Rosa FERRENTINO | Mathematics for Economics

cod. 0212400006

MATHEMATICS FOR ECONOMICS

	0212400006
	DEPARTMENT OF ECONOMICS AND STATISTICS
	EQF6
	ECONOMICS
	2021/2022

CURRICULUM ECONOMICO FINANZIARIO

	OBBLIGATORIO
	YEAR OF COURSE 1
	YEAR OF DIDACTIC SYSTEM 2016
	AUTUMN SEMESTER

TEACHING UNITS

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

	Objectives
	KNOWLEDGE AND UNDERSTANDING THE STUDENTS WILL BE ABLE TO KNOW THE FUNDAMENTAL BASIC NOTIONS OF LINEAR ALGEBRA AND OF THE DIFFERENTIAL AND INTEGRAL CALCULATION AS WELL AS THE BASIC ELEMENTS OF THE OPTIMIZATION, NOTIONS INDISPENSABLE FOR THE UNDERSTANDING OF THE ECONOMIC-QUANTITATIVE THEMES DEALT IN THE OTHER DISCIPLINES OF THE TRAINING COURSE. IN OTHER WORDS, THE STUDENTS, ON THE BASE OF THE ACQUIRED TECHNIQUES, MUST BE ABLE TO: FACE PROBLEMS OF ECONOMIC-FINANCIAL NATURE , TO DEEPEN THEIR COMPETENCES THROUGH THE CONSULTATION OF PUBLICATIONS IN THEME AND TO DEVELOP CRITICAL CAPACITY TO USE IN APPROPRIATE APPLICATIONS AND IN THE MOST ADVANCED MATHEMATICS COURSES. ABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING THE STUDENTS WILL BE ABLE TO ACQUIRE ANALYTICAL AND CRITICAL ABILITIES WITH REGARD TO THE DEVELOPED INSTRUMENTS AND RULES, NAMELY THE STUDENTS WILL BE ABLE TO USE THE MATHEMATICAL TOOLS LEARNED FOR TO UNDERSTAND AND TO RESOLVE PROBLEMS OF ECONOMIC-FINANCIAL CHARACTER AND TO MAKE DECISIONS IN THE BUSINESS AREA.

KNOWLEDGE AND UNDERSTANDING

THE STUDENTS WILL BE ABLE TO KNOW THE FUNDAMENTAL BASIC NOTIONS OF LINEAR ALGEBRA AND OF THE DIFFERENTIAL AND INTEGRAL CALCULATION AS WELL AS THE BASIC ELEMENTS OF THE OPTIMIZATION, NOTIONS INDISPENSABLE FOR THE UNDERSTANDING OF THE ECONOMIC-QUANTITATIVE THEMES DEALT IN THE OTHER DISCIPLINES OF THE TRAINING COURSE.
IN OTHER WORDS, THE STUDENTS, ON THE BASE OF THE ACQUIRED TECHNIQUES, MUST BE ABLE TO: FACE PROBLEMS OF ECONOMIC-FINANCIAL NATURE , TO DEEPEN THEIR COMPETENCES THROUGH THE CONSULTATION OF PUBLICATIONS IN THEME AND TO DEVELOP CRITICAL CAPACITY TO USE IN APPROPRIATE APPLICATIONS AND IN THE MOST ADVANCED MATHEMATICS COURSES.

ABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING

THE STUDENTS WILL BE ABLE TO ACQUIRE ANALYTICAL AND CRITICAL ABILITIES WITH REGARD TO THE DEVELOPED INSTRUMENTS AND RULES, NAMELY THE STUDENTS WILL BE ABLE TO USE THE MATHEMATICAL TOOLS LEARNED FOR TO UNDERSTAND AND TO RESOLVE PROBLEMS OF ECONOMIC-FINANCIAL CHARACTER AND TO MAKE DECISIONS IN THE BUSINESS AREA.

