Lyoubomira SOFTOVA PALAGACHEVA | MATHEMATICS AND STATISTICS
Lyoubomira SOFTOVA PALAGACHEVA MATHEMATICS AND STATISTICS
cod. 0512800024
MATHEMATICS AND STATISTICS
| 0512800024 | |
| DEPARTMENT OF CHEMISTRY AND BIOLOGY "ADOLFO ZAMBELLI" | |
| EQF6 | |
| BIOLOGICAL SCIENCES | |
| 2018/2019 |
| OBBLIGATORIO | |
| YEAR OF COURSE 1 | |
| YEAR OF DIDACTIC SYSTEM 2016 | |
| PRIMO SEMESTRE |
| SSD | CFU | HOURS | ACTIVITY | |
|---|---|---|---|---|
| MAT/05 | 10 | 80 | LESSONS |
| Objectives | |
|---|---|
| THE AIM OF THE COURSE IS TO PROVIDE A SOLID UNDERSTANDING OF THE MATHEMATICAL PRINCIPLES UNDERLYING OTHER RELEVANT DISCIPLINES, SUCH AS CHEMISTRY, PHYSICS AND BIOLOGY. THE COURSE AIMS TO PROVIDE KNOWLEDGE, IN A CONCISE AND SUITABLE FOR APPLICATIONS, THE MAIN MATHEMATICAL TOOLS NECESSARY TO CREATE MATHEMATICAL MODELS AND PERFORM STATISTICAL PROCESSING OF DATA. |
| Prerequisites | |
|---|---|
| TO FOLLOW THE COURSE, THE STUDENT MUST HAVE KNOWLEDGE AND MASTERY OF THE FOLLOWING TOPICS. FIRST AND SECOND DEGREE EQUATIONS AND INEQUALITIES; FRACTIONAL INEQUALITIES; IRRATIONAL INEQUALITIES. EQUATION OF THE LINE, OF THE PARABOLA AND OF THE CIRCLE IN THE PLANE. TRIGONOMETRY: MAIN RELATIONSHIPS. PROPERTIES OF POWERS AND LOGARITHMS. |
| Contents | |
|---|---|
| REAL NUMBERS AND COMPLEX NUMBERS. ALGEBRA OF COMPLEX NUMBERS. REAL FUNCTIONS OF A REAL VARIABLE. GRAPHICS OF ELEMENTARY FUNCTIONS. DEFINITION OF LIMIT. OPERATIONS WITH LIMITS. INDEFINITE FORMS. NUMERICAL SUCCESSIONS AND LIMITS OF SUCCESSIONS. CONTINUOUS FUNCTIONS. THE THEOREM OF WEIERSTRASS. CHANGE OF VARIABLE INTO A LIMIT. FUNDAMENTAL LIMITS. DERIVATIVE: GEOMETRIC AND PHYSICAL MEANING. DERIVATIVE OF ELEMENTARY FUNCTIONS. OPERATIONS WITH DERIVATIVES. THEOREMS OF ROLLE AND LAGRANGE, CONSEQUENCES. RELATIVE AND ABSOLUTE MAXIMA AND MINIMA. FUNCTIONAL STUDY AND DRAWING OF HIS GRAPH. APPLICATIONS OF DERIVATIVES. MAXIMUM AND MINIMUM PROBLEMS. PRIMITIVES OF A FUNCTION. UNDEFINED INTEGRAL. INTEGRATION BY SUBSTITUTION, BY PARTS. INTEGRATION OF RATIONAL FUNCTIONS AND METHOD OF INDETERMINATE COEFFICIENTS. THE DEFINITE INTEGRAL. THEOREM OF THE MEAN AND FUNDAMENTAL THEOREM OF THE INTEGRAL CALCULUS. CALCULATION OF FLAT AREAS BY INTEGRATION. EXAMPLES OF INTEGRALS IN A GENERALIZED SENSE. VECTOR CALCULATION. SUM, MULTIPLE OF A VECTOR, SCALAR PRODUCT. DETERMINANT OF A MATRIX. VECTOR PRODUCT. MIXED PRODUCT. PLAN EQUATION. VARIOUS TYPES OF EQUATIONS OF A LINE. GENERALITIES ON DIFFERENTIAL EQUATIONS. LINEAR DIFFERENTIAL EQUATIONS OF THE FIRST ORDER. DESCRIPTIVE STATISTICS. PROBABILITY CALCULATION ELEMENTS UNIFORM PROBABILITY. RANDOM VARIABLES. LAW AND DISTRIBUTION FUNCTION OF A RANDOM VARIABLE. CONDITIONAL PROBABILITY AND INDEPENDENCE. DISCRETE ALEATORY VARIABLES (OF BERNOULLI, BINOMIAL, OF POISSON) AND THEIR PROPERTIES. MATHEMATICAL HOPE AND VARIANCE. CONTINUOUS RANDOM VARIABLES (NORMAL, CHI SQUARE, STUDENT) AND THEIR PROPERTIES. POISSON APPROXIMATION. LIMIT THEOREMS, NORMAL APPROXIMATION. ESTIMATES SAMPLE MEAN AND VARIANCE. PERCENTILES AND QUANTILES. GENERAL THEORY OF TESTS: HYPOTHESIS AND ALTERNATIVE, CRITICAL REGION, CRITICAL VALUE, FIRST AND SECOND SPECIES ERRORS, VALUE P. STUDENT TEST. CONFIDENCE INTERVALS DEFINITION AND MEANING OF THE CONFIDENCE INTERVAL. USE OF CONFIDENCE INTERVALS FOR HYPOTHESIS TESTING. CONFIDENCE INTERVALS FOR THE AVERAGE. DISCRETE STATISTICS ESTIMATES, CONFIDENCE INTERVALS AND HYPOTHESIS TESTS FOR PROPORTIONS AND PROPORTIONS DIFFERENCES. CONTINGENCY TABLE METHOD: THE CHI-SQUARE TEST. LINEAR REGRESSION THE LINEAR MODEL. STANDARD ERRORS, CONFIDENCE INTERVALS AND HYPOTHESIS TESTING ON THE REGRESSION COEFFICIENTS. |
| Teaching Methods | |
|---|---|
| LECTURES AND EXERCISES. |
| Verification of learning | |
|---|---|
| WRITTEN AND ORAL EXAM. |
| Texts | |
|---|---|
| SERGIO INVERNIZZI, MAURIZIO RINALDI, FEDERICO COMOGLIO MODULI DI MATEMATICA E STATISTICA, ZANICHELLI, 2018 |
| More Information | |
|---|---|
| LSOFTOVA@UNISA.IT |
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