# MATHEMATICS, FIRST PART

Degree course:
Corso di First cycle degree in ECONOMICS AND MANAGEMENT
Academic year when starting the degree:
2019/2020
Year:
1
Academic year in which the course will be held:
2019/2020
Course type:
Basic compulsory subjects
Language:
Italian
Credits:
6
Period:
Second semester
Standard lectures hours:
40
Detail of lecture’s hours:
Lesson (40 hours)
Requirements:

None.
The course will cover the analytical tools necessary to deal with the study of mathematics in economics courses. It is however recommended students verify their mastery of the basic techniques of:
1. Algebraic calculus: remarkable products, decomposition of polynomials, recollection with common factor, produced between algebraic expressions.
2. Equations: solution of first degree equations in an unknown, second degree in an unknown, fractional rationals, of superior degree the second one by polynomial decomposition. First degree systems of equations.
3. Inequalities: solution of first-degree inequalities in an unknown, second-degree in an unknown, fractional rationals, with a higher degree than the second by polynomial decomposition.
4. Analytical geometry: Cartesian coordinates, line equation, parabola (with vertical axis), equilateral hyperbola with parallel axes, Cartesian axes and circumference (with center in the origin). Intersection problems between curves in the Cartesian plane.

Final Examination:
Orale

Exam is a written test designed to assess the achievement of each goal of the course.

Students can take the exam with two alternatives

General Exam.
During exams'session, students can attend a 90 minutes exam consisting of 5 multiple choice questions and 5 open answer problems. Both theoretical and practical skills are tested. Exercises require both theoretical issues and practical (e.g. calculus) skills.

Each multiple choice question credits 2 points when the correct answer is given, 0 points if the answer is wrong or missing. Open answer problems credits up to 22 points. The exam paper will provide with the maximum score for each exercise.

The final grade is the sum of the points obtained. To pass the exam a grade no less than 18 (eighteen) is required. Total greater than 30 grants honor marks.

Partial exams.

At the end of the first part of lectures (approximatively after 20 hours) and at the end of the lectures, students can take part to partial exams. The test consists of 5 multiple choice questions and 4 open answer problems, covering mainly the topics of the lectures delivered during the midterm ended. To solve the proposed exercises both theoretical and practical skills are required. Exam time is 60 minutes.

Each multiple choice question credits 2 points when the correct answer is given, 0 points if the answer is wrong or missing. Open answer problems credits up to 22 points. The exam paper will provide with the maximum score for each exercise.

Students need at least 15 points to pass a single partial exam. The final grade is the simple average of the two grades, rounded up. If the average is no less than 18 (eighteen), the exam is passed. Average greater than 30 credit honor marks.

POP QUIZ.
Randomly, during the lectures, attending students will be assigned a quiz on the topics of previous lectures. Tests will be solved in class and graded accordingly to class performance. During the semester 5 quiz will be proposed, and among the students who attended no less than 3 of these quiz, a bonus of up to 2 points will be credited. Those students with an average performance in the top 3 quiz graded in the top 25% of the class will be granted 2 points. Those performing in the bottom 25% will have 0 points, the others 1 point.

Assessment:
Voto Finale

The course aims to provide students with basic analytical tools to address quantitative study of economic and management subjects.
At the end of the course students will be able to
• graph elementary functions representing basic models for economic analysis;
• operate with the analytical expression of functions of one and several real variables;
• solve calculus problems with functions of one and several variables;
• solve linear algebra problems, involving matrices and vectors;
• study and solve linear systems, involving real parameters.

Main topics covered are:

Functions of one variable (ch. 2,3,4):
Number sets. Set R: metric structure and topology.
Real functions of real variable, domain, elementary functions, monotonicity, extreme points, concavity and convexity, geometric transformations.

Differential calculus in one variable (ch. 8,9):
Intuitive concept of derivative and its geometrical meaning. Derivatives of elementary functions. Calculus, higher order derivatives. Stationary points, test for monotonicity, convexity's test.

Functions of several variables (ch. 14, 17):
Functions of two variables, domain and level curve.
Partial derivatives, stationary points. First order condition for uncostrained otpimization.

Linear algebra (ch. 15, 16):
Vectors, matrices, matrix calculus and determinant, rank, linear systems.

At the beginning of the course, students will be given, via e-learning repository, a detailed program of each lecture's topics.

At the beginning of the course, students will be given, via e-learning repository, a detailed program of each lecture's topics.
Main topics covered are:

Functions of one variable (ch. 2,3,4):
Number sets. Set R: metric structure and topology.
Real functions of real variable, domain, elementary functions, monotonicity, extreme points, concavity and convexity, geometric transformations.

Differential calculus in one variable (ch. 8,9):
Intuitive concept of derivative and its geometrical meaning. Derivatives of elementary functions. Calculus, higher order derivatives. Stationary points, test for monotonicity, convexity's test.

Functions of several variables (ch. 14, 17):
Functions of two variables, domain and level curve.
Partial derivatives, stationary points. First order condition for uncostrained otpimization.

Linear algebra (ch. 15, 16):
Vectors, matrices, matrix calculus and determinant, rank, linear systems.

Angelo Guerraggio, Matematica – Seconda edizione, Pearson, Milano, 2009.

Detailed references will be provided during classes.

Convenzionale

Lectures will discuss both theoretical arguments and solution techniques for most common exercises related to the subject. Additional exercise will be assigned during classes both for individual study and to be solved in the next lecture. Active attendance is strongly recommended.

## Professors

CRESPI GIOVANNI PAOLO