Anna CANALE | MATHEMATICAL INSTITUTIONS
Anna CANALE MATHEMATICAL INSTITUTIONS
cod. 0512400014
MATHEMATICAL INSTITUTIONS
| 0512400014 | |
| DEPARTMENT OF CHEMISTRY AND BIOLOGY "ADOLFO ZAMBELLI" | |
| EQF6 | |
| CHEMISTRY | |
| 2024/2025 |
| OBBLIGATORIO | |
| YEAR OF COURSE 1 | |
| YEAR OF DIDACTIC SYSTEM 2023 | |
| FULL ACADEMIC YEAR |
| SSD | CFU | HOURS | ACTIVITY | |
|---|---|---|---|---|
| MAT/05 | 3 | 24 | LESSONS | |
| MAT/05 | 6 | 72 | EXERCISES |
| Exam | Date | Session | |
|---|---|---|---|
| ISTITUZIONI DI MATEMATICHE | 17/01/2025 - 10:00 | SESSIONE ORDINARIA | |
| ISTITUZIONI DI MATEMATICHE | 17/01/2025 - 10:00 | SESSIONE DI RECUPERO | |
| ISTITUZIONI DI MATEMATICHE | 13/02/2025 - 10:00 | SESSIONE ORDINARIA | |
| ISTITUZIONI DI MATEMATICHE | 13/02/2025 - 10:00 | SESSIONE DI RECUPERO |
| Objectives | |
|---|---|
| COURSE AIM THE COURSE AIMS AT THE ACQUISITION OF THE BASIC ELEMENTS OF MATHEMATICAL ANALYSIS. THE EDUCATIONAL OBJECTIVES OF THE COURSE CONSISTS IN THE ACQUISITION OF RESULTS AND DEMONSTRATION TECHNIQUES, AS WELL AS THE ABILITY TO USE THE RELATED CALCULATION TOOLS. KNOWLEDGE AND UNDERSTANDING UNDERSTANDING THE BASIC CONCEPTS OF MATHEMATICAL ANALYSIS AND LINEAR ALGEBRA. KNOWLEDGE OF THE TOPICS: REAL FUNCTIONS, LIMITS, CONTINUITY, DERIVATIVE, FUNDAMENTAL THEOREMS OF DIFFERENTIAL CALCULUS, INTEGRATION OF FUNCTIONS OF ONE VARIABLE, NUMERICAL SEQUENCES AND SERIES, SEQUENCES AND SERIES OF FUNCTIONS, FUNCTIONS OF MULTIPLE VARIABLES, DIFFERENTIAL EQUATIONS, DIFFERENTIAL FORMS. APPLYING KNOWLEDGE AND UNDERSTANDING APPLY THE THEOREMS AND RULES STUDIED TO PROBLEM SOLVING. PERFORM CALCULATIONS OF LIMITS, DERIVATIVES, INTEGRALS. DETERMINING THE GRAPH OF A FUNCTION. SOLVE DIFFERENTIAL EQUATIONS. IDENTIFY THE BEHAVIOR OF NUMERICAL SERIES AND POWER SERIES. IDENTIFY THE MOST APPROPRIATE METHODS TO EFFICIENTLY SOLVE A MATHEMATICAL PROBLEM. MAKING JUDGMENTS THE STUDENT SHOULD BE ABLE TO INDEPENDENTLY ASSESS THE MOST APPROPRIATE TOOL TO SOLVE A MATHEMATICAL ANALYSIS PROBLEM AND THE AREAS OF USE OF THE MATHEMATICAL TOOLS AVAILABLE. COMMUNICATION SKILLS THE STUDENT SHOULD BE ABLE TO HOLD CONVERSATIONS ON ISSUES RELATED TO THE CONCEPTS OF MATHEMATICAL ANALYSIS BY USING ADEQUATE TECHNICAL TERMINOLOGY AND TOOLS OF THE SYMBOLIC AND GRAPHIC REPRESENTATION OF THE MAIN CONCEPTS DESCRIBED. LEARNING SKILL THE STUDENT SHOULD BE ABLE TO SHOW ABILITY IN INDEPENDENTLY DEALING WITH PROBLEMS NOT EXPRESSLY TREATED IN THE COURSE OF HIS STUDIES USING THE TOOLS, KNOWLEDGE AND SKILLS ACQUIRED. |
