CALCULUS

Single discipline educational activity

Course Sheet

Course code:

00075L

Academic Year of enrolment:

2021

Year of supply:

2021/2022

Type of Course:

Related/Supplementary

Degree:

Course of 1st Cycle Degree in ECONOMICS AND COMMERCE

Disciplinary Sector:

MATHEMATICAL ANALYSIS

Language:

Italian

Location:

PESCARA

Credits:

Programme Year:

Professor and Collaborators:

ANTONACCI FLAVIA

Cycle:

First semester

Hours of classroom activity:

Individual study hours:

153

Prerequisites:

Basic notions of logic and set theory.
Algebraic computation: powers, logarithms, exponentials; algebraic
equations and inequalities (integer and fractional), irrational, logarithmic
and exponential; systems of equations and inequalities.
Basic elements of analytical geometry.
The preliminary knowledge is recalled within the lessons of the OFA course.

Objectives

The training course of the discipline is aimed at developing both the
inductive capacity and the logical-deductive process of the students.
The aim of the course is, in fact, to provide students with some basic
tools to be used in dealing with economic-financial problems that can be
solved through mathematical modeling and to stimulate students to
acquire a rigorous and essential language.
In particular, we will study the preparatory knowledge for learning
professional subjects, such as financial mathematics, statistics, probability and
economic-financial- business subjects present in the training courses of the Degree
Course.
To this aim, we will provide the basics of linear algebra, differential and
integral calculus and optimization, which constitute an effective tool for
the detection, measurement and quantitative analysis of economic and financial
phenomena.
At the end of the course the student will be able to formalize some
economic and financial problems in mathematical terms, identifying the initial
data and the most suitable mathematical tools for an efficient and
rigorous solution, as well as providing an economic interpretation of the
results obtained .
Expected learning outcomes:
Knowledge and understanding and ability to apply them:
The student will receive the basic tools that will allow him to compare
himself with modern formal approaches to economics and financial sciences. We will also try to give an idea of the possible applications of
the tools introduced, educating the student to a rigorous approach to the
analysis of economic phenomena.
In particular, the student will be able to rigorously analyze a
mathematical problem and use the basic concepts in order to draw
appropriate conclusions. He will be able to conduct mathematical
reasoning through the introduction of rigorous definitions and the
demonstration of some particularly significant theorems and to apply the
learned knowledge to the formalization of some basic economic, financial and
business.
The rigor of the mathematical treatment will allow the student to acquire
a mindset that can be useful to him for the other subjects of his
university course and, later, more generally, for all the professional
themes he will meet.
Autonomy of judgment:
The teaching of general mathematics will allow the student to acquire the
tools to evaluate economic phenomena also in terms of
quantity, as well as the usual legal and economic aspects studied in other
disciplines of the Degree Course in Economics and Commerce.
The student will be educated to autonomously elaborate the most
appropriate approach to the proposed problems and to judge the
formalization proposed by different points of view such as, for example,
the power of the mathematical tool.
Communication skills:
The student must be able to use the technical terms, to be able to
express appropriately the formalization of a problem and the results
obtained with it. The course will provide the student with the ability to
transfer the acquired knowledge and will enable him to possess and know
how to use the appropriate tools both to highlight the quantitative
aspects of typical economic problems, and to solve them after
their mathematical formalization.
Learning ability:
Passing the exam must have enabled the student to acquire skills that
can address not only the study of other courses in the mathematical statistical area, but also the resolution of economic-financial problems.

Contents

Differential and integral calculus for one variable functions. Numerical series. Elements of Linear Algebra.

Extended Syllabus

REVIEW (1 CFU): Sets theory. The set of real numbers: properties e
geometric representation. Integer, fractional, irrational equations and
inequalities and with the absolute value. Review of analytical geometry.
Exponentials and logarithms: definitions and properties. Exponential and
logarithmic equations and inequalities.
ELEMENTARY FUNCTIONS (1 CFU): Definition and properties of
real functions of one real variable. Inverse function. Composed function.
Monotone functions. Limited and unlimited functions, maximum and
minimum of a function. Polynomials functions and rational functions.
Exponential functions and logarithmic functions. Trigonometric functions.
Sequences: definitions and properties.
FUNCTION LIMITS (1 CFU): Definition and properties of the limits for a
function. Properties on
calculation of limits. Indeterminate forms. Notable limits. Continuous
functions.
Discontinuity. Theorems on continuous functions.
DIFFERENTIAL CALCULATION (2 CFU): Incremental fraction.
Definition of derivative. Derivability and differentiability. Geometric
meaning of the
derivative. Derivability and continuity. Angular and cusp points. Higher
order derivatives. Rules of derivation. Rolle's theorem. Theorem of mean
value (of Lagrange). Monotone functions and first derivative. De L’Hospital
theorems and their applications. Relative and absolute maxima and
minima of a function. Convex functions. Applications: study of the graph
of a function. Optimization problems.
INTEGRAL CALCULATION (1 CFU): Primitive of a function.
The indefinite integral and its properties. The definite integral:
construction and properties. The
fundamental theorem of integral calculus. Integration by parts and by
replacement. Calculation of areas of plane figures. Generalized integrals.
ELEMENTS OF LINEAR ALGEBRA (2 CFU): Matrices and operations
between matrices. Square matrices.
Inverse of a matrix. Transposed of a matrix. Determinants: calculation
and properties.
Rank of a matrix. Resolution of linear systems. Cramer's and Rouchè Capelli's theorems.
NUMERICAL SERIES (1 CFU): Definition and properties. Convergence and divergence: criterion for positive and with alternate terms series.

Methods of Provision

Conventional

Teaching Methods

The course is based on about seventy hours of lectures, where the
program topics will first be presented in an intuitive way and then strictly
formalized. Both the theoretical aspects of each topic and the
applications of the mathematical tools described will be studied in depth,
paying particular attention to possible applications in economics and finance. Within the lectures, exercises similar to those
required during the exam will be carried out, which will allow the student
to master the topics of the course.
Each week, students will be offered homework exercises through the
course webpage.

Evaluation methods

Verification of learning:

The final verification of the learning will take place with a written exam
consisting of 6 exercises. The correct resolution of the first exercise,
containing questions on the basic notions, is preparatory to the correction
of the rest of the paper. The other five exercises will tend to check if the
course objectives have been achieved; in particular we will verify the
knowledge of the notions deepened during the lessons and related to the
differential calculus in one and two variables and integral with respect to
a variable, to the optimization and to the bases of linear algebra. The
student must demonstrate that he has developed the ability to master
and understand the quantitative tools in the areas described in the
course objectives. The overall score is given by the sum of the scores
attributed to the individual exercises. The minimum mark for passing the
exam is 16/30. For a vote between 16 and 18 excluded it will be
compulsory to take an oral exam to pass the exam. For an assessment
from 18/30 onwards, the oral exam will be optional, except if explicitly
requested by the teacher when the results of the written exam are
published. During the written test, the date and time of any oral test and
verbalization will be established by mutual agreement.
The duration of the written test is two and a half hours.

Contacts/More Information

For any other information to contact flavia.antonacci@unich.it

Università degli Studi
"G. d'Annunzio"

Chieti - Pescara

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