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  3. Teaching

MATHEMATICS

Ciro D'APICE MATHEMATICS

0212700170
DEPARTMENT OF MANAGEMENT & INNOVATION SYSTEMS
EQF6
BUSINESS MANAGEMENT
2024/2025



OBBLIGATORIO
YEAR OF COURSE 1
YEAR OF DIDACTIC SYSTEM 2023
AUTUMN SEMESTER
CFUHOURSACTIVITY
1060LESSONS


CIRO D'APICE T Curriculum
GERARDO DURAZZO Curriculum
ExamDate
D'APICE / DURAZZO (A-C)11/12/2024 - 15:00
D'APICE / DURAZZO (A-C)11/12/2024 - 15:00
D'APICE / DURAZZO (D-G)11/12/2024 - 15:00
D'APICE / DURAZZO (D-G)11/12/2024 - 15:00
D'APICE / DURAZZO ((PEU-Z)11/12/2024 - 15:00
D'APICE / DURAZZO ((PEU-Z)11/12/2024 - 15:00
D'APICE ANNI PRECEDENTI11/12/2024 - 15:00
D'APICE ANNI PRECEDENTI11/12/2024 - 15:00
D'APICE (C. AMM. FIN. CONT.)11/12/2024 - 15:00
D'APICE (C. AMM. FIN. CONT.)11/12/2024 - 15:00
D'APICE (C. MANAGEMENT)11/12/2024 - 15:00
D'APICE (C. MANAGEMENT)11/12/2024 - 15:00
MANZO (C. MANAG. SOSTENIB.)11/12/2024 - 15:00
MANZO (C. MANAG. SOSTENIB.)11/12/2024 - 15:00
RARITA' (C. MANAG. INFORMATICA)11/12/2024 - 15:00
RARITA' (C. MANAG. INFORMATICA)11/12/2024 - 15:00
RARITA' (H-PET)11/12/2024 - 15:00
RARITA' (H-PET)11/12/2024 - 15:00
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.

KNOWLEDGE AND UNDERSTANDING
THE STUDENT WILL ACQUIRE KNOWLEDGE ABOUT:
•NUMERIC SETS,
•REAL FUNCTIONS OF A REAL VARIABLE,
•LIMITS,
•CONTINUOUS FUNCTIONS,
•DERIVATIVES,
•INTEGRALS,
•MATRICES AND LINEAR SYSTEMS,
•REAL FUNCTIONS OF TWO REAL VARIABLES.

ABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING
THE STUDENT WILL BE ABLE TO:
•CALCULATE SIMPLE FUNCTION LIMITS,
•CALCULATE THE DERIVATIVE OF A FUNCTION,
•DRAW THE QUALITATIVE GRAPH OF A FUNCTION,
•INTERPRET THE GRAPH OF A FUNCTION,
•CALCULATE SIMPLE INTEGRALS,
•PERFORM OPERATIONS WITH MATRICES,
•SOLVE LINEAR SYSTEMS,
•DETERMINE MAXIMA AND MINIMA OF FUNCTIONS OF TWO VARIABLES,
•APPLY THE LEARNING TECHNIQUES AND METHODS FOR THE RESOLUTION OF REAL PROBLEMS.

MAKING JUDGEMENTS
THE STUDENT WILL BE ABLE TO IDENTIFY THE MOST APPROPRIATE METHODS TO EFFICIENTLY SOLVE A MATHEMATICAL PROBLEM, OF BOTH THEORETICAL AND APPLICATIVE TYPE.

COMMUNICATION SKILLS
THE STUDENT WILL BE ABLE TO DESCRIBE TRENDS IN ECONOMIC AND FINANCIAL PHENOMENA BY THE LANGUAGE OF MATHEMATICS.

LEARNING SKILLS
THE STUDENT WILL BE ABLE TO APPLY THE ACQUIRED KNOWLEDGE ACQUIRED WITHIN ECONOMICS AND FINANCE CONTEXTS.
Prerequisites
FOR THE SUCCESSFUL ACHIEVEMENT OF THE PREDEFINED OBJECTIVES AND, IN PARTICULAR, FOR AN ADEQUATE UNDERSTANDING OF THE CONTENTS PROVIDED BY THE TEACHING, KNOWLEDGE RELATED TO EQUATIONS AND INEQUALITIES ARE PARTICULARLY USEFUL AND, THEREFORE, REQUIRED TO THE STUDENT.

