Sara MONSURRO' | MATHEMATICAL ANALYSIS I / MATHEMATICAL ANALYSIS II
Sara MONSURRO' MATHEMATICAL ANALYSIS I / MATHEMATICAL ANALYSIS II
cod. 0512300001
MATHEMATICAL ANALYSIS I / MATHEMATICAL ANALYSIS II
| 0512300001 | |
| DEPARTMENT OF MATHEMATICS | |
| EQF6 | |
| MATHEMATICS | |
| 2024/2025 |
| OBBLIGATORIO | |
| YEAR OF COURSE 1 | |
| YEAR OF DIDACTIC SYSTEM 2018 | |
| FULL ACADEMIC YEAR |
| SSD | CFU | HOURS | ACTIVITY | ||
|---|---|---|---|---|---|
| ANALISI MATEMATICA I | |||||
| MAT/05 | 8 | 64 | LESSONS | ||
| ANALISI MATEMATICA II | |||||
| MAT/05 | 8 | 64 | LESSONS | ||
| Exam | Date | Session | |
|---|---|---|---|
| ANALISI MATEMATICA I/AN. MATEMATICA II | 15/01/2025 - 14:30 | SESSIONE DI RECUPERO | |
| ANALISI MATEMATICA I/AN. MATEMATICA II | 03/02/2025 - 14:30 | SESSIONE DI RECUPERO | |
| ANALISI MATEMATICA I/AN. MATEMATICA II | 25/02/2025 - 14:30 | SESSIONE DI RECUPERO |
| Objectives | |
|---|---|
| THE COURSE AIMS TO PROVIDE STUDENTS WITH THE BASICS OF MATHEMATICAL ANALYSIS, BOTH FROM A METHODOLOGICAL AND THE CALCULUS POINT OF VIEW. STUDENTS WILL ACQUIRE A KNOWLEDGE OF THE ELEMENTARY TECHNIQUES OF DIFFERENTIAL AND INTEGRAL CALCULUS, AND OF THE MAIN APPLICATIONS. KNOWLEDGE AND UNDERSTANDING: THE STUDENT WILL HAVE TO KNOW THE FUNDAMENTAL PROPERTIES OF DIFFERENTIAL AND INTEGRAL CALCULUS OF FOR REAL FUNCTIONS OF ONE VARIABLE, OF COMPLEX NUMBERS AND OF NUMERICAL SERIES. APPLYING KNOWLEDGE AND UNDERSTANDING: THE STUDENT WILL BE ABLE TO USE THE KNOWLEDGE ACQUIRED TO SOLVE EXERCISES AND PROBLEMS RELATED TO TOPICS SUCH AS THE QUALITATIVE BEHAVIOR OF FUNCTION GRAPHS, THE CALCULATION OF SIMPLE INTEGRALS AND THE CHARACTER OF A NUMERICAL SERIES. MAKING JUDGEMENTS: THE STUDENTS MUST BE ABLE TO APPLY ANALYTICAL TECHNIQUES FOR SOLVING EXERCISES AND PROBLEMS ALSO IN RELATION TO OTHER SCIENTIFIC DISCIPLINES. COMMUNICATION SKILLS: THE STUDENT MUST BE ABLE TO CLEARLY EXPLAIN THE DEFINITIONS AND THE STATEMENTS OF THEOREMS, DISTINGUISHING WITH CERTAINTY HYPOTHESIS AND THESIS. HE MUST ALSO BE ABLE TO COHERENTLY EXPLAIN THE LOGICAL STEPS OF THE PROOFS. LEARNING SKILLS: THE STUDENT WILL HAVE TO CRITICALLY USE THE TOOLS AND CONCEPTS STUDIED BOTH IN THE PROOF OF SOME SIMPLE STATEMENTS AND IN THE CONTEXT OF THE STUDY OF OTHER DISCIPLINES. HE MUST ALSO BE ABLE TO WORK IN A GROUP DURING THE PROPOSED ACTIVITIES AND TUTORING ACTIVITIES. |
| Prerequisites | |
|---|---|
| BASIC KNOWLEDGE ACQUIRED THROUGH HIGH SCHOOL COURSES. IN PARTICULAR, KNOWLEDGE OF ELEMENTARY ALGEBRA, TRIGONOMETRY AND FIRST AND SECOND ORDER INEQUALITIES IS REQUIRED. |
| Contents | |
|---|---|
| MODULE I BASIC NOTIONS OF SET THEORY: LOGIC SYMBOLS, SET OPERATIONS, ALGEBRAIC RELATIONS, FUNCTIONS, MATHEMATICAL INDUCTION. (3 HOURS OF THEORETICAL LESSONS + 2 HOURS OF EXERCISES) NUMERICAL SETS: AXIOMS FOR THE REAL NUMBERS, EXTREMA OF NUMERICAL SETS, COMPLETENSS, DENSITY, CONTIGUOUS SETS, ALGEBRAIC ROOTS, NATURAL POWER FUNCTIONS. (6 HOURS OF THEORETICAL LESSONS) REAL FUNCTIONS: ALGEBRAIC OPERATIONS, EXTREMA, MONOTONICITY, SEQUENCES. (4 HOURS OF THEORETICAL LESSONS) ELEMENTARY FUNCTIONS: DEFINITIONS, PROPERTIES, DOMAINS. (7 HOURS OF THEORETICAL LESSONS + 8 HOURS OF EXERCISES) LIMITS OF REAL SEQUENCES: DEFINITIONS, PROPERTIES, ALGEBRAIC OPERATIONS, INDETERMINATE FORMS, COMPARISON THEOREMS, REGULARITY OF MONOTONE