CALCULUS

Single discipline educational activity

Course Sheet

Course code:

00075L

Academic Year of enrolment:

2020

Year of supply:

2020/2021

Type of Course:

Characterising

Degree:

Course of 1st Cycle Degree in BUSINESS ADMINISTRATION

Disciplinary Sector:

MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES

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-business 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 and business-economic subjects present in the training courses of the Degree Course.
To this end, 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 business phenomena.
At the end of the course the student will be able to formalize some economic-business 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 business 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 and business 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 and business problems such as, for example, profit maximization and utility.
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 and business phenomena also in terms of quantity, as well as the usual legal and economic aspects studied in other disciplines of the Degree Course in Business Economics.
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 business-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 concerning business management.

Contents

Differential and integral calculus for one variable functions. Elements of Linear Algebra. Basic properties of two variable functions.

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.
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.
FUNCTIONS OF TWO VARIABLES (1 CFU): Definition and domain, basic properties, research of stationary points and study of their nature through the use of the Hessian matrix.

Recommended Bibliography

Paolo Marcellini e Carlo Sbordone: “Calcolo”, Liguori Editore.
Exercises provided on dedicated website.

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 business management. 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 total duration of the written test is two and a half hours.

Contacts/More Information

E-mail: flavia.antonacci@unich.it

Università degli Studi
"G. d'Annunzio"

Chieti - Pescara

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