Teacher
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FRAGNELLI Genni
(syllabus)
Functions and number sets Introduction: operations among sets. Function; domain, co-domain, image and graph of functions. Injective, surjective, inverse function and composition. Increasing and decreasing, odd and even functions, Number sets N, Z, Q, R.
Elementary functions Review on lines, parabolas, exponential, logarithmic and trigoniometric functions. Absolute value. Neighborhood of a real number.
Limit and continuity Finite and infinite limit; sign permanence theorem. Right-side and left-side limit. Existence and uniqueness of the limit. Comparison theorem. Algebra of limits and indeterminate forms. Infinite and infinitesimal. Vertical, horizontal and oblique asymptote. Continuous functions. Weierstrass theorem. Intermediate value theorem. Intermediate zero theorem.
Derivatives Definition of derivative and its geometric interpretation. Calculation of derivatives. Differentiability and continuity. Point of non differentiability. Higher derivatives. Rolle's and Lagrange's theorem. De L’Hôpital's theorems. Taylor's theorem and McLaurin's expansion. Fermat's theorem. Maximum and minimum points. Convexity and concavity. Inflection point. Study of a function.
Integral Definition of indefinite integral and its properties. Straightforward anti-derivatives. Integration by parts. Integration by substitution. Definite integral and its properties. The fundamental theorem of calculus. generalized integral. Area.
Differential Equations Differential Equations: an introduction. Differential Equations of first and second order and Cauchy problems. Separate variables differential equations. Malthus model; bacterial growth; epidemic diffusion; radioactive decay. Logistic growth.
Descriptive statistics: tables and graphs, histograms and pie charts. Position indices: average, fashion and median percentiles and quartiles, weighted average. Dispersion indices: variance and standard deviation. Assessment of uncertainties in measurements: absolute, relative and percentage errors. Least squares method, Covariance, Linear correlation coefficient. Combinatorial calculus. Simple and repetitive arrangements; simple and repeating permutations; simple combinations and with repetitions; binomial coefficient in its different forms, power of a binomial with Newton's formula. Classical definition of probability: relative examples. Frequentist and subjective definition of probability. Total probability theorem. The concept of random variable and discrete and continuous distributions. Expected value and variance of a random variable distribution Discrete distributions: binomial distribution, definition and relative examples; Continuous distributions: normal distribution: density function, Gauss curve. Introduction of the distribution function and use of tables for the calculation of the probability of random events with standardized normal distribution: adequate examples of each topic will be carried out.
(reference books)
Elementi di calcolo. Versione semplificata per i nuovi corsi di laurea di Paolo Marcellini, Carlo Sbordone Editore: Liguori Data di Pubblicazione: febbraio 2016 EAN: 9788820736651 ISBN: 8820736659
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