# Economia e Management | MATHEMATICS FOR ECONOMICS

## Economia e Management MATHEMATICS FOR ECONOMICS

 0212700117 DEPARTMENT OF MANAGEMENT & INNOVATION SYSTEMS EQF6 BUSINESS MANAGEMENT 2021/2022

 OBBLIGATORIO YEAR OF COURSE 1 YEAR OF DIDACTIC SYSTEM 2014 AUTUMN SEMESTER
SSD CFU HOURS ACTIVITY TYPE OF ACTIVITY SECS-S/06 10 60 LESSONS BASIC COMPULSORY SUBJECTS

 FRANCESCO SAVERIO TORTORIELLO T GERARDO DURAZZO
Objectives
STUDENTS WILL HAVE AT THEIR DISPOSAL FUNDAMENTAL MATHEMATICAL TOOLS FOR AN APPROPRIATE QUANTITATIVE APPROACH TO THE BUSINESS AND FINANCIAL ISSUES THAT WILL BE ADDRESSED DURING THE DEGREE COURSE.
STUDENTS WILL BE ABLE TO APPLY THE QUANTITATIVE TOOLS LEARNED TO SOLVE SOME CLASSICAL PROBLEMS IN ECONOMICS AND FINANCIAL CHOICES.

KNOWLEDGE AND UNDERSTANDING
THE COURSE AIMS AT THE ACQUISITION OF THE FOLLOWING ELEMENTS OF MATHEMATICAL ANALYSIS AND LINEAR ALGEBRA: NUMERICAL SETS, REAL FUNCTIONS OF ONE REAL VARIABLE, EQUATIONS AND INEQUALITIES, LIMITS, CONTINUOUS FUNCTIONS, DERIVATIVES, GRAPH OF A FUNCTION, INTEGRALS, MATRICES AND LINEAR SYSTEMS, REAL FUNCTIONS OF SEVERAL REAL VARIABLES.
THE SPECIFIC EDUCATIONAL OBJECTIVES OF THE COURSE CONSIST ESSENTIALLY IN THE ACQUISITION OF RESULTS AND DEMONSTRATIVE TECHNIQUES, AS WELL AS IN THE ABILITY TO SOLVE EXERCISES AND TO CONSTRUCTIVELY DEAL WITH TEXTBOOKS FOR A SUFFICIENTLY AUTONOMOUS APPROACH TO PROBLEM SOLVING.
STUDENTS WILL HAVE AT THEIR DISPOSAL FUNDAMENTAL MATHEMATICAL TOOLS FOR AN APPROPRIATE QUANTITATIVE APPROACH TO THE BUSINESS AND FINANCIAL ISSUES THAT WILL BE ADDRESSED DURING THE DEGREE COURSE.

ABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING
STUDENTS WILL BE ABLE TO APPLY THE QUANTITATIVE TOOLS LEARNED TO SOLVE SOME CLASSICAL PROBLEMS IN ECONOMICS AND IN FINANCIAL CHOICES.
IN PARTICULAR, THEY WILL BE ABLE TO APPLY THE THEOREMS AND THE RULES STUDIED TO SOLVE PROBLEMS, PERFORM CALCULATIONS WITH LIMITS, DERIVATIVES, INTEGRALS, STUDY THE GRAPH OF A FUNCTION, PERFORM CALCULATIONS WITH MATRICES AND SOLVE LINEAR SYSTEMS, CALCULATE DERIVATIVES AND MAXIMA AND MINIMA OF FUNCTIONS OF SEVERAL REAL VARIABLES.

AUTONOMY OF JUDGMENT
KNOW HOW TO IDENTIFY THE MOST APPROPRIATE METHODS TO EFFICIENTLY SOLVE A MATHEMATICAL PROBLEM.

COMMUNICATION SKILLS
BE ABLE TO PRESENT ORALLY A TOPIC RELATED TO MATHEMATICS.

ABILITY TO LEARN
BE ABLE TO APPLY THE KNOWLEDGE ACQUIRED TO EXAMPLES OTHER THAN THOSE PRESENTED DURING THE LESSONS.

Prerequisites
PREREQUISITES
IN ORDER TO SUCCESSFULLY ACHIEVE THE OBJECTIVES SET AND, IN PARTICULAR, FOR AN ADEQUATE UNDERSTANDING OF THE CONTENTS OF THE COURSE, KNOWLEDGE OF EQUATIONS AND INEQUALITIES ARE PARTICULARLY USEFUL AND THEREFORE REQUIRED TO THE STUDENT.

