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Farmacia - Chimica e tecnologia farmaceutiche

• being able to compute the first derivative and the primitives of a function;
• starting from the plot of the graph of a function: being able to estimate the value of the first derivative in a point; being able to draw the graph of its first derivative; being able to draw the graph of its primitives;
• for population evolution models: being able to interpret the graph of the time evolution of the number of individuals, and deduce from it the plot of the graph of the increase/decrease rate with respect to time;
• for simple motion models: being able to interpret the plot of the space-time graph of the motion of an object moving along a straight line: being able to deduce from it the plot of the graph speed-time (and viceversa);
• being able to approximate a function through polynomials, and being able to use such approximation to estimate the value of the function in a given point;
• being able to compute a definite integral; being able to compute approximately a definite integral, and to estimate the error of such computation;
  
• given a function and a differential equation, being able to show if the given function is a solution of the differential equation; being able to draw a qualitative graph of the solutions of simple differential equations; being able to compute an approximate solution of a Cauchy problem associated with a first order differential equation through the Euler method;
• being able to distinguish between population and sample, and acquring the appropriate terminology in each of the two cases; being able to distinguish between estimate and estimator; being able to recognize the main families of probabilistic models;
• being able to describe and represent graphically in R small structured data collections; being able to deduce the first qualitative consideration on the variables under analysis;
  
• being able to complete the descriptive deductions of simple samples with quantitative answers; being able to estimate the uncertainty of the statistical answer.

The enrollment to the exams through the Esse3 system is compulsory.

The students not regularly enrolled within the indicated deadlines will not, under any circumstance, be admitted to the examination tests.

In case of enrollment and absence from an examination test, not previously cancelled or communicated with reasonable advance (with the exception of proven cases of "major force", and anyway under the final decision and judgement of the Examination Comittee), it will not be possible to participate to the next examination test in the calendar. 

The examination tests are subdivided into two parts:

1. Test of the basic knowledges, for all the students enrolled to the examination tests; it consists of 5 questions and/or exercises about notions considered fundamental in differential and integral calculus; allotted time 20'; the test is considered positive with a score of at least 4 correct answers out of the 5 assigned; the outcome is communicated at the end of the time allotted for the first part;
2. Test on the contents of the course, accessible only if the Test of the basic knowledges is positive; it consists of various questions and/or exercises, of different types, about all the topics included in the examination program; allotted time 120'; it is subdivided into a parte of integral and differential calculus and a part of statistics; the part of statistics is accessible only if the part of calculus is positive; the test is considered positive with a score (weighted average of the scores of the part of differential and integral calculus, and the part of statistics) of at least 18/30.

The final score of the exam, expressed in thirtieths, is the one achieved in the part of Test on on the contents of the course.

• Function graph plots and their transformations.
• Numerical sequences. The geometric sequence and its properties.
• Calculus: limits, continuity, indeterminate forms, asymptotes.
• Differential calculus: derivatives, derivation rules, increasing and decreasing functions, points of maximum and minimum, higher order derivatives, convexity and concavity, points of inflection. Rule of de l'Hospital.
• Approximation of functions through polynomials. Taylor expansion of a function.
• Integral calculus: primitive function, rules of indefinite integration, calculation of an area, integral function; fundamental theorem of integral calculus, improper integrals.
• Differential equations: examples of mathematical models based on differential equations; first order differential equations; the Cauchy problem, theorem for the existence and uniqueness of the solution.

PROBABILITY and STATISTICS

• Elements of combinatorics.
• Elements of Probability Theory:  introduction to the probabilistic model for data; definiton of probability and elementary probability calculus; random variables; mean and variance of a random variable (continuous and discrete case).
• Descriptive statistics: introduction to R; quantitative and qualitative variables; univariate variables; indeces of position and variability; graphic representations (histogram, boxplot); bivariate variables; graphic representations (scatterplot, histogram, boxplot); qualititative comparisons; independence and measures of association; categorial bivariate data and tables.
• Sampling: statistics and sampling distributions; examples of families of distributions.
• Inferential Statistic: control of variability: interval estimates for proportions, for the mean, for the variance; for differences (of proportions, of means), for the median; hypothesis tests for proportions, for the mean, for the median; test for two samples (independent and coupled).