Ciro D'APICE | MATHEMATICS FOR ECONOMICS

cod. 0212700117

MATHEMATICS FOR ECONOMICS

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

CURRICULUM ACCOUNTING, FINANCE AND AUDITING

	OBBLIGATORIO
	YEAR OF COURSE 1
	YEAR OF DIDACTIC SYSTEM 2014
	AUTUMN SEMESTER

TEACHING UNITS

	SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
	SECS-S/06	10	60	LESSONS	BASIC COMPULSORY SUBJECTS

PROFESSORS

	FRANCESCO SAVERIO TORTORIELLO T Curriculum
	GERARDO DURAZZO Curriculum

	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.

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

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.

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.

	More Information
	THE LANGUAGE OF INSTRUCTION IS ITALIAN.

BETA VERSION Data source ESSE3 [Ultima Sincronizzazione: 2022-11-21]

Ciro D'APICE | MATHEMATICS FOR ECONOMICS