| 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 | |
|---|---|
| REAL NUMBERS. 2 HOURS COMPLEX NUMBERS. 2 HOURS REAL FUNCTIONS. 6 HOURS LIMITS OF FUNCTIONS AND CONTINUOUS FUNCTIONS. 6 HOURS DERIVATIVES. 5 HOURS APPLICATION OF DIFFERENTIAL CALCULUS. GRAPHS OF FUNCTIONS. 5 HOURS VECTOR SPACES. 10 HOURS RIEMANN INTEGRATION FOR REAL FUNCTIONS OF ONE REAL VARIABLE. 10 HOURS NUMERICAL SEQUENCES AND SERIES. 6 HOURS FUNCTION SEQUENCES AND SERIES. POWER SERIES. 6 HOURS REAL FUNCTIONS OF TWO REAL VARIABLES. 10 HOURS DIFFERENTIAL EQUATIONS. 12 HOURS DOUBLE INTEGRALS OVER NORMAL DOMAINS. 8 HOURS CURVES. 2 HOURS DIFFERENTIAL FORMS IN THE PLANE AND LINE INTEGRALS. 6 HOURS |
| Teaching Methods | |
|---|---|
| MODULES COMPRISE TEACHING LESSONS AT THE BLACKBOARD AND EXERCISES AT THE BLACKBOARD IN THE CLASSROOM (96H) |
| Verification of learning | |
|---|---|
| THE EXAM, NECESSARY TO EVALUATE THE ACHIEVEMENT OF THE LEARNING OBJECTIVES, INVOLVES CARRYING OUT EXERCISES AND KNOWLEDGE OF THE TOPICS CONTAINED IN THE PROGRAM AND CONSISTS OF A WRITTEN TEST ON EXERCISES AND THEORETICAL TOPICS AND A DISCUSSION OF THE PAPER WITH ANY INSIGHTS. THE EVALUATION WILL TAKE INTO ACCOUNT THE METHOD OF SOLVING THE PROPOSED PROBLEMS, THE KNOWLEDGE OF THE TOPICS COVERED IN CLASS AND THE CLARITY OF THE PRESENTATION. THE FINAL GRADE, EXPRESSED IN THIRTIETHS WITH POSSIBLE LAUDE, DERIVES FROM THE OVERALL EVALUATION OF THE STUDENT'S PREPARATION IN RELATION TO THESE ASPECTS. THE STUDENT REACHES THE LEVEL OF EXCELLENCE IF HE OR SHE IS ABLE TO INDEPENDENTLY DEAL WITH PROBLEMS NOT EXPRESSLY COVERED IN CLASS. |
| Texts | |
|---|---|
| P. MARCELLINI, C. SBORDONE, ANALISI MATEMATICA UNO, LIGUORI EDITORE. N. FUSCO, P. MARCELLINI, C. SBORDONE, ANALISI MATEMATICA DUE, LIGUORI EDITORE. N. FUSCO, P. MARCELLINI, C. SBORDONE, ELEMENTI DI ANALISI MATEMATICA DUE, LIGUORI EDITORE. P. MARCELLINI, C. SBORDONE, ESERCITAZIONI DI MATEMATICA, VOLUME I, PARTE PRIMA E SECONDA, LIGUORI EDITORE. P. MARCELLINI, C. SBORDONE, ESERCITAZIONI DI MATEMATICA, VOLUME II, PARTE PRIMA E SECONDA, LIGUORI EDITORE. |
| More Information | |
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