FEDERICA GREGORIO | CALCULUS II
FEDERICA GREGORIO CALCULUS II
cod. 0512600002
CALCULUS II
| 0512600002 | |
| DEPARTMENT OF PHYSICS "E. R. CAIANIELLO" | |
| EQF6 | |
| PHYSICS | |
| 2024/2025 |
| OBBLIGATORIO | |
| YEAR OF COURSE 2 | |
| YEAR OF DIDACTIC SYSTEM 2017 | |
| AUTUMN SEMESTER |
| SSD | CFU | HOURS | ACTIVITY | |
|---|---|---|---|---|
| MAT/05 | 8 | 64 | LESSONS | |
| MAT/05 | 1 | 12 | EXERCISES |
| Exam | Date | Session | |
|---|---|---|---|
| APPELLO DI GENNAIO 2025 | 09/01/2025 - 10:00 | SESSIONE ORDINARIA | |
| APPELLO DI GENNAIO 2025 | 09/01/2025 - 10:00 | SESSIONE DI RECUPERO | |
| APPELLO DI FEBBRAIO 2025 | 13/02/2025 - 10:00 | SESSIONE ORDINARIA | |
| APPELLO DI FEBBRAIO 2025 | 13/02/2025 - 10:00 | SESSIONE DI RECUPERO |
| Objectives | |
|---|---|
| AIM OF THE COURSE IS TO PROVIDE THE STUDENTS WITH SOME OF THE BASIC NOTIONS OF THE DIFFERENTIAL AND INTEGRAL CALCULUS IN HIGHER DIMENSIONS, OF CERTAIN KINDS OF ORDINARY DIFFERENTIAL EQUATIONS AND OF SEQUENCES AND SERIES OF FUNCTIONS. KNOWLEDGE AND UNDERSTANDING: THE COURSE WILL FOCUS ON THE BASIC NOTIONS OF MATHEMATICAL ANALYSIS NECESSARY FOR A SECOND YEAR STUDENT OF THE DEGREE IN PHISICS. CERTAIN KINDS OF ORDINARY DIFFERENTIAL EQUATIONS, SEQUENCES AND SERIES OF FUNCTIONS, INFINITESIMAL, DIFFERENTIAL AND INTEGRAL CALCULUS, ELEMENTARY THEORY OF CURVES AND SURFACES AND DIFFERENTIAL FORMS WILL BE STUDIED. ALSO, POURPOSE OF THE COURSE IS TO GET THE STUDENT ACCUSTOMED WITH RIGOROUS ARGUMENTS AND WITH A CRITICAL USE OF THE TECHNIQUES. APPLYING KNOWLEDGE AND UNDERSTANDING: THE STUDENT IS SUPPOSED TO LEARN THEORETICAL ASPECTS OF THE COURSE AND TO EXPLOIT THEM IN ORDER TO SOLVE EXERCISES AND PROBLEMS INCLUDING THOSE THAT ARE RELATED TO PRACTICAL APPLICATIONS OF THE SCIENCE. AT THE SAME TIME THE COURSE IS DESIGNED TO ENABLE STUDENTS TO INTERPRET THE MAIN CONCEPTS THOUGHT ANALYTICALLY, GRAPHICALLY AND VERBALLY, DEVELOP THEIR ABILITY TO THINK IN A CRITICAL MANNER, IMPROVE THEIR SKILLS IN ACQUIRING NEW UNDERSTANDING AND EXPERIENCE. |
| Prerequisites | |
|---|---|
| KNOWLEDGE OF THE TOPICS TREATED IN “CALCULUS I”. |
| Contents | |
|---|---|
