MATHEMATICS FOR ECONOMICS AND FINANCE

Course Sheet

Course code:

MECOF19

Academic Year of enrolment:

2020

Year of supply:

2020/2021

Divisions:

Cognomi E-Z

Type of Course:

Basic

Degree:

Course of 1st Cycle Degree in MANAGEMENT AND ECONOMICS

Disciplinary Sector:

MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES

Is part of:

MATHEMATICS FOR ECONOMICS AND FINANCE

Location:

PESCARA

Credits:

Programme Year:

Professor and Collaborators:

AMATO Gianluca

Cycle:

First semester

Hours of classroom activity:

Individual study hours:

136

Prerequisites:

It is required that the students know the following topics, which are part of the math program of high schools: algebraic symbolic calculus, 1st and 2nd order equations and inequations, radicals, equation of the straight line.

Objectives

In accordance with the didactic regulation, the aim of this course is to provide the student with the basic mathematical knowledge which will be useful for the following economic studies, in particular with respect to mathematical analysis and finance. We wil focus on fully understanding the meaning of the important concepts, rather than acquiring strong computational skills.

LEARNING OUTCOMES

KNOWLEDGE AND UNDERSTANDING:

At the end of the course, the student will be able to:
* clearly and correctly expose the basic definitions and theorems of mathematical analysis and linear algebra;
* exemplify definitions and theorems;
* illustrate the importance and usefulness of the hypotheses in the statement of theorems.

APPLYING KNOWLEDGE AND UNDERSTANDING:

At the end of the course, the student will be able to:
* solve equations and inequations (integral, fractional, irrational, with absolute value, exponential and logarithmic);
* draw approximated graphs and determine simple properties of functions whose closed formula is known;
* determine, in an approximate manner, the fundamental properties of functions whose graph is known;
* determine the area of plain figures using integral calculus;
* operate with vectors and matrices.

COMMUNICATION SKILLS:

At the end of the course, the student will be able to express quantitative concepts using a correct and accurate mathematical language.

Contents

Introduction to propositional and first-order logic. Functions and numerical sets. Elementary functions. Limits. Continuous functions. Derivatives. Study of functions. Indefinite integrals. Definite integrals. Vectors. Matrices.

Extended Syllabus

Elements of logic

Propositions
Propositional connectives
Quantifiers
Definitions, theorems and proofs

Functions and numerical sets

Sets and operations between sets
The concept of function
Injective functions, composition and inverse function
Natural, integer, rational and real numbers
Intervals
Extended system of real numbers
Correspondence between a function and its graph

The elementary functions

Increasing and decreasing functions
Concave and convex functions
Even and odd functions
Linear functions, straight lines, first-order equations and inequations
Quadratic functions, parabolas, second-order equations and inequations
The power function with integer exponent, polynomial equations and inequations
Hyperbole, rational equation and inequations
The power function with fractional exponent, roots, equations and inequations with radicals
The exponential function, equations and inequations with exponentials
The logarithmic function, equations and inequations with logarithms
The "integer part" functions and the absolute value, equations and inequations with absolute values
Almost-elementary functions
Sequences
Sequences defined by recurrence

Limits

Neighbourhood of a number and accumulation points
Definition of limit
One-sided limit.
Limits of sequences.
Existence of the limit for increasing or decreasing functions
Squeeze theorem
Uniqueness of the limit

Continuous functions

Definition of continuous functions
Properties of continuous functions: Weierstrass, Bolzano and intermediate values theorems
Calculation of limits and indeterminate forms
Infinites and infinitesimals
The "little-O" notation

Derivatives

Definition of derivative of a function
Geometric meaning of the derivative
Calculation of derivatives
Derivability and continuity
Higher derivatives
Maxima and minima of functions
Convexity, concavity and inflection points
Study of a function

Integrals

The anti-derivative (or primitive) of a function
Immediate and quasi-immediate anti-derivatives
The definite integral
Property of the definite integral
Fundamental theorem of calculus
Improper integrals

Vectors and matrices

Vectors of R^n
Operations on vectors: sum, scalar multiplication, internal product
Geometric interpretation of operations between vectors
Linear combination of vectors, linear independence, bases and generators
Distance between vectors, norm of a vector, neighborhood of a vector
Matrices: definition and special types
Operations between matrices: sum, scalar multiplication, matrix product, transposition
Determinant of a matrix in the cases 1x1, 2x2, 3x3
Definition of inverse of a square matrix
Rank of a matrix

Recommended Bibliography

The reference book is:

* Angelo Guerraggio. Matematica (third edizione). Pearson.

Lecture notes provided by the teacher will cover the part of the course program relative to logic.

We also recommend the use of an exercise book, such as the following:

* Marco Castellani, Fausto Gozzi. Matematica di base per l'economia e l'azienda. Società Editrice Esculapio.

Teaching Methods

The course is divided into lectures of two hours each, for a total of 64 hours. Lectures consist of theoretical lessons and exercises. Attendance is optional but recommended.

During the course, students will be presented with on-line self-assessment exercises which can be attemped on-line from their own house.

The foregoing may be subject to change should the teaching be delivered remotely.

Evaluation methods

Verification of learning:

The exam consists of a written test and an oral test.

The written test is a quiz with closed and open-ended questions, whose purpose is to evaluate the level of skills acquired by the student. The maximum mark of the written test is 24, while the minimum to be admitted to the following exam phases is 14.

If the student has passed the written test with a mark of at least 18, the oral test is optional, and can be requested by either the student or the teacher. If, on the other hand, the written test has been passed, but with a mark of less than 18, then the oral test is compulsory. The oral test aims to assess the degree of understanding of the conceptual aspects of the subject, the ability to express himself in a correct language and the capacity of reasoning. The maximum mark of the oral test is 10, and the minimum to be admitted to the final evaluation is 4.

The final mark is obtained by adding the mark of the written test to that of any oral test, obviously up to a maximum of 30. The overall test is considered successfully passed if the student, arrived at the final evaluation, has obtained a final mark of at least 18. If the sum of the mark of the oral test and that of the written test is greater than or equal to 32, the teacher will evaluate whether to grant the honors. The exam is the same for attending and non-attending students.

Contacts/More Information

Further information is available on the web page of the course within the university e-elearning platform.

Università degli Studi
"G. d'Annunzio"

Chieti - Pescara

Aree