Tiziana DURANTE | CALCULUS 1
Tiziana DURANTE CALCULUS 1
cod. 0612700112
CALCULUS 1
| 0612700112 | |
| DIPARTIMENTO DI INGEGNERIA DELL'INFORMAZIONE ED ELETTRICA E MATEMATICA APPLICATA | |
| EQF6 | |
| COMPUTER ENGINEERING | |
| 2021/2022 |
| OBBLIGATORIO | |
| YEAR OF COURSE 1 | |
| YEAR OF DIDACTIC SYSTEM 2017 | |
| AUTUMN SEMESTER |
| SSD | CFU | HOURS | ACTIVITY | |
|---|---|---|---|---|
| MAT/05 | 5 | 40 | LESSONS | |
| MAT/05 | 4 | 32 | EXERCISES |
| Objectives | |
|---|---|
| THE COURSE PRESENTS THE BASIC ELEMENTS OF MATHEMATICAL ANALYSIS. THE TRAINING OBJECTIVES THE TEACHING CONSISTS IN THE ACQUISITION OF RESULTS AND DEMONSTRATIVE TECHNIQUES, AS WELL AS IN THE ABILITY TO USE THE RELATED CALCULATION TOOLS. KNOWLEDGE AND UNDERSTANDING NUMERICAL SETS. REAL FUNCTIONS. REFERENCES ON EQUATIONS AND INEQUATIONS. NUMERICAL SUCCESSIONS. LIMITS OF A FUNCTION. CONTINUOUS FUNCTIONS. DERIVATIVE OF A FUNCTION. FUNDAMENTAL THEOREMS OF DIFFERENTIAL CALCULATION. STUDY OF THE GRAPH OF A FUNCTION. INTEGRATION OF FUNCTIONS OF A VARIABLE. SOFTWARE TOOLS FOR MATHEMATICS. APPLYING KNOWLEDGE AND UNDERSTANDING APPLY THE THEOREMS AND RULES STUDIED TO TROUBLESHOOTING. PERFORM CALCULATIONS WITH LIMITS, DERIVATIVES, INTEGRAL. CONDUCT THE STUDY OF THE GRAPH OF A FUNCTION. |
| Prerequisites | |
|---|---|
| IN ORDER TO REACH THE OBJECTIVES STUDENTS SHOULD HAVE A BACKGROUND RELATING TO ALGEBRA, IN PARTICULAR ALGEBRAIC EQUATIONS AND INEQUALITIES, LOGARITHMIC, EXPONENTIAL, TRIGONOMETRIC AND TRANSCENDENTAL INEQUALITIES, AND THEY SHOULD UNDERSTAND TRIGONOMETRY, WITH PARTICULAR REFERENCE TO THE BASIC THEORY OF TRIGONOMETRIC FUNCTIONS. |
| Contents | |
|---|---|
| NUMERICAL SETS: INTRODUCTION TO THE THEORY OF THE SETS. INTRODUCTION TO REAL NUMBERS. EXTREME OF A NUMERICAL SET. INTERVALS. INTORNI, ACCUMULATION POINTS. CLOSED AND OPEN SETS. INTRODUCTION TO COMPLEX NUMBERS. IMAGINARY UNIT. OPERATIONS ON COMPLEX NUMBERS. ALGECRICA FORM AND TRIGONOMETRIC FORM. DE MOIVRE FORMULA. N-ESIME ROOTS. LESSON / EXERCISES : HOURS 4/2 REAL FUNCTIONS: DEFINITION. EXTREME OF A REAL FUNCTION. MONOTONE FUNCTIONS. COMPOSED FUNCTIONS. INVERTIBLE FUNCTIONS. ELEMENTARY FUNCTIONS: N-MA POWER FUNCTION AND N-MA ROOT, EXPONENTIAL FUNCTION, LOGARITHMIC FUNCTION, POWER FUNCTION, TRIGONOMETRIC FUNCTIONS AND THEIR INVERSE. LESSON / EXERCISES : HOURS 2/2 BASIC NOTIONS OF EQUATIONS AND INEQUALITIES: FIRST ORDER, QUADRATIC, BINOMIAL, IRRATIONAL, TRIGONOMETRIC, EXPONENTIAL, LOGARITHMIC EQUATIONS. SYSTEMS OF EQUATIONS. FIRST ORDER, SECOND ORDER, RATIONAL, IRRATIONAL, TRIGONOMETRIC, EXPONENTIAL, LOGARITHMIC INEQUALITIES. SYSTEMS. LESSON / EXERCISES : HOURS 2/4 NUMERICAL SEQUENCES: DEFINITIONS. BOUNDED, CONVERGENT, DIVERGENT AND OSCILLATING SEQUENCES. MONOTONE SEQUENCES. NEPERO’S NUMBER. CAUCHY'S CRITERION FOR CONVERGENCE. NUMERICAL SERIES: INTRODUCTION. CONVERGENCE. ARMONIC AND GEOMETRIC SERIES. POSITIVE SERIES AND CONVERGENCE CRITERIA. LESSON /EXERCISE HOURS: 4/4 LIMITS OF A FUNCTION: DEFINITION. RIGHT AND LEFT-HAND LIMITS. UNIQUENESS AND COMPARISON THEOREMS. OPERATIONAL IDENTITIES AND INDETERMINATE FORMS. NOTABLE SPECIAL LIMITS. LESSON /EXERCISE HOURS: 4/4 CONTINUOUS FUNCTIONS: DEFINITION. CONTINUITY AND