Teachings
FA/0095  MATHEMATICS AND ELEMENTS OF STATISTICS
Academic Year 2019/2020
Free text for the University
 Professor

MARIA ANTONIETTA FARINA (Tit.)
 Period

First Semester
 Teaching style

Convenzionale
 Lingua Insegnamento

Informazioni aggiuntive
Course  Curriculum  CFU  Length(h) 

[60/76] BIOTECHNOLOGY  [76/10  Ord. 2018] Industriale e Ambientale  7  60 
Objectives
KNOWLEDGE AND SKILLS 'UNDERSTANDING:
 Adequate knowledge and interpretation of the problems related to the analysis and statistics;
 Capacity 'problemsolving through the correct application of the methods of analysis;
 Correct application of the results obtained.
JUDGEMENT:
the student must 'be able to highlight the problems of analysis which occur in different disciplines with their more' correct and straightforward resolution.
'' COMMUNICATION SKILLS:
capacity 'of communication through scientific language written and oral.
CAPACITY 'to learn independently:
the course encourages students to work independently as well in order to be able to use alternative sources of information on the material provided by the teacher.
Prerequisites
Basic scientific knowledge of arithmetic, algebra and geometry according to the programs of the school.
Contents
Sets and numbers, absolute value. First and second degree. Fractional equations. Irrational equations. First and second degree inequalities. Fractional inequalities. Systems of inequalities.
Equation of a line; parallelism and orthogonality of lines; distance between two points, distance between a point and a line. Intersection between lines.
Circles and parabola. Intersection of a line and a conic, tangent line.
Functions. Definition. Real functions. Graph of a function. Composition of two functions. Invertible functions. Increasing and decreasing functions. Even and odd functions. Maximal and minimum of a function. Linear functions, power functions, exponential functions, logarithmical functions, periodic functions, sine, cosine and tangent function.
Differential calculus. Limits of a function. Some techniques of solution of indeterminate forms.
Asymptote. Continuous function, point of discontinuity.
The notion of derivative. Properties of derivatives: derivative of the sum, of the product and of the quotient of two functions, of composite function. The second derivative.
The relationship between continuity and differentiability function. L’Hopital’s rule. Fermat’s theorem, maximum and minimum with derivative. The sign of the first derivative of the function to determine if the function is increasing or decreasing. Convexity and concavity with derivatives. Study of a function.
Indefinite integrals. Definition and properties. Integration by substituction and integration by parts.
Definite integrals. Properties; function Riemann integrable (continuous function). Integration by substituction and integration by parts.
Statistics. Graphical representations of data. Arithmetic and geometric mean. Median. Mode. Variance. Standard deviation. Brief outline of Linear regression and Correlation coefficient.
Probability. Random event, absolute and relative frequency, sample space, independent and dependent events, compatible and incompatible events, conditional probability.
Verification of learning
During the course, there will be a test “in itinere” performed on the first part of the program. The test will be considered for the final evaluation.
The exam will be written, it will last 2 hours.
Description:
The exam is a test with mathematical exercises and some theory questions.
The final grade takes into account several factors:
Quality of the knowledge, skills, competences:
a) appropriateness, accuracy and consistency of knowledge, abilities, and abilities to apply knowledge and understanding;
The judgment can indeed be:
a) Sufficient (from 18 to 20/30)
The candidate shows little acquisition of knowledge, superficial level, many gaps;
b) Moderate (21 to 23)
The applicant shows moderate acquisition of knowledge, a few gaps;
c) Good (24 to 26)
The candidate demonstrates a rather large wealth of knowledge, moderate indepth, with small gaps
d) Outstanding (27 to 29)
The candidate shows a very extensive wealth of notions, high indepth, with marginal gaps;
e) Excellent (30)
The candidate demonstrates a wealth of very extensive and indepth knowledge, irrelevant gaps
The praise is attributed to the candidates clearly above average.
If any, the oral exam will comprise both theory and exersises. The teacher will have the choice of integrating the written exam with a supplementary colloquium.
Texts
D. Benedetto, M. Degli Esposito, C. Maffei, Matematica per le Scienze della Vita, Casa Editrice Ambrosiana, 2011, ISBN: 9788808183361
M. Bramante, C. D. Pagani, S. Salsa, Analisi Matematica 1, Zanichelli, ISBN: 9788808064851
C. Belingeri, F. Bongiorno, F. Rosati, Matematica–30, Aracne, ISBN: 8879990144
More Information
There are some mathematical exercises and small exam papers online, which are partially answered.