MANDATORY PREPARATORY TEACHINGS
NONE.
Contents
NUMERICAL SETS.
(HOURS LECTURE/EXERCISE/LABORATORY 2/0/0)
INTRODUCTION. 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 OF A REAL VARIABLE.
(HOURS LECTURE/EXERCISE/WORKSHOP 5/1/0)
DEFINITION. DOMAIN, CODOMAIN AND GRAPH OF FUNCTION. EXTREMES OF A REAL FUNCTION. MONOTONE FUNCTIONS. COMPOUND FUNCTIONS. INVERTIBLE FUNCTIONS. ELEMENTARY FUNCTIONS: N-TH POWER FUNCTION AND N-TH ROOT FUNCTION, EXPONENTIAL FUNCTION, LOGARITHMIC FUNCTION, POWER FUNCTION.

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

NUMERICAL SEQUENCES (BASIC ELEMENTS).
(HOURS LECTURE/EXERCISE/WORKSHOP 1/0/0)
BOUNDED, CONVERGENT, OSCILLATING AND DIVERGENT SUCCESSIONS. MONOTONE SEQUENCES.

LIMIT OF A FUNCTION.
(HOURS LECTURE/EXERCISE/WORKSHOP 3/3/0)
DEFINITION. RIGHT LIMIT AND LEFT LIMIT. UNIQUENESS THEOREM OF THE LIMIT. THEOREM OF PERMANENCE OF SIGN. COMPARISON THEOREMS. OPERATIONS AND INDETERMINATE FORMS. KNOWN LIMITS.

CONTINUOUS FUNCTIONS.
(HOURS LECTURE/EXERCISE/WORKSHOP 3/1/0)
DEFINITION. CONTINUITY AND DISCONTINUITY. WEIERSTRASS THEOREM. INTERMEDIATE VALUE THEOREM. ZEROS THEOREM.

DERIVATIVE OF A FUNCTION.
(HOURS LECTURE/EXERCISE/LABORATORY 3/4/0)
DEFINITION. RIGHT AND LEFT DERIVATIVES. GEOMETRIC MEANING, TANGENT LINE TO THE GRAPH OF A FUNCTION. DERIVABILITY AND CONTINUITY. DERIVATION RULES. DERIVATIVES OF ELEMENTARY FUNCTIONS. DERIVATIVES OF COMPOUND FUNCTIONS. HIGHER ORDER DERIVATIVES.

FUNDAMENTAL THEOREMS OF DIFFERENTIAL CALCULUS.
(HOURS LECTURE/EXERCISE/LABORATORY 4/1/0)
ROLLE THEOREM. CAUCHY THEOREM. LAGRANGE THEOREM AND COROLLARIES. DE L'HOSPITAL THEOREM. CONDITIONS FOR RELATIVE MAXIMA AND MINIMA.

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

INTEGRATION OF FUNCTIONS OF ONE VARIABLE.
(HOURS LECTURE/EXERCISE/WORKSHOP 2/4/0)
DEFINITE INTEGRAL AND GEOMETRIC MEANING. MEAN VALUE THEOREM. INTEGRAL FUNCTION AND FUNDAMENTAL THEOREM OF INTEGRAL CALCULUS. DEFINITION OF PRIMITIVE FUNCTION AND INDEFINITE INTEGRAL. IMMEDIATE INTEGRALS. RULES AND METHODS OF INTEGRATION. INTEGRAL OF RATIONAL FUNCTIONS.

ELEMENTS OF LINEAR ALGEBRA.
(HOURS LECTURE/EXERCISE/LABORATORY 2/4/0)
MATRICES AND DETERMINANTS. RESOLUTION OF LINEAR SYSTEMS: REDUCTION TO ROW ECHELON FORM.

