Ciro D'APICE | MATHEMATICS

cod. 0212700170

MATHEMATICS

	0212700170
	DEPARTMENT OF MANAGEMENT & INNOVATION SYSTEMS
	EQF6
	BUSINESS MANAGEMENT
	2023/2024

CURRICULUM ACCOUNTING, FINANCE AND AUDITING

	OBBLIGATORIO
	YEAR OF COURSE 1
	YEAR OF DIDACTIC SYSTEM 2023
	AUTUMN SEMESTER

TEACHING UNITS

	SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
	SECS-S/06	10	60	LESSONS	COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS

PROFESSORS

	CIRO D'APICE T Curriculum
	MARIA PIA D'ARIENZO Curriculum

	Objectives
	THE COURSE PRESENTS THE BASIC ELEMENTS OF MATHEMATICS. THE EDUCATIONAL AIMS OF THE COURSE CONSIST IN THE ACQUISITION OF THE RESULTS AND DEMONSTRATION TECHNIQUES, AS WELL AS IN THE ABILITY OF USING THE RELATED CALCULATION TOOLS. STUDENTS WILL HAVE AT THEIR DISPOSAL MATHEMATICAL TOOLS THAT ARE FUNDAMENTAL FOR A SUITABLE QUANTITATIVE APPROACH FOR THE BUSINESS AND FINANCIAL ISSUES THAT WILL BE ADDRESSED DURING THE DEGREE COURSE. STUDENTS WILL BE ABLE TO APPLY THE QUANTITATIVE LEARNED INSTRUMENTS TO SOLVE SOME CLASSICAL PROBLEMS WITHIN THE CONTEXT OF ECONOMICS AND FINANCIAL CHOICES.

THE COURSE PRESENTS THE BASIC ELEMENTS OF MATHEMATICS. THE EDUCATIONAL AIMS OF THE COURSE CONSIST IN THE ACQUISITION OF THE RESULTS AND DEMONSTRATION TECHNIQUES, AS WELL AS IN THE ABILITY OF USING THE RELATED CALCULATION TOOLS.
STUDENTS WILL HAVE AT THEIR DISPOSAL MATHEMATICAL TOOLS THAT ARE FUNDAMENTAL FOR A SUITABLE QUANTITATIVE APPROACH FOR THE BUSINESS AND FINANCIAL ISSUES THAT WILL BE ADDRESSED DURING THE DEGREE COURSE. STUDENTS WILL BE ABLE TO APPLY THE QUANTITATIVE LEARNED INSTRUMENTS TO SOLVE SOME CLASSICAL PROBLEMS WITHIN THE CONTEXT OF ECONOMICS AND FINANCIAL CHOICES.

	Prerequisites
	FOR A SUCCESSFUL ACHIEVEMENT OF THE PROPOSED GOALS AND, IN PARTICULAR, FOR A PROPER UNDERSTANDING OF THE CONTENTS SCHEDULED FOR THE TEACHING, STUDENTS ARE REQUIRED TO MASTER THE FOLLOWING PARTICULARLY USEFUL KNOWLEDGE ABOUT EQUATION AND INEQUALITIES. MANDATORY PREPARATORY TEACHINGS NONE.