PROPAEDEUTICITIES
NONE.
Contents
NUMERICAL SETS.
INTRODUCTION. OPERATIONS ON SUBSETS OF A SET. INTRODUCTION TO REAL NUMBERS. EXTREMES OF A NUMERICAL SET. INTERVALS OF R. CONTOURS, ACCUMULATION POINTS. CLOSED AND OPEN SETS.
REAL FUNCTION OF A REAL VARIABLE.
DEFINITION. FIELD OF EXISTENCE, CODOMAIN AND GRAPH OF FUNCTION. EXTREMES OF A REAL FUNCTION. MONOTONOUS FUNCTIONS. COMPOUND FUNCTIONS. INVERTIBLE FUNCTIONS. ELEMENTARY FUNCTIONS: N-TH POWER FUNCTION AND N-TH ROOT, EXPONENTIAL FUNCTION, LOGARITHMIC FUNCTION, POWER FUNCTION.
RECALLS ON EQUATIONS AND INEQUALITIES.
EQUATIONS OF FIRST DEGREE. EQUATIONS OF SECOND DEGREE. IRRATIONAL EQUATIONS. EXPONENTIAL AND LOGARITHMIC EQUATIONS. SYSTEMS OF EQUATIONS. INEQUALITIES OF FIRST DEGREE. INEQUALITIES OF SECOND DEGREE. FRATERNAL INEQUALITIES. IRRATIONAL INEQUALITIES. EXPONENTIAL AND LOGARITHMIC INEQUALITIES. SYSTEMS OF INEQUALITIES.
LIMIT OF A FUNCTION.
DEFINITION. RIGHT LIMIT AND LEFT LIMIT. UNIQUENESS THEOREM. THEOREMS OF COMPARISON. OPERATIONS AND INDETERMINATE FORMS. REMARKABLE LIMITS.
NUMERICAL SUCCESSIONS.
LIMITED, CONVERGING, OSCILLATING AND DIVERGING SUCCESSIONS. MONOTONOUS SUCCESSIONS.
CONTINUOUS FUNCTIONS.
DEFINITION. CONTINUITY AND DISCONTINUITY. WEIERSTRASS THEOREM. THEOREM OF ZEROS.
DERIVATIVE OF A FUNCTION.
DEFINITION. LEFT AND RIGHT DERIVATIVES. GEOMETRIC MEANING, TANGENT LINE TO THE GRAPH OF A FUNCTION. DERIVABILITY AND CONTINUITY. RULES OF DERIVATION. DERIVATIVES OF ELEMENTARY FUNCTIONS. DERIVATIVES OF COMPOUND FUNCTION. HIGHER ORDER DERIVATIVES.
FUNDAMENTAL THEOREMS OF DIFFERENTIAL CALCULUS.
ROLLE'S THEOREM. CAUCHY THEOREM. LAGRANGE'S THEOREM AND COROLLARIES. DE L'HOSPITAL THEOREM. CONDITIONS FOR RELATIVE MAXIMA AND MINIMA.
STUDY OF THE GRAPH OF A FUNCTION.
ASYMPTOTES OF A GRAPH. SEARCH FOR RELATIVE MAXIMA AND MINIMA. CONCAVE AND CONVEX FUNCTIONS IN A POINT, FLEXES. GRAPH OF A FUNCTION THROUGH ITS CHARACTERISTIC ELEMENTS.
INTEGRATION OF FUNCTIONS OF ONE VARIABLE.
DEFINITION OF PRIMITIVE FUNCTION AND INDEFINITE INTEGRAL. IMMEDIATE INTEGRALS. RULES AND METHODS OF INTEGRATION. INTEGRAL OF RATIONAL FUNCTIONS. DEFINITE INTEGRAL AND GEOMETRIC MEANING. MEAN VALUE THEOREM. INTEGRAL FUNCTION AND FUNDAMENTAL THEOREM OF INTEGRAL CALCULUS.
ELEMENTS OF LINEAR ALGEBRA.
MATRICES AND DETERMINANTS. RESOLUTION OF LINEAR SYSTEMS: ROUCHÉ-CAPELLI THEOREM; CRAMER'S THEOREM
Teaching Methods
THE COURSE INCLUDES THEORETICAL LECTURES AND CLASSROOM EXERCISES.
Verification of learning
IN RELATION TO THE LEARNING OBJECTIVES OF THE COURSE, THE EXAM IS AIMED AT EVALUATING: THE KNOWLEDGE AND UNDERSTANDING OF THE CONCEPTS PRESENTED DURING THE LESSONS; THE MASTERY OF THE MATHEMATICAL LANGUAGE IN THE WRITTEN AND ORAL EXAM; THE ABILITY TO PROVE THEOREMS; THE ABILITY TO SOLVE EXERCISES; THE ABILITY TO IDENTIFY AND APPLY THE MOST APPROPRIATE AND EFFICIENT METHODS IN SOLVING AN EXERCISE; THE ABILITY TO APPLY THE ACQUIRED KNOWLEDGE TO SOLVE DIFFERENT EXERCISES THAN THOSE PRESENTED DURING THE EXERCISES.
THE EXAMINATION NECESSARY TO EVALUATE THE ACHIEVEMENT OF THE LEARNING OBJECTIVES CONSISTS OF A WRITTEN TEST, PREPARATORY TO THE ORAL TEST, AND AN ORAL INTERVIEW.
THE WRITTEN TEST CONSISTS OF THE RESOLUTION OF QUESTIONS IMPLEMENTED ON THE BASIS OF WHAT HAS BEEN PROPOSED DURING THE TEACHING ACTIVITIES AND EXERCISES. THE WRITTEN TEST, WHICH THE STUDENT WILL BE REQUIRED TO ADDRESS IN TOTAL AUTONOMY, HAS A DURATION OF 2 HOURS AND A HALF.
IN THE CASE OF PASSING THE WRITTEN TEST, IT WILL BE GIVEN AN ASSESSMENT IN QUALITATIVE BANDS.
THE ORAL INTERVIEW IS MAINLY AIMED AT ASCERTAINING THE DEGREE OF KNOWLEDGE OF ALL TOPICS COVERED BY THE COURSE, AND FOCUSES ON DEFINITIONS, STATEMENTS AND DEMONSTRATION OF THEOREMS, SOLVING EXERCISES.
THE FINAL GRADE, EXPRESSED IN THIRTIETHS WITH POSSIBLE HONORS, IS DETERMINED STARTING FROM THE GRADE OBTAINED THROUGH THE WRITTEN TEST AND MODULATING IT, IN EXCESS OR IN DEFECT, ON THE BASIS OF THE ORAL INTERVIEW.

Texts
C. D’APICE, T. DURANTE, R. MANZO, VERSO L’ESAME DI MATEMATICA I, MAGGIOLI, 2015.
C. D’APICE, R. MANZO, VERSO L’ESAME DI MATEMATICA II MAGGIOLI, 2015.