LAW AND INFORMATION TECHNOLOGY - 9 credits - Characterising
STATISTICS - 9 credits - Basic

Course year: 2

ENGLISH LANGUAGE - 9 credits - Related/Supplementary
INNOVATION AND OPERATIONS MANAGEMENT - 6 credits - Characterising
INTRODUCTION TO FINANCIAL MANAGEMENT - 6 credits - Characterising
INTRODUCTION TO STATISTICAL INFERENCE - 6 credits - Characterising
LINEAR ALGEBRA AND CALCULUS II - 6 credits - Characterising
MACROECONOMICS - 9 credits - Characterising
OPERATIONS RESEARCH - 9 credits - Related/Supplementary
PRIVATE LAW AND ECONOMIC RELATIONSHIPS - 6 credits - Basic
STATISTICS FOR ECONOMICS AND DIGITAL FIRM - 9 credits - Characterising

Course year: 3

ADMINISTRATION AND MANAGEMENT CONTROL OF TOURISM ENTERPRISES - 6 credits - Student's own choice
BANKING - 9 credits - Student's own choice
BUSINESS MANAGEMENT - 9 credits - Student's own choice
BUSINESS ORGANISATION - 6 credits - Student's own choice
BUSINESS ORGANIZATION - 6 credits - Student's own choice
COMMERCIAL LAW - 12 credits - Student's own choice
COMPUTATIONAL METHODS - 6 credits - Related/Supplementary
DATA ANALYSIS AND BIG DATA LAB - 9 credits - Characterising
DECISION ANALYSIS FOR BUSINESS - 6 credits - Student's own choice
ECONOMIC HISTORY - 6 credits - Student's own choice
ECONOMIC POLICY - 9 credits - Student's own choice
EMPIRICAL ECONOMICS - 9 credits - Characterising
ENVIRONMENTAL ECONOMICS - 6 credits - Student's own choice
FINAL TEST - 4 credits - Language/Final Examination
FINANCIAL AND ACTUARIAL CALCULUS - 6 credits - Student's own choice
FINANCIAL ECONOMICS - 6 credits - Characterising
FINANCIAL MANAGEMENT MODELS - 9 credits - Student's own choice
FINANCIAL MARKETS AND ISTITUTIONS - 9 credits - Student's own choice
FOUNDATIONS OF PUBLIC ECONOMICS - 6 credits - Student's own choice
FRENCH LANGUAGE - 6 credits - Student's own choice
GEOGRAPHY AND SOCIOLOGY OF TOURISM
Attendance grouping
9 credits - Raggruppamento di frequenza
GERMAN LANGUAGE - 6 credits - Student's own choice
HERITAGE AND TOURISM POLICY - 9 credits - Student's own choice
INTERNSHIP - 3 credits - For stages and internships
INVESTMENTS - 9 credits - Student's own choice
LABOUR LAW - 9 credits - Student's own choice
MANAGEMENT CONTROL - 9 credits - Student's own choice
MARKETING - 9 credits - Student's own choice
OPERATIONS MANAGEMENT - 6 credits - Student's own choice
PORTFOLIO CHOICES - 6 credits - Student's own choice
PROFESSIONAL PRACTICE ISSUES IN ACCOUNTING - 6 credits - Student's own choice
PUBLIC AND INNOVATION ECONOMICS - 9 credits - Characterising
PUBLIC ECONOMICS - 9 credits - Student's own choice
SPANISH LANGUAGE - 6 credits - Student's own choice
STRATEGY ANALYSIS - 9 credits - Student's own choice
TOURISM MANAGEMENT - 6 credits - Student's own choice

LINEAR ALGEBRA AND CALCULUS II

Single discipline educational activity

Course Sheet

Academic Year of enrolment:

2019/2020

Academic Year of provision:

2020/2021

Type of Course:

Characterising

Degree:

Bachelor's Degree Programme in ECONOMICS AND DIGITAL FIRM

Location:

BRESCIA

Disciplinary Sector:

MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES

Language:

Italian

Grouping type:

Credits:

Programme Year:

Professor and Collaborators:

RICCARDI Rossana Professor

OGGIONI Giorgia Collaborator

CARTAPANI GIULIA Collaborator

Cycle:

First four months

Hours of classroom activity:

Hours of individual study:

110

The topics of the course of Linear Algebra and Calculus are an essential pre-requisite.

Educational Goals

The course aims at stimulating the student to identify situations in which the tools introduced can be applied profitably.