	Contents
	NUMERICAL SETS. (LECTURE/ PRACTICE/LABORATORY HOURS 2/0/0) INTRODUCTION TO SET THEORY. OPERATIONS ON SUBSETS OF A SET. INTRODUCTION TO REAL NUMBERS. EXTREMES OF A NUMERICAL SET. INTERVALS OF R. NEIGHBORHOODS, POINTS OF ACCUMULATION. CLOSED SETS AND OPEN SETS. REAL FUNCTIONS. (LECTURE/ PRACTICE/LABORATORY HOURS 4/2/0) DEFINITION. DOMAIN, CODOMAIN AND GRAPH OF A FUNCTION. EXTREMES OF A REAL FUNCTION. MONOTONE FUNCTIONS. COMPOSITE FUNCTIONS. INVERTIBLE FUNCTIONS. ELEMENTARY FUNCTIONS: N-TH POWER AND N-TH ROOT FUNCTIONS, EXPONENTIAL, LOGARITHMIC FUNCTION, POWER FUNCTION. BASIC NOTIONS OF EQUATIONS AND INEQUALITIES. (LECTURE/ PRACTICE/LABORATORY HOURS 1/4/0) EQUATIONS OF FIRST ORDER. QUADRATIC EQUATIONS. IRRATIONAL EQUATIONS. EXPONENTIAL AND LOGARITHMIC EQUATIONS. SYSTEMS OF EQUATIONS. LINEAR INEQUALITIES. INEQUALITIES OF THE SECOND ORDER. FACTIONAL INEQUALITIES. IRRATIONAL INEQUALITIES. EXPONENTIAL AND LOGARITHMIC INEQUALITIES. SYSTEMS OF INEQUALITIES. LIMITS OF A FUNCTION. (LECTURE/ PRACTICE/LABORATORY HOURS 2/4/0) DEFINITION. RIGHT AND LEFT HAND-SIDE LIMITS. UNIQUENESS THEOREM. COMPARISON THEOREMS. OPERATIONS AND INDETERMINATE FORMS. KNOWN LIMITS. NUMERICAL SEQUENCES (BASIS ELEMENTS) (LECTURE/ PRACTICE/LABORATORY HOURS 1/0/0) DEFINITION. NUMERICAL SEQUENCES. BOUNDED, CONVERGENT, DIVERGENT AND OSCILLATING SEQUENCES. MONOTONE SEQUENCES. CONTINUOUS FUNCTIONS. (LECTURE/ PRACTICE/LABORATORY HOURS 2/2/0) DEFINITION. CONTINUITY AND DISCONTINUITY. WEIERSTRASS THEOREM. ZEROS THEOREM. DERIVATIVE OF A FUNCTION. (LECTURE/ PRACTICE/LABORATORY HOURS 2/4/0) DEFINITION. LEFT AND RIGHT DERIVATIVES. GEOMETRIC MEANING, THE TANGENT LINE TO THE GRAPH OF A FUNCTION. DIFFERENTIABILITY AND CONTINUITY. DERIVATION RULES. DERIVATIVES OF ELEMENTARY FUNCTIONS. DERIVATIVES OF COMPOSITE FUNCTION. HIGHER ORDER DERIVATIVES. FUNDAMENTAL THEOREMS OF DIFFERENTIAL CALCULUS. (LECTURE/ PRACTICE/LABORATORY HOURS 4/3/0) ROLLE'S THEOREM. CAUCHY'S THEOREM. LAGRANGE'S THEOREM AND COROLLARIES. THEOREM OF DE L'HOSPITAL. CONDITIONS FOR MAXIMA AND MINIMA. GRAPH OF A FUNCTION. (LECTURE/ PRACTICE/LABORATORY HOURS 1/4/0) ASYMPTOTES OF A GRAPH. SEARCH OF MAXIMA AND MINIMA. CONCAVE AND CONVEX FUNCTIONS AT A POINT, INFLECTION POINTS. GRAPH OF A FUNCTION BY ITS CHARACTERISTIC ELEMENTS. INTEGRATION OF ONE VARIABLE FUNCTIONS. (LECTURE/ PRACTICE/LABORATORY HOURS 2/4/0) DEFINITE INTEGRAL AND GEOMETRICAL MEANING. FUNDAMENTAL THEOREM OF CALCULUS. DEFINITION OF INDEFINITE INTEGRAL. BASIC INTEGRALS. RULES AND METHODS OF INTEGRATION. INTEGRAL OF RATIONAL FUNCTIONS. MATRICES AND LINEAR SYSTEMS. (LECTURE/ PRACTICE/LABORATORY HOURS 2/4/0) MATRICES AND DETERMINANTS. LINEAR SYSTEMS: ROUCHE-CAPELLI THEOREM, CRAMER THEOREM. REDUCED ROW ECHELON FORM. MULTIVARIABLE FUNCTIONS. (LECTURE/ PRACTICE/LABORATORY HOURS 3/4/0) DEFINITIONS. LIMITS AND CONTINUITY. WEIERSTRASS THEOREM. PARTIAL DIFFERENTIATION. SCHWARZ THEOREM. GRADIENT AND DIFFERENTIABILITY. DIRECTIONAL DERIVATIVES. LOCAL MINIMA AND MAXIMA. TOTAL LECTURE/ PRACTICE/LABORATORY HOURS 26/34/0

Contents

NUMERICAL SETS.
(LECTURE/ PRACTICE/LABORATORY HOURS 2/0/0)
INTRODUCTION TO SET THEORY. OPERATIONS ON SUBSETS OF A SET. INTRODUCTION TO REAL NUMBERS. EXTREMES OF A NUMERICAL SET. INTERVALS OF R. NEIGHBORHOODS, POINTS OF ACCUMULATION. CLOSED SETS AND OPEN SETS.