	Prerequisites
	INTRODUCTORY ELEMENTARY NOTIONS, EQUATIONS AND INEQUALITIES OF VARIOUS TYPES. ANALYTIC GEOMETRY ELEMENTS. MORE PRECISELY: NATURAL, RELATED, RATIONAL AND REAL NUMBERS AND THEIR REPRESENTATION ON THE LINE. EQUATIONS AND INEQUALITIES OF FIRST AND SECOND GRADE, ENTIRE AND FRACTIONAL . SYSTEMS OF INEQUALITIES. EXPONENTIAL AND LOGARITHMIC EQUATIONS AND INEQUATIONS. IRRATIONAL EQUATIONS AND INEQUALITIES. NOTES OF ANALYTICAL GEOMETRY : EQUATION OF A LINE AND OF A PARABOLE. SOME OF THESE PREREQUISITES CAN BE FOUND IN THE SUGGESTED TEXTS; IN ANY CASE, THEY ARE AVAILABLE ON ANY TEXTBOOK FOR HIGHER SCHOOLS.

Prerequisites

INTRODUCTORY ELEMENTARY NOTIONS, EQUATIONS AND INEQUALITIES OF VARIOUS TYPES. ANALYTIC GEOMETRY ELEMENTS. MORE PRECISELY: NATURAL, RELATED, RATIONAL AND REAL NUMBERS AND THEIR REPRESENTATION ON THE LINE. EQUATIONS AND INEQUALITIES OF FIRST AND SECOND GRADE, ENTIRE AND FRACTIONAL . SYSTEMS OF INEQUALITIES. EXPONENTIAL AND LOGARITHMIC EQUATIONS AND INEQUATIONS. IRRATIONAL EQUATIONS AND INEQUALITIES.
NOTES OF ANALYTICAL GEOMETRY : EQUATION OF A LINE AND OF A PARABOLE.
SOME OF THESE PREREQUISITES CAN BE FOUND IN THE SUGGESTED TEXTS; IN ANY CASE, THEY ARE AVAILABLE ON ANY TEXTBOOK FOR HIGHER SCHOOLS.

	Contents
	ELEMENTS OF THEORY OF SETS. ELEMENTS OF COMBINATORY CALCULATION . ELEMENTS OF LINEAR ALGEBRA: VECTORS, MATRICES AND LINEAR SYSTEMS. WITH AND WITHOUT PARAMETER, EIGENVALUES AND EIGENVECTORS. NUMERICAL SETS. REAL FUNCTIONS OF REAL VARIABLE. DOMAIN AND LIMITS OF A FUNCTION. OPERATIONS AND THEOREMS ON THE LIMITS. INDETERMINATE FORMS. ASYMPTOTES. ELEMENTS OF DIFFERENTIAL CALCULUS: DERIVATIVE OF A FUNCTION AND ITS GEOMETRIC MEANING. DERIVABILITY AND CONTINUITY. DERIVATION RULES. RELATIVE EXTREMES. FUNDAMENTAL THEOREMS OF DIFFERENTIAL CALCULATION. SUBSEQUENT DERIVATIVES. RULE OF DE L 'HOSPITAL, CONCAVITY, CONVEXITY AND FLEXES. FUNCTIONS STUDY SUCCESSIONS AND NUMERICAL SERIES. FIRST DIFFERENTIAL AND ITS GEOMETRIC MEANING. ELEMENTS OF THE INTEGRAL CALCULATION: INDEFINITE INTEGRAL AND INTEGRATION METHODS. DEFINED INTEGRAL AND ITS GEOMETRIC MEANING. FUNCTIONS OF MORE VARIABLES: DOMAIN, PARTIAL DERIVATIVES, MAXIMA AND MINIMA (FREE AND SUBJECT TO CONSTRAINTS). APPLICATION OF THE ANALYSIS TO THE ECONOMY.