SEQUENCES, CONVERGENCE CRITERIA (7 HOURS OF THEORETICAL LESSONS + 3 HOURS OF EXERCISES) LIMITS OF REAL FUNCTIONS: ACCUMULATION POINTS, RELATION BETWEEN LIMITS OF FUNCTIONS AND LIMITS OF SEQUENCES, LIMITS AND ALGEBRAIC STRUCTURE OF R, COMPARISON RESULTS, LIMITS OF COMPOSITIONS OF FUNCTIONS (5 HOURS OF THEORETICAL LESSONS + 3 HOURS OF EXERCISES) CONTINUOUS FUNCTIONS: DEFINITIONS AND DISCONTINUITY POINTS, MAIN PROPERTIES ON INTERVALS, MAIN LIMITS, EXERCISES ON FUNCTIONS’ LIMITS. (6 HOURS OF THEORETICAL LESSONS + 6 HOURS OF EXERCISES) COMPLEX NUMBERS: FIELD STRUCTURE, ALGEBRAIC AND TRIGONOMETRIC FORMS, POWERS AND ROOTS. (2 HOURS OF THEORETICAL LESSONS + 2 HOURS OF EXERCISES) MODULE II DIFFERENTIAL CALCULUS: DIFFERENTIABILITY, OPERATIONS WITH DERIVATIVES, DERIVATIVES OF COMPOSITION OF FUNCTIONS, DERIVATIVES OF ELEMENTARY FUNCTIONS, MAIN THEOREMS OF DIFFERENTIAL CALCULUS, LOCAL EXTREMA, CONVEX FUNCTIONS, DE L’HOPITAL THEOREMS AND APPLICATIONS, GRAPH OF A FUNCTION, INFINITY AND INFINITESIMAL, TAYLOR FORMULA. (14 HOURS OF THEORETICAL LESSONS + 10 HOURS OF EXERCISES) INTEGRAL CALCULUS: RIEMANN INTEGRATION AND ITS PROPERTIES, MEAN VALUE THEOREMS FOR INTEGRALS, FUNDAMENTAL THEOREM OF THE INTEGRAL CALCULUS, DEFINITE INTEGRAL, INTEGRATION METHODS, IMPROPER INTEGRALS. (10 HOURS OF THEORETICAL LESSONS + 10 HOURS OF EXERCISES) NUMERICAL SERIES: DEFINITIONS AND FIRST PROPERTIES, SERIES OF NONNEGATIVE TERMS AND CONVERGENCE CRITERIA, ALTERNATING SERIES, GENERAL SERIES, ABSOLUTELY CONVERGING SERIES. (10 HOURS OF THEORETICAL LESSONS + 10 HOURS OF EXERCISES) |
| Teaching Methods | |
|---|---|
| THE COURSE CONSISTS IN 128 HOURS OF CLASSROOM TEACHING DIVIDED INTO TWO MODULES. THE FIRST MODULE PROVIDES 64 HOURS OF LESSONS DIVIDED INTO 40 HOURS DEDICATED TO THEORETICAL ASPECTS OF CALCULUS AND 24 HOURS DEVOTED TO APPLIED ONES. IN THE SECOND MODULE THERE ARE 34 HOURS DEDICATED TO THEORETICAL ASPECTS AND 30 HOURS DEVOTED TO APPLIED ONES. THERE IS NO OBLIGATION TO ATTEND THE LESSONS EVEN IF AN ACTIVE PARTICIPATION IS STRONGLY RECOMMENDED FOR THE ACHIEVEMENT OF THE EDUCATIONAL OBJECTIVE. |
| Verification of learning | |
|---|---|
| THE EXAMINATION TEST IS MADE UP OF A WRITTEN TEST FOLLOWED BY AN ORAL ONE. THE WRITTEN TEST IS FINALIZED TO SOLVE EXERCISES ON THE WHOLE PROGRAM OF THE COURSE: CALCULATIONS OF DOMAINS, LIMITS, INTEGRALS, QUALITATIVE STUDY OF REAL FUNCTIONS, CONVERGENCE OF NUMERICAL SERIES. TO BE ADMITTED TO THE ORAL TEST, THE STUDENT MUST HAVE SUFFICIENT EVALUATION AT THE WRITTEN ONE OR AT SOME PARTIAL TEST. IF THE EVALUATION OF THE PARTIAL TESTS IS SUFFICIENT THE STUDENT MAY NOT TAKE THE COMPLETE TEST. STUDENTS ABLE TO MANAGE INDEPENDENTLY THEIR KNOWLEDGE ALSO IN DIFFERENT FRAMEWOKS WILL BE EVALUATED WITH 30 CUM LAUDE. |
| Texts | |
|---|---|
| C.PAGANI- S.SALSA, ANALISI MATEMATICA 1, ZANICHELLI. M. TROISI, ANALISI MATEMATICA I, LIGUORI EDITORE. P. MARCELLINI - C. SBORDONE, ANALISI MATEMATICA UNO, LIGUORI EDITORE. P. MARCELLINI - C. SBORDONE, ESERCITAZIONI DI MATEMATICA I, LIGUORI EDITORE. A. ALVINO - L. CARBONE - G. TROMBETTI, ESERCITAZIONI DI MATEMATICA I, LIGUORI EDITORE. D. GRECO - G. STAMPACCHIA, ESERCITAZIONI DI MATEMATICA, VOL. I, LIGUORI EDITORE. |
| More Information | |
|---|---|
| EMAIL ADDRESS: SMONSURRO@UNISA.IT |
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