REAL FUNCTIONS.
(LECTURE/ PRACTICE/LABORATORY HOURS 4/2/0)
DEFINITION. DOMAIN, CODOMAIN AND GRAPH OF A FUNCTION. EXTREMES OF A REAL FUNCTION. MONOTONE FUNCTIONS. COMPOSITE FUNCTIONS. INVERTIBLE FUNCTIONS. ELEMENTARY FUNCTIONS: N-TH POWER AND N-TH ROOT FUNCTIONS, EXPONENTIAL, LOGARITHMIC FUNCTION, POWER FUNCTION.

BASIC NOTIONS OF EQUATIONS AND INEQUALITIES.
(LECTURE/ PRACTICE/LABORATORY HOURS 1/4/0)
EQUATIONS OF FIRST ORDER. QUADRATIC EQUATIONS. IRRATIONAL EQUATIONS. EXPONENTIAL AND LOGARITHMIC EQUATIONS. SYSTEMS OF EQUATIONS. LINEAR INEQUALITIES. INEQUALITIES OF THE SECOND ORDER. FACTIONAL INEQUALITIES. IRRATIONAL INEQUALITIES. EXPONENTIAL AND LOGARITHMIC INEQUALITIES. SYSTEMS OF INEQUALITIES.

LIMITS OF A FUNCTION.
(LECTURE/ PRACTICE/LABORATORY HOURS 2/4/0)
DEFINITION. RIGHT AND LEFT HAND-SIDE LIMITS. UNIQUENESS THEOREM. COMPARISON THEOREMS. OPERATIONS AND INDETERMINATE FORMS. KNOWN LIMITS.

NUMERICAL SEQUENCES (BASIS ELEMENTS)
(LECTURE/ PRACTICE/LABORATORY HOURS 1/0/0)
DEFINITION. NUMERICAL SEQUENCES. BOUNDED, CONVERGENT, DIVERGENT AND OSCILLATING SEQUENCES. MONOTONE SEQUENCES.

CONTINUOUS FUNCTIONS.
(LECTURE/ PRACTICE/LABORATORY HOURS 2/2/0)
DEFINITION. CONTINUITY AND DISCONTINUITY. WEIERSTRASS THEOREM. ZEROS THEOREM.

DERIVATIVE OF A FUNCTION.
(LECTURE/ PRACTICE/LABORATORY HOURS 2/4/0)
DEFINITION. LEFT AND RIGHT DERIVATIVES. GEOMETRIC MEANING, THE TANGENT LINE TO THE GRAPH OF A FUNCTION. DIFFERENTIABILITY AND CONTINUITY. DERIVATION RULES. DERIVATIVES OF ELEMENTARY FUNCTIONS. DERIVATIVES OF COMPOSITE FUNCTION. HIGHER ORDER DERIVATIVES.

FUNDAMENTAL THEOREMS OF DIFFERENTIAL CALCULUS.
(LECTURE/ PRACTICE/LABORATORY HOURS 4/3/0)

ROLLE'S THEOREM. CAUCHY'S THEOREM. LAGRANGE'S THEOREM AND COROLLARIES. THEOREM OF DE L'HOSPITAL. CONDITIONS FOR MAXIMA AND MINIMA.

GRAPH OF A FUNCTION.
(LECTURE/ PRACTICE/LABORATORY HOURS 1/4/0)
ASYMPTOTES OF A GRAPH. SEARCH OF MAXIMA AND MINIMA. CONCAVE AND CONVEX FUNCTIONS AT A POINT, INFLECTION POINTS. GRAPH OF A FUNCTION BY ITS CHARACTERISTIC ELEMENTS.