DISCONTINUITY. WEIERSTRASS, ZEROS, BOLZANO THEOREMS. UNIFORM CONTINUITY. LESSON / EXERCISES : HOURS 4/0 DERIVATIVE OF A FUNCTION: DEFINITION. LEFT AND RIGHT DERIVATIVES. GEOMETRIC MEANING. TANGENTIAL LINE. DIFFERENTIABILITY AND CONTINUITY. DERIVATION RULES. DERIVATIVES OF ELEMENTARY, COMPOSITE, INVERSE FUNCTIONS. HIGHER ORDER DERIVATIVES. DIFFERENTIAL OF A FUNCTION AND ITS GEOMETRIC MEANING. LESSON / EXERCISES : HOURS 4/2 FUNDAMENTAL THEOREMS OF DIFFERENTIAL CALCULUS: ROLLE, CAUCHY, LAGRANGE THEOREMS AND COROLLARIES. DE L'HOSPITAL THEOREM. MAXIMA AND MINIMA. TAYLOR AND MAC-LAURIN FORMULAS. LESSON / EXERCISES : HOURS 4/2 GRAPH OF A FUNCTION: ASYMPTOTES OF A GRAPH. LOCAL MAXIMA AND MINIMA. CONCAVE AND CONVEX FUNCTIONS AT A POINT, INFLECTION POINTS. DRAWING GRAPH. SOFTWARE TOOLS FOR MATHEMATICS. LESSON / EXERCISES : HOURS 4/8 INTEGRATION OF ONE VARIABLE FUNCTIONS: PRIMITIVE FUNCTIONS AND INDEFINITE INTEGRAL. DEFINITE INTEGRAL AND GEOMETRICAL MEANING. BASIC INTEGRALS. RULES AND METHODS OF INTEGRATION. INTEGRAL OF RATIONAL FUNCTIONS. FUNDAMENTAL THEOREM OF CALCULUS: 6/6 |
| Teaching Methods | |
|---|---|
| THE COURSE CONSISTS IN THEORETICAL LECTURES AND EXERCISES. 72 HOURS IN TOTAL: 38 HOURS FOR THE THEORY AND 34 HOURS FOR THE EXERCISES. THE COURSE IS DELIVERED IN PRESENCE WITH MANDATORY FREQUENCY, CERTIFIED BY THE STUDENT THROUGH THE USE OF THE PERSONAL BADGE. IN ORDER TO BE ABLE TO SUSTAIN THE FINAL VERIFICATION OF PROFITS AND OBTAIN THE CFU RELATED TO THE EDUCATIONAL ACTIVITY, THE STUDENT MUST HAVE ATTENDED AT LEAST 70% OF THE SCHEDULED HOURS OF TEACHING ACTIVITY. |
| Verification of learning | |
|---|---|
| THE FINAL 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 IN THE WRITTEN AND ORAL TEST. 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 EXAM CONSISTS OF A WRITTEN TEST AND AN ORAL EXAMINATION. WRITTEN TEST: THE WRITTEN TEST CONSISTS IN SOLVING TYPICAL PROBLEMS PRESENTED IN THE COURSE (THERE ARE SAMPLES AVAILABLE ON THE WEBSITE) AND THE TOOLS USED IN SOLVING THE EXERCISES AND THE CLARITY OF ARGUMENTATION WILL BE TAKEN INTO CONSIDERATION IN THE EVALUATION. THERE WILL BE A MID TERM TEST CONCERNING THE TOPICS ALREADY PRESENTED IN THE COURSE, WHICH IN CASE OF A SUFFICIENT MARK, WILL EXEMPT THE STUDENTS ON THIS TOPICS AT THE WRITTEN TEST. THE WRITTEN TEST WILL BE EVALUATED IN THIRTIETHS. THE ORAL INTERVIEW IS DEVOTED TO EVALUATE THE DEGREE OF KNOWLEDGE AND MASTERY IN ALL THE TOPICS OF THE COURSE, AS DEFINITIONS, AS PROOFS OF THEOREMS AND IN SOLVING EXERCISES. THE FINAL MARK, EXPRESSED IN THIRTIETHS (EVENTUALLY WITH LAUDE), DEPENDS ON THE GLOBAL VALUTATION OF THE STUDENT. |
| Texts | |
|---|---|
| BASIC TEXT FOR THEORY: P.MARCELLINI, C. SBORDONE, ELEMENTI DI ANALISI MATEMATICA UNO, LIGUORI EDITORE. BASIC TEXT FOR THE EXERCISES: P.MARCELLINI-C.SBORDONE}, ESERCITAZIONI DI MATEMATICA I, VOL.I, PARTE I,II, LIGUORI EDITORE. SUPPLEMENTARY TEACHING MATERIAL WILL BE AVAILABLE ON THE UNIVERSITY E-LEARNING PLATFORM (HTTP://ELEARNING.UNISA.IT) ACCESSIBLE TO STUDENTS USING THEIR OWN UNIVERSITY CREDENTIALS. |
| More Information | |
|---|---|
| THE COURSE IS HELD IN ITALIAN |
BETA VERSION Data source ESSE3 [Ultima Sincronizzazione: 2022-11-21]