Knowledge and understanding:
At the end of the course the student must have acquired a good command on the topics of dynamical systems and financial mathematics. Examples are shown in the classroom during lessons and tutorials.

Applying knowledge and understanding:
At the end of the course, the student will be able to formulate economic and financial problems in mathematical terms and to use mathematical tools to solve them.

Making judgments:
At the end of the course the student will have a good ability to analyze topics and problems of dynamic modeling and financial mathematics. Moreover, the student will know the strategic interactions with mathematical tools and he will be able to critically interpret the results obtained

Communication skills:
At the end of the course, the student must have acquired a good ability to clearly communicate the statements and considerations regarding the program carried out in class and in-depth on the recommended texts.

Learning skills:
At the end of the course the student will be autonomous in studying the discipline, in reading and interpreting mathematical models in economics and finance.

Content

The aim of the course is to present some mathematical tools useful in the formulation and the treatment of models that regulate economic and financial phenomena.
The first part of the course will be dedicated to the acquisition of the mathematical instruments at the basis of various classes of economic and financial problems. The second part of the course will introduce the main concepts of classical financial mathematics.

FIRST PART

Integrals
- Generalized integrals
- Generalized integral over an unbounded interval
- Generalized integral of unbounded functions
- Generalized integral of unbounded functions over an unbounded interval
- Eigenvalues and eigenvectors of square matrices.

Quadratic forms
- Definition of eigenvalue and eigenvector
- Square matrices and diagonal matrices
- Diagonalization of symmetric matrices
- Application to the study of quadratic forms

Dynamical systems
- Differential equations
- First order differential equations
- Linear differential equations with constant coefficients
- Difference equations
- First order difference equations
- Difference equations with constant coefficients
- Introduction to systems of differential equations
- Linear systems of difference and differential equations

SECOND PART

Financial Mathematics
- Capitalization and discounting regimes
- The simple interest regims
- The compound interest regime
- The commercial discount regime
- Equivalent rates, variable rateAnnuities and repayment plans

NPV and IRR selection criteria

Extended Syllabus

FIRST PART

Integrals.
- Generalized integrals
- Generalized integral over an unbounded interval
- Generalized integral of unbounded functions
- Generalized integral of unbounded functions over an unbounded interval
- Eigenvalues and eigenvectors of square matrices.

Quadratic forms.
- Definition of eigenvalue and eigenvector
- Square matrices and diagonal matrices
- Diagonalization of symmetric matrices
- Application to the study of quadratic forms

Dynamical systems.
- Differential equations
- First order differential equations
- Linear differential equations with constant coefficients
- Difference equations
- First order difference equations
- Difference equations with constant coefficients
- Introduction to systems of differential equations
- Linear systems of difference and differential equations

SECOND PART

Financial Mathematics.
- Capitalization and discounting regimes
- The simple interest regims
- The compound interest regime
- The commercial discount regime
- Equivalent rates, variable rateAnnuities and repayment plans

NPV and IRR selection criteria.

Recommended Bibliography

TEXTBOOKS
- Salsa S., A. Squellati, Dynamical Systems and Optimal Control, BUP Egea, 2018, ISBN Domestic Edition 978-88-99902-11-7.

- Sydsaeter K., A. Seierstad, P. Hammond, A. Strom, Further Mathematics for Economic Analysis, Pearson College Div, 2nd edition, 2008, ISBN 978-0273713289.

- Chan W.-S. , Y.-K. Tse, Financial and Actuarial Mathematics, McGraw-Hill, 2007, ISBN 9780071258562.

OTHER MATERIAL
Other teaching material (available in the “comunità didattica” of “Matematica II” from the Moodle platform integrated into the student’s ESSE3 web page)

Methods of Provision

Conventional

Teaching Methods

The teaching methods include various activities by the instructor and the students. The participation of students in teaching activities is not compulsory, although it is strongly recommended for the full achievement of the educational objectives.

The course consists of 16 lectures and 8 tutorials.

In the a.y. 2020/21, all lectures and all tutorials will be delivered online through the support of the software Microsoft Teams.

Assessment Methods

Each exam, which students must register to through their ESSE3 web page, consists of a written test.
The written examination lasts 2 hours.

Assessment:

Final Mark

Programme of Educational Activities

Start date of teaching period:

Monday, September 14, 2020

End date of teaching period:

Tuesday, December 15, 2020