INTEGRATION OF ONE VARIABLE FUNCTIONS.
(LECTURE/ PRACTICE/LABORATORY HOURS 2/4/0)
DEFINITE INTEGRAL AND GEOMETRICAL MEANING. FUNDAMENTAL THEOREM OF CALCULUS. DEFINITION OF INDEFINITE INTEGRAL. BASIC INTEGRALS. RULES AND METHODS OF INTEGRATION. INTEGRAL OF RATIONAL FUNCTIONS.

MATRICES AND LINEAR SYSTEMS.
(LECTURE/ PRACTICE/LABORATORY HOURS 2/4/0)
MATRICES AND DETERMINANTS. LINEAR SYSTEMS: ROUCHE-CAPELLI THEOREM, CRAMER THEOREM. REDUCED ROW ECHELON FORM.

MULTIVARIABLE FUNCTIONS.
(LECTURE/ PRACTICE/LABORATORY HOURS 3/4/0)
DEFINITIONS. LIMITS AND CONTINUITY. WEIERSTRASS THEOREM. PARTIAL DIFFERENTIATION. SCHWARZ THEOREM. GRADIENT AND DIFFERENTIABILITY. DIRECTIONAL DERIVATIVES. LOCAL MINIMA AND MAXIMA.

TOTAL LECTURE/ PRACTICE/LABORATORY HOURS 26/34/0

	Teaching Methods
	THE TEACHING CONSISTS OF FRONTAL LECTURES FOR A TOTAL OF 26 HOURS AND CLASSROOM EXERCISE SESSIONS FOR A TOTAL OF 34 HOURS. THE FREQUENCY OF CLASSROOM LECTURES AND EXERCISES, WHILE NOT REQUIRED, IS STRONGLY RECOMMENDED IN ORDER TO OBTAIN FULL ACHIEVEMENT OF THE LEARNING OBJECTIVES.

	Verification of learning
	WITH REGARD TO THE LEARNING OUTCOMES OF THE TEACHING, THE FINAL EXAM AIMS TO EVALUATE: THE KNOWLEDGE AND UNDERSTANDING OF THE CONCEPTS PRESENTED DURING THE THEORETICAL LECTURES AND THE CLASSROOM EXERCISE SESSIONS; THE MASTERY OF THE MATHEMATICAL LANGUAGE IN WRITTEN AND ORAL TESTS; THE SKILL OF PROVING THEOREMS; THE SKILL OF SOLVING EXERCISES; THE ABILITY TO IDENTIFY AND APPLY THE BEST AND EFFICIENT METHODS IN EXERCISES SOLVING; THE ABILITY TO APPLY THE ACQUIRED KNOWLEDGE TO DIFFERENT CONTEXTS FROM THOSE PRESENTED DURING THE LESSONS. THE EXAM NECESSARY TO ASSESS THE ACHIEVEMENT OF THE LEARNING OBJECTIVES CONSISTS IN A WRITTEN TEST, PRELIMINARY WITH RESPECT TO THE ORAL EXAMINATION, AND IN AN ORAL TEST. THE WRITTEN TEST CONSISTS IN SOLVING PROBLEMS IMPLEMENTED ON THE BASIS OF WHAT HAS BEEN PROPOSED IN THE FRAMEWORK OF THE THEORETICAL LECTURES AND EXERCISE SESSIONS. SUCH A WRITTEN TEST, THAT THE STUDENT WILL HAVE TO FACE IN TOTAL AUTONOMY, WILL LAST 2 AND HALF HOURS IN THE CASE OF A SUFFICIENT WRITTEN PROOF, IT WILL BE EVALUATED THROUGH QUALITATIVE SCALES (RANGES OF MARKS). THE INTERVIEW IS DEVOTED TO EVALUATE THE DEGREE OF KNOWLEDGE OF ALL THE TOPICS OF THE TEACHING, AND WILL COVER DEFINITIONS, THEOREMS PROOFS, EXERCISES SOLVING. THE FINAL MARK, EXPRESSED IN THIRTIETHS (EVENTUALLY CUM LAUDE), WILL DEPEND ON THE RANGE OF MARKS OF THE WRITTEN TEST, WITH CORRECTIONS IN EXCESS OR DEFECT ON THE BASIS OF THE ORAL TEST.