FUNCTIONS OF SEVERAL VARIABLES.
(HOURS LECTURE/EXERCISE/LABORATORY 3/4/0)
DEFINITIONS. LIMIT AND CONTINUITY. PARTIAL DERIVATIVES. SCHWARZ'S THEOREM. GRADIENT AND DIFFERENTIABILITY. DIRECTIONAL DERIVATIVES. RELATIVE MAXIMA AND MINIMA.

TOTAL HOURS LECTURE/EXERCISE/LABORATORY 30/30/0
Teaching Methods
THE TEACHING INCLUDES THEORETICAL LECTURES IN THE CLASSROOM FOR A TOTAL OF 30 HOURS AND CLASSROOM EXERCISES FOR A TOTAL OF 30 HOURS.
ATTENDANCE OF CLASSROOM LECTURES AND EXERCISES, ALTHOUGH NOT MANDATORY, IS STRONGLY RECOMMENDED FOR THE FULL ACHIEVEMENT OF THE LEARNING OBJECTIVES.
Verification of learning
THE EXAMINATION IS DESIGNED TO ASSESS: KNOWLEDGE AND UNDERSTANDING OF THE CONCEPTS PRESENTED DURING THE LECTURES; MASTERY OF THE MATHEMATICAL LANGUAGE IN THE WRITTEN AND ORAL EXAM; ABILITY TO PROVE THEOREMS; ABILITY TO SOLVE EXERCISES; ABILITY TO IDENTIFY AND APPLY THE MOST APPROPRIATE AND EFFICIENT METHODS IN SOLVING AN EXERCISE; AND ABILITY TO APPLY THE ACQUIRED KNOWLEDGE TO SOLVE DIFFERENT PROBLEMS WITH RESPECT TO THOSE PRESENTED DURING THE EXERCISES LECTURES.
THE EXAMINATION, NECESSARY TO ASSESS THE ACHIEVEMENT OF THE LEARNING OBJECTIVES, CONSISTS OF A WRITTEN TEST, PREPARATORY TO THE ORAL TEST, AND AN ORAL DISCUSSION.
THE WRITTEN TEST INVOLVES THE RESOLUTION OF PROBLEMS SIMILAR TO THOSE PROPOSED DURING THE EXERCISES LECTURES. THE OUTCOME OF THE WRITTEN TEST IS “PASSED” OR “FAILED”.
STUDENTS WHO PASS THE WRITTEN TEST WILL HAVE TO TAKE AND PASS THE ORAL TEST. THE ORAL TEST IS DESIGNED TO ASCERTAIN THE DEGREE OF KNOWLEDGE OF ALL TOPICS COVERED IN THE TEACHING, AND COVERS DEFINITIONS, STATEMENTS AND DEMONSTRATIONS OF THEOREMS, AND RESOLUTION OF EXERCISES.
THE FINAL GRADE, EXPRESSED IN THIRTIETHS WITH POSSIBLE LAUDE, IS DETERMINED AFTER THE OUTCOME OF THE ORAL DISCUSSION. IN EVALUATING THE EXAMINATION, ACCOUNT WILL BE TAKEN NOT ONLY OF KNOWLEDGE OF THE SUBJECT MATTER, BUT ALSO OF EXPOSITORY ABILITY, ACCURACY OF LANGUAGE, AND THE ABILITY TO USE CRITICALLY THE MATHEMATICAL ACQUIRED TOOLS.
LAUDE WILL BE AWARDED TO STUDENTS WHO DEMONSTRATE EXCELLENT KNOWLEDGE OF COURSE CONTENTS, OPTIMAL EXPOSITORY SKILLS, AND HIGH MATURITY IN APPLYING THE KNOWLEDGE GAINED TO SOLVE PROBLEMS NOT ADDRESSED DURING CLASSROOM LECTURES.
Texts
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 MATERIALS WILL BE AVAILABLE IN THE TEACHING SECTION WITHIN THE UNIVERSITY'S E-LEARNING AREA (HTTP://ELEARNING.UNISA.IT), ACCESSIBLE TO STUDENTS IN THE COURSE VIA THE UNIQUE UNIVERSITY CREDENTIALS.
More Information
TEACHING IS PROVIDED IN ITALIAN.
Lessons Timetable

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