Contents

ELEMENTS OF THEORY OF SETS. ELEMENTS OF COMBINATORY CALCULATION . ELEMENTS OF LINEAR ALGEBRA: VECTORS, MATRICES AND LINEAR SYSTEMS. WITH AND WITHOUT PARAMETER, EIGENVALUES AND EIGENVECTORS. NUMERICAL SETS. REAL FUNCTIONS OF REAL VARIABLE. DOMAIN AND LIMITS OF A FUNCTION. OPERATIONS AND THEOREMS ON THE LIMITS. INDETERMINATE FORMS. ASYMPTOTES. ELEMENTS OF DIFFERENTIAL CALCULUS: DERIVATIVE OF A FUNCTION AND ITS GEOMETRIC MEANING. DERIVABILITY AND CONTINUITY. DERIVATION RULES. RELATIVE EXTREMES. FUNDAMENTAL THEOREMS OF DIFFERENTIAL CALCULATION. SUBSEQUENT DERIVATIVES. RULE OF DE L 'HOSPITAL, CONCAVITY, CONVEXITY AND FLEXES. FUNCTIONS STUDY
SUCCESSIONS AND NUMERICAL SERIES. FIRST DIFFERENTIAL AND ITS GEOMETRIC MEANING. ELEMENTS OF THE INTEGRAL CALCULATION: INDEFINITE INTEGRAL AND INTEGRATION METHODS. DEFINED INTEGRAL AND ITS GEOMETRIC MEANING.
FUNCTIONS OF MORE VARIABLES: DOMAIN, PARTIAL DERIVATIVES, MAXIMA AND MINIMA (FREE AND SUBJECT TO CONSTRAINTS). APPLICATION OF THE ANALYSIS TO THE ECONOMY.

	Teaching Methods
	THE TEACHING INCLUDES 60 HOURS OF DIDACTICS BETWEEN FRONTAL LESSONS AND EXERCISES (10 CFUS). FURTHERMORE, STUDY GROUPS AND CLASSROOM DISCUSSIONS ARE PREDICTED. THE STUDENT WILL HAVE TO ATTEND THE LESSON HELD BY THE TEACHER AND, AUTONOMOUSLY, MUST PROCESS AND ELABORATE THE LISTENED CONTENT. THE FREQUENCY TO THE TEACHING ACTIVITIES IS NOT MANDATORY BUT HIGHLY RECOMMENDED.

	Verification of learning
	EXERCISES PROVIDED BY THE TEACHER, SIMULATIONS, WRITTEN TEST AND FINAL ORAL TEST. THE STUDENTS, ON THE BASIS OF THE ACQUIRED TECHNIQUES, WILL HAVE TO BE ABLE TO ENUNCIATE AND TO DEMONSTRATE THEOREMS AND TO SUSTAIN, IN CLEAR AND EFFECTIVE WAY, AN ORAL DISCUSSION WITH OPPORTUNE REFERENCES TO THE CONTENTS OF THE COURSE. IN PARTICULAR, THE ACHIEVEMENT OF THE TEACHING OBJECTIVES IS CERTIFIED BY PASSING AN EXAMINATION WITH A EVALUATION IN THIRTY. THE EXAM FORECASTS A WRITTEN TEST AND AN ORAL TEST THAT MAY TAKE PLACE IN DIFFERENT DAYS. THE WRITTEN TEST IS PROPAEDEUTIC TO THE ORAL TEST. THE DATE OF THE WRITTEN TEST IS THAT PROVIDED BY THE DEPARTMENT CALENDAR WHILE THE DAY OF THE ORAL TEST IS AGREED WITH THE STUDENTS ON THE DAY OF THE WRITTEN TEST. EACH TEST IS EVALUATED IN THIRTY, AND IS EXCEEDED WITH A MINIMUM VOTE OF 18/30. THE FINAL VOTE IS GIVEN BY THE AVERAGE OF THE VOTES REPORTED IN EACH TEST. THE WRITTEN TEST, WHICH LASTS ABOUT 120 MINUTES, IS AIMED TO VERIFY THE LEVEL OF KNOWLEDGE AND THE ABILITY TO UNDERSTAND THE TOPICS INDICATED IN THE PROGRAM AND PROPOSED DURING THE COURSE, THE MASTERY THE ANALYTICAL TOOLS, THE ABILITY TO APPLY THE ACQUIRED THEORETICAL KNOWLEDGE AND, FINALLY, THE ABILITY TO COMMUNICATE IN AN EFFECTIVE AND PERTINENT MANNER IN WRITTEN FORM.. IT CONSISTS IN SOLVING A CERTAIN NUMBER OF EXERCISES CONCERNING THE ARGUMENTS OF THE COURSE, AT EACH OF WHICH IS ASSIGNED A SCORE THAT VARIES DEPENDING ON THE COMPLEXITY OF THE CALCULATIONS REQUIRED AND WHICH IS DECLARED TO THE STUDENT BY THE TEACHER. THE EXERCISES PROPOSED ARE SIMILAR TO THOSE RESOLVED DURING THE HOURS OF LESSON. THE WRITTEN TEST IS PASSED IF THE STUDENT HAS CORRECTLY RESOLVED THE PROPOSED EXERCISES (WITH A TOTAL SCORE OF NOT LESS THAN 18 THIRTIETH). THE SCORE OF THE WRITTEN TEST IS EQUAL TO THE SUM OF THE POINTS ASSIGNED TO THE INDIVIDUAL QUESTIONS CARRIED OUT BY THE STUDENT. DURING THE WRITTEN TEST IT IS NOT PERMITTED TO CONSULT TEXTS, USE PC AND MOBILE PHONES; THE CALCULATOR IS ALLOWED ONLY IN SOME CASES. THE ORAL TEST, WHICH LASTS APPROXIMATELY 30 MINUTES, CONSISTS IN A DISCUSSION ON DEMONSTRATIONS OF THE THEOREMS PROPOSED DURING THE LESSONS AND ON THE THEORETICAL AND METHODOLOGICAL CONTENTS INDICATED IN THE PROGRAM, IN ORDER TO ENSURE NOT ONLY THE LEVEL OF KNOWLEDGE AND THE ABILITY TO UNDERSTANDING REACHED BY THE STUDENT BUT ALSO THE ABILITY TO EXPOSE THE TOPICS WITH THE APPROPRIATE TERMINOLOGY. INTERCURSE TESTS ARE NOT PROVIDED