Verification of learning

WITH REGARD TO THE LEARNING OUTCOMES OF THE TEACHING, THE FINAL EXAM AIMS TO EVALUATE: THE KNOWLEDGE AND UNDERSTANDING OF THE CONCEPTS PRESENTED DURING THE THEORETICAL LECTURES AND THE CLASSROOM EXERCISE SESSIONS; THE MASTERY OF THE MATHEMATICAL LANGUAGE IN WRITTEN AND ORAL TESTS; THE SKILL OF PROVING THEOREMS; THE SKILL OF SOLVING EXERCISES; THE ABILITY TO IDENTIFY AND APPLY THE BEST AND EFFICIENT METHODS IN EXERCISES SOLVING; THE ABILITY TO APPLY THE ACQUIRED KNOWLEDGE TO DIFFERENT CONTEXTS FROM THOSE PRESENTED DURING THE LESSONS.
THE EXAM NECESSARY TO ASSESS THE ACHIEVEMENT OF THE LEARNING OBJECTIVES CONSISTS IN A WRITTEN TEST, PRELIMINARY WITH RESPECT TO THE ORAL EXAMINATION, AND IN AN ORAL TEST.
THE WRITTEN TEST CONSISTS IN SOLVING PROBLEMS IMPLEMENTED ON THE BASIS OF WHAT HAS BEEN PROPOSED IN THE FRAMEWORK OF THE THEORETICAL LECTURES AND EXERCISE SESSIONS. SUCH A WRITTEN TEST, THAT THE STUDENT WILL HAVE TO FACE IN TOTAL AUTONOMY, WILL LAST 2 AND HALF HOURS
IN THE CASE OF A SUFFICIENT WRITTEN PROOF, IT WILL BE EVALUATED THROUGH QUALITATIVE SCALES (RANGES OF MARKS).
THE INTERVIEW IS DEVOTED TO EVALUATE THE DEGREE OF KNOWLEDGE OF ALL THE TOPICS OF THE TEACHING, AND WILL COVER DEFINITIONS, THEOREMS PROOFS, EXERCISES SOLVING.
THE FINAL MARK, EXPRESSED IN THIRTIETHS (EVENTUALLY CUM LAUDE), WILL DEPEND ON THE RANGE OF MARKS OF THE WRITTEN TEST, WITH CORRECTIONS IN EXCESS OR DEFECT ON THE BASIS OF THE ORAL TEST.

	Texts
	WRITTEN NOTES GIVEN BY THE TEACHER. C. D'APICE, R. MANZO: VERSO L'ESAME DI MATEMATICA 1, RACCOLTA DI ESERCIZI CON SVOLGIMENTO, MAGGIOLI EDITORE, APOGEO EDUCATION, 2015. C. D'APICE, T. DURANTE, R. MANZO: VERSO L'ESAME DI MATEMATICA 2, RACCOLTA DI ESERCIZI CON SVOLGIMENTO, MAGGIOLI EDITORE, APOGEO EDUCATION, 2015. SUPPLEMENTARY TEACHING MATERIAL WILL BE AVAILABLE ON THE UNIVERSITY E-LEARNING PLATFORM (HTTP://ELEARNING.UNISA.IT) ACCESSIBLE BY STUDENTS USING THEIR OWN UNIVERSITY CREDENTIALS.

Texts

WRITTEN NOTES GIVEN BY THE TEACHER.
C. D'APICE, R. MANZO: VERSO L'ESAME DI MATEMATICA 1, RACCOLTA DI ESERCIZI CON SVOLGIMENTO, MAGGIOLI EDITORE, APOGEO EDUCATION, 2015.

C. D'APICE, T. DURANTE, R. MANZO: VERSO L'ESAME DI MATEMATICA 2, RACCOLTA DI ESERCIZI CON SVOLGIMENTO, MAGGIOLI EDITORE, APOGEO EDUCATION, 2015.

SUPPLEMENTARY TEACHING MATERIAL WILL BE AVAILABLE ON THE UNIVERSITY E-LEARNING PLATFORM (HTTP://ELEARNING.UNISA.IT) ACCESSIBLE BY STUDENTS USING THEIR OWN UNIVERSITY CREDENTIALS.

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Ciro D'APICE | MATHEMATICS