| -DIFFERENTIAL CALCULUS FOR FUNCTIONS OF SEVERAL VARIABLES (T:8H; P:3H) LIMITS AND CONTINUITY. DIRECTIONAL DERIVATIVES, DIFFERENTIAL, TANGENT PLANE. HIGHER ORDER PARTIAL DERIVATIVES. COMPOSITE FUNCTIONS. FREE EXTREMA. -ODES (T:6H; P:6H) DIFFERENTIAL MODELS. FIRST ORDER, SEPARABLE, LINEAR, BERNOULLI, HOMOGENEOUS ODES. CAUCHY PROBLEM. N-TH ORDER LINEAR ODES. -INTEGRAL CALCULUS FOR FUNCTIONS OF SEVERAL VARIABLES (T:4H; P:8H) DOUBLE INTEGRALS. TRIPLE INTEGRALS. DERIVATIVE OF THE INTEGRAL. -INFINITESIMAL CALCULUS FOR CURVES (T:8H; P:2H) VECTOR VALUED FUNCTIONS, LIMITS AND CONTINUITY. REGULAR CURVES, VECTORIAL DIFFERENTIAL CALCULUS. LENGHT OF A CURVE. LINE INTEGRALS. ELEMENTS OF DIFFRENTIAL GEOMETRY FOR CURVES. PHYSICAL APPLICATIONS. -VECTOR FIELDS (T:10H; P:4H) FIELD LINES. GRADIENT, CURL AND DIVERGENCE. LINE INTEGRAL OF A VECTOR FIELD. WORK AND CIRCULATION. CONSERVATIVE FIELDS AND POTENTIALS. DIFFERENTIAL FORMS. GAUSS-GREEN FORMULA. AREA AND SURFACE INTEGRALS. DIVERGENCE AND CURL THEOREMS. -IMPLICIT FUNCTIONS (T:4H; P:4H) DINI THEOREM. CONSTRAINED EXTREMA. LAGRANGE'S THEOREM. -SERIES OF FUNCTIONS (T:6H; P:3H) SEQUENCES AND SERIES OF FUNCTIONS. POWER SERIES. TAYLOR SERIES. |
| Teaching Methods | |
|---|---|
| THE COURSE IS STRUCTURED AS A COMBINATION OF THEORETICAL LECTURES AND EXERCISES SESSIONS. THE THEORETICAL TOOLS WILL BE EXPLOITED ALSO IN VARIOUS PHYSICAL APPLICATIONS. |
| Verification of learning | |
|---|---|
| THE FINAL EXAM CONSISTS OF A WRITTEN TEST AND AN ORAL EXAMINATION. THE EXAM IS DESIGNED TO EVALUATE AS A WHOLE: THE KNOWLEDGE AND UNDERSTANDING OF THE CONCEPTS PRESENTED DURING THE COURSE, THE MASTERY OF THE MATHEMATICAL LANGUAGE, THE SKILL OF PROVING THEOREMS, THE SKILL OF SOLVING EXERCISES, THE ABILITY TO IDENTIFY AND APPLY THE BEST AND MORE EFFICIENT METHOD IN EXERCISES SOLVING, THE ABILITY TO USE THE ACQUIRED KNOWLEDGE. THE WRITTEN EXAMS ARE SCHEDULED ATHE THE BEGINNING OF THE YEAR, THE DAY OF THE ORAL EXAM IS AGREED WITH THE STUDENTS. IN THE WRITTEN TEST THERE ARE 4 EXERCISES ABOUT: EXTREMA OF FUNCTIONS, POWER SERIES, DIFFERENTIAL FORMS, FIELDS, DOUBLE, TRIPLE AND SURFACE INTEGRALS, ODES. THE SCORE OF THE WRITTEN TEST IS EQUAL TO THE SUM OF THE POINTS ASSIGNED TO EACH EXERCISE. A MINIMUM OF 18/30 IS NEEDED TO HAVE ACCESS TO THE ORAL EXAMINATION THE FINAL MARK, EXPRESSED IN THIRTIETHS (EVENTUALLY WITH LAUDE), DEPENDS ON THE GLOBAL VALUTATION OF THE STUDENT. |
| Texts | |
|---|---|
| "LEZIONI DI ANALISI MATEMATICA 2", N. FUSCO, P. MARCELLINI, C. SBORDONE, ZANICHELLI, 2020 "ESERCITAZIONI DI ANALISI MATEMATICA 2", P. MARCELLINI, C. SBORDONE, ZANICHELLI, 2017 |
| More Information | |
|---|---|
| TEACHING IN ITALIAN. |
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