Verification of learning

EXERCISES PROVIDED BY THE TEACHER, SIMULATIONS, WRITTEN TEST AND FINAL ORAL TEST.
THE STUDENTS, ON THE BASIS OF THE ACQUIRED TECHNIQUES, WILL HAVE TO BE ABLE TO ENUNCIATE AND TO DEMONSTRATE THEOREMS AND TO SUSTAIN, IN CLEAR AND EFFECTIVE WAY, AN ORAL DISCUSSION WITH OPPORTUNE REFERENCES TO THE CONTENTS OF THE COURSE.
IN PARTICULAR, THE ACHIEVEMENT OF THE TEACHING OBJECTIVES IS CERTIFIED BY PASSING AN EXAMINATION WITH A EVALUATION IN THIRTY.
THE EXAM FORECASTS A WRITTEN TEST AND AN ORAL TEST THAT MAY TAKE PLACE IN DIFFERENT DAYS. THE WRITTEN TEST IS PROPAEDEUTIC TO THE ORAL TEST. THE DATE OF THE WRITTEN TEST IS THAT PROVIDED BY THE DEPARTMENT CALENDAR WHILE THE DAY OF THE ORAL TEST IS AGREED WITH THE STUDENTS ON THE DAY OF THE WRITTEN TEST.
EACH TEST IS EVALUATED IN THIRTY, AND IS EXCEEDED WITH A MINIMUM VOTE OF 18/30. THE FINAL VOTE IS GIVEN BY THE AVERAGE OF THE VOTES REPORTED IN EACH TEST.
THE WRITTEN TEST, WHICH LASTS ABOUT 120 MINUTES, IS AIMED TO VERIFY THE LEVEL OF KNOWLEDGE AND THE ABILITY TO UNDERSTAND THE TOPICS INDICATED IN THE PROGRAM AND PROPOSED DURING THE COURSE, THE MASTERY THE ANALYTICAL TOOLS, THE ABILITY TO APPLY THE ACQUIRED THEORETICAL KNOWLEDGE AND, FINALLY, THE ABILITY TO COMMUNICATE IN AN EFFECTIVE AND PERTINENT MANNER IN WRITTEN FORM.. IT CONSISTS IN SOLVING A CERTAIN NUMBER OF EXERCISES CONCERNING THE ARGUMENTS OF THE COURSE, AT EACH OF WHICH IS ASSIGNED A SCORE THAT VARIES DEPENDING ON THE COMPLEXITY OF THE CALCULATIONS REQUIRED AND WHICH IS DECLARED TO THE STUDENT BY THE TEACHER. THE EXERCISES PROPOSED ARE SIMILAR TO THOSE RESOLVED DURING THE HOURS OF LESSON.
THE WRITTEN TEST IS PASSED IF THE STUDENT HAS CORRECTLY RESOLVED THE PROPOSED EXERCISES (WITH A TOTAL SCORE OF NOT LESS THAN 18 THIRTIETH).
THE SCORE OF THE WRITTEN TEST IS EQUAL TO THE SUM OF THE POINTS ASSIGNED TO THE INDIVIDUAL QUESTIONS CARRIED OUT BY THE STUDENT.
DURING THE WRITTEN TEST IT IS NOT PERMITTED TO CONSULT TEXTS, USE PC AND MOBILE PHONES; THE CALCULATOR IS ALLOWED ONLY IN SOME CASES.
THE ORAL TEST, WHICH LASTS APPROXIMATELY 30 MINUTES, CONSISTS IN A DISCUSSION ON DEMONSTRATIONS OF THE THEOREMS PROPOSED DURING THE LESSONS AND ON THE THEORETICAL AND METHODOLOGICAL CONTENTS INDICATED IN THE PROGRAM, IN ORDER TO ENSURE NOT ONLY THE LEVEL OF KNOWLEDGE AND THE ABILITY TO UNDERSTANDING REACHED BY THE STUDENT BUT ALSO THE ABILITY TO EXPOSE THE TOPICS WITH THE APPROPRIATE TERMINOLOGY.
INTERCURSE TESTS ARE NOT PROVIDED

