Gerardo IOVANE | MATHEMATICAL ANALYSIS
Gerardo IOVANE MATHEMATICAL ANALYSIS
cod. 0512100001
MATHEMATICAL ANALYSIS
| 0512100001 | |
| COMPUTER SCIENCE | |
| EQF6 | |
| COMPUTER SCIENCE | |
| 2024/2025 |
| OBBLIGATORIO | |
| YEAR OF COURSE 1 | |
| YEAR OF DIDACTIC SYSTEM 2017 | |
| SPRING SEMESTER |
| SSD | CFU | HOURS | ACTIVITY | |
|---|---|---|---|---|
| MAT/05 | 6 | 48 | LESSONS | |
| MAT/05 | 3 | 24 | EXERCISES |
| Exam | Date | Session | |
|---|---|---|---|
| APPELLO PROF. IOVANE (D-G) | 17/06/2025 - 12:00 | SESSIONE ORDINARIA | |
| APPELLO PROF. IOVANE (RESTO 1) | 17/06/2025 - 12:00 | SESSIONE ORDINARIA |
| Objectives | |
|---|---|
| KNOWLEDGE AND UNDERSTANDING: TO PROVIDE STUDENTS WITH THE BASIC NOTIONS OF CALCULUS. APPLYING KNOWLEDGE AND UNDERSTANDING: LEARN CALCULUS THEORY AND APPLICATIONS, SO AS TO BE ABLE TO SOLVE A RANGE OF SIMPLE EXERCISES. IN PARTICULAR, STUDENTS WILL BE ABLE TO DRAW THE GRAPHIC OF A FUNCTION GIVEN ITS ALGEBRAIC FORM AND TO CALCULATE SIMPLE INTEGRALS. TO BE ABLE TO PRESENT, IN A CLEAR AND RIGOROUS MANNER, THE THEOREMS, DEFINITIONS AND PROBLEMS STUDIED THROUGHOUT THE COURSE. TO BE ABLE TO USE THE ACQUIRED KNOWLEDGE IN REASONING AND ALGORITHMS |
| Prerequisites | |
|---|---|
| ELEMENTARY ASPECTS OF ALGEBRA ARE MANDATORY AS WELL AS FAMILIARITY WITH SOLUTION METHODS FOR FIRST AND SECOND ORDER EQUALITIES AND INEQUALITIES. KNOWLEDGE OF SOME ELEMENTS OF TRIGONOMETRY ARE ALSO CONSIDERED A PREREQUISITE. |
| Contents | |
|---|---|
| NUMERICAL SETS. 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. (4,1) COMBINATORIAL CALCULUS AND AND PRINCIPLE OF INDUCTION (2,1) COMPLEX NUMBERS (3,2) REAL FUNCTIONS. 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. (6,1) BASIC NOTIONS OF EQUATIONS AND INEQUALITIES. 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. (1,3) NUMERICAL SEQUENCES (BASIS ELEMENTS). DEFINITION. NUMERICAL SEQUENCES. BOUNDED, CONVERGENT, DIVERGENT AND OSCILLATING SEQUENCES. MONOTONE SEQUENCES. (3,1) LIMITS OF A FUNCTION. DEFINITION. RIGHT AND LEFT HAND-SIDE LIMITS. UNIQUENESS THEOREM. COMPARISON THEOREMS. OPERATIONS AND INDETERMINATE FORMS. KNOWN LIMITS. (5,3) CONTINUOUS FUNCTIONS. DEFINITION. CONTINUITY AND DISCONTINUITY. WEIERSTRASS THEOREM. ZEROS THEOREM. (2,0) DERIVATIVE OF A FUNCTION. 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. (5,2) FUNDAMENTAL THEOREMS OF DIFFERENTIAL CALCULUS. ROLLE'S THEOREM. CAUCHY'S THEOREM. LAGRANGE'S THEOREM AND COROLLARIES. THEOREM OF DE L'HOSPITAL. CONDITIONS FOR MAXIMA AND MINIMA. (5,2) GRAPH OF A FUNCTION. 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. (3,3) INTEGRATION OF ONE VARIABLE FUNCTIONS. DEFINITION OF INDEFINITE INTEGRAL. BASIC INTEGRALS. RULES AND METHODS OF INTEGRATION. INTEGRAL OF RATIONAL FUNCTIONS. DEFINITE INTEGRAL AND GEOMETRICAL MEANING. FUNDAMENTAL THEOREM OF CALCULUS. (3,3) MULTIVARIABLE FUNCTIONS. DEFINITIONS. LIMITS AND CONTINUITY. WEIERSTRASS THEOREM. PARTIAL DIFFERENTIATION. SCHWARZ THEOREM. GRADIENT AND DIFFERENTIABILITY. DIRECTIONAL DERIVATIVES. LOCAL MINIMA AND MAXIMA. (2,1) TAYLOR'S FORMULA (2,0) NUMERICAL SERIES: DEFINITIONS AND PROPERTIES (2,1) TOTAL HOURS: (48,24) |
| Teaching Methods | |
|---|---|
| • LESSONS • PRACTICE LESSON |
| Verification of learning | |
|---|---|
| THE KNOWLEDGE AND UNDERSTANDING OF THE TOPICS DESCRIBED WITHIN THE COURSE WILL BE TESTED BY MEANS OF A FINAL WRITTEN EXAMINATION, FOLLOWED BY AN ORAL EXAM. THE WRITTEN TEST HELP TO ASSESS THE ABILITY OF STUDENT OF APPLIED MATHEMATICS CONCEPTS FOR THE RESOLUTION OF EXERCISES ON THE STUDY OF FUNCTION AND CALCULATING INTEGRTALE . THE ORAL EXAM HELP TO ASSESS THE ABILITY OF STUDENT OF EXHIBIT CLEARLY AND RIGOROUSLY MATHEMATICAL CONCEPTS AND THEOREMS DEMONSTRATED DURING THE LESSONS. EXEMPTIONS OF THE EXAMINATIONS (WRITTEN AND ORAL) WILL BE FORWARDED DURING THE COURSE |
| Texts | |
|---|---|
| • P.DIGIRONIMO-G.IOVANE-E.BENEDETTO-A.BRISCIONE, ANALISI MATEMATICA PER INFORMATICI-TEORIA ED ESERCIZI, ED. ARACNE • E. GIUSTI “ANALISI MATEMATICA I“, BOLLATI BORINGHIERI • P. MARCELLINI - C. SBORDONE, “ANALISI MATEMATICA UNO “, LIGUORI EDITORE • P. MARCELLINI - C. SBORDONE, “ELEMENTI DI ANALISI MATEMATICA UNO “, LIGUORI EDITORE TEXTS DEPTH • M. TROISI “ANALISI MATEMATICA I“, LIGUORI EDITORE • M.BRAMANTI-C.PAGANI-S. SALSA, “ANALISI MATEMATICA I“, LIGUORI ZANICHELLI • P. MARCELLINI - C. SBORDONE, “ESERCITAZIONI DI MATEMATICA I “, LIGUORI EDITORE • A. ALVINO - L. CARBONE- G. TROMBETTI, “ESERCITAZIONI DI MATEMATICA I “, LIGUORI EDITORE |
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