	Texts
	S. GRECO, B. MATARAZZO, S. MILICI: MATEMATICA GENERALE, G. GIAPPICHELLI EDITORE, SECONDA EDIZIONE 2016. R. FERRENTINO: INTRODUZIONE AI CORSI DI MATEMATICA GENERALE E STATISTICA, CUSL, 2012. G. GIORGI: ELEMENTI DI MATEMATICA, GIAPPICHELLI EDITORE, 1999. G. TOMMEI: MATEMATICA DI BASE. SECONDA EDIZIONE MAGGIOLI EDITORE, 2015. C. MATTALIA- F.PRIVILEGGI: MATEMATICA PER LE SCIENZE ECONOMICHE E SOCIALI. FUNZIONI DI UNA VARIABILE. MAGGIOLI EDITORE, 2015. G. ANICHINI- A.CARBONE- P.CHIARELLI-G.CONTI: PRECORSO DI MATEMATICA, PEARSON EDITORE, 2018 G.BOSI- C.CORSATO- M.E.ZUANON: ESSENTIAL MATHEMATICS FOR ECONOMICS, MAGGIOLI EDITORE, 2018

Texts

S. GRECO, B. MATARAZZO, S. MILICI: MATEMATICA GENERALE, G. GIAPPICHELLI EDITORE, SECONDA EDIZIONE 2016.
R. FERRENTINO: INTRODUZIONE AI CORSI DI MATEMATICA GENERALE E STATISTICA, CUSL, 2012.
G. GIORGI: ELEMENTI DI MATEMATICA, GIAPPICHELLI EDITORE, 1999.
G. TOMMEI: MATEMATICA DI BASE. SECONDA EDIZIONE MAGGIOLI EDITORE, 2015.
C. MATTALIA- F.PRIVILEGGI: MATEMATICA PER LE SCIENZE ECONOMICHE E SOCIALI. FUNZIONI DI UNA VARIABILE. MAGGIOLI EDITORE, 2015.
G. ANICHINI- A.CARBONE- P.CHIARELLI-G.CONTI: PRECORSO DI MATEMATICA, PEARSON EDITORE, 2018
G.BOSI- C.CORSATO- M.E.ZUANON: ESSENTIAL MATHEMATICS FOR ECONOMICS, MAGGIOLI EDITORE, 2018

	More Information
	THERE ARE NO INTER-COURSE TESTS

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Rosa FERRENTINO | Mathematics for Economics

MATHEMATICS FOR ECONOMICS

CURRICULUM ECONOMICO FINANZIARIO

TEACHING UNITS

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Rosa FERRENTINO | Mathematics for Economics