65965 - Mathematics, Statistics and Physics

Learning outcomes

At the end of the course, the student is able to operate with real numbers, knows algebraic calculation and the fundamental properties of geometric figures. In particular, the student is able to: - use mathematical technical knowledge and tools to a good level; - set up and solve problems; - assimilate new concepts based on previous experience and knowledge. The student learns the main methods and basic tools of the quantitative study of collective phenomena. In particular, the student is able to: - interpret and critically evaluate information of a statistical nature (reading and understanding articles in journals and/or specialized publications); - autonomously produce and process statistical data; - apply some tools of the statistical methodology for the description and quantitative study of phenomena of biological and economic interest. At the end of the course, the student knows the fundamental principles of point mechanics and thermodynamics, in order to describe and interpret the physical phenomena involved in the main processes of the agricultural and agroforestry sector.

Course contents

Mathematics (Module 1)

Introduction. Numerical sets; functions; order relations; powers and logarithms; Analytic geometry; trigonometry: basic trigonometric functions and identities; Limits and continuous functions: neighborhoods and accumulation points; definition of limit and continuous function; sum, product, reciprocal and compound limit theorems; limits of elementary functions and indeterminate forms; comparison theorems; limits of sequences and the Nepero number; notable limits and calculation rules. Differential calculus: differentiable and derived functions; theorem on the derivative of sum, product, ratio, compound and inverse; derivative of elementary functions; higher order derivatives; main theorems of differential calculus: Fermat, mean value, intervals of monotonicity and convexity; function study. Riemann integration: definition of integral over an interval; properties of the integral and of integrable functions; integrals of continuous functions; integral mean theorem; fundamental theorem of calculus; integration methods: by parts, substitution, rational functions; improper integrals.

 

Statistics (Module 2)

THEORY

Introduction: Definition and aims of statistics, Phases of the statistical method, Structure of statistics. Concept of universe, collective, population, sample. Elements of statistical research. Classification schemes: homograde and heterograde classes. Numerousness, intensity and frequencies. Graphic representations. Measures of centrality: The arithmetic and geometric mean. The central value, the median and the mode. Measures of variability: range, standard deviation, variance, coefficient of variation. Probability: Definitions and axioms of probability. Binomial distribution and normal distribution. Standard normal distribution. Error theory. Sampling. Statistical inference: sum and sample mean, confidence interval, chi-square test. Hypothesis testing. Correlation and linear regression. Covariance, correlation coefficient and simple linear regression. Analysis of variance.

EXERCISES

application of descriptive and inferential statistics techniques to simple cases related to animal production.

 

Physics (Module 3)

History of Physics in brief. Measurements and systems of units of measurement: physical quantities, symbols and units of measurement; standards and instruments, systems of units of measurement, the SI system, the c.g.s. system, fundamental and derived units. Vectors: vector quantities and scalar quantities; operations with vectors: sum, product of a scalar by a vector, scalar product. Kinematics: kinematics of the material point: position and displacement, average and instantaneous velocity, average and instantaneous acceleration; uniform rectilinear motion, uniform circular motion, uniformly accelerated rectilinear motion. Dynamics: concepts of force and examples: gravitational force, weight force, elastic force. Center of mass. Newton's laws. The phenomenon of friction. Examples: inclined plane. Work and potential energy; kinetic energy; principle of conservation of mechanical energy. Examples: work done by gravitational force, elastic force. Thermodynamics: concepts of temperature and heat. The principles of thermodynamics. Heat capacity, specific heat. Examples of thermodynamic transformations: adiabatic, isochoric, isobaric, isotherm, cyclic transformations, free expansion. The concept of entropy and its importance; reversible and irreversible phenomena; the arrow of time. Equation of state of perfect gases. Thermal machines and Carnot cycle, efficiency of the Carnot machine. At the end of each topic some exercises will be discussed and carried out to meditate and better understand the concepts discussed.

Readings/Bibliography

Mathematics (Module 1)

• teacher's notes

• annotated lecture notes

• further references will be provided during lectures

Statistics (Module 2)

• teacher's notes

Physics (Modulo 3)

• teacher's notes

• Mazzoldi P., Nigro M., Voci C., Elementi di Fisica - Meccanica e Termodinamica. EdiSES

• Halliday D., Resnick R., Walker J., Fondamenti di Fisica. Meccanica, Termologia. Casa Editrice Ambrosiana

• further references will eventually be provided during lectures

Teaching methods

Theory classes and exercises.

Assessment methods

The final grade of the exam consists of the synthesis (by weighted average) of the evaluations of the three modules that make up the integrated course.

The final examination for Mathematics module consists in a written test and an oral exam. The written test is divided into two parts: a preliminary quiz to verify the learning of the minimum knowledge, and one in which the learning is evaluated in more detail and includes the resolution of exercises. The second part of the written test is accessed only if the preliminary part of the written test is passed. The oral exam is optional, but necessary in order to achieve a grade higher than 28.

The final examination for Statistics module consists in a written test. This test includes closed questions aimed at understanding the students' familiarity with the fundamental terms and concepts of Statistics; open questions are also foreseen which consist in reading and interpreting the results of descriptive and inferential statistical analyses. Duration of the test 3 hours.

The final examination for Physics module consists in a written test (duration: 90 minutes) composed by 4 short numerical exercises and 4 open-ended theory questions.

Teaching tools

Laboratory tools and instruments will occasionally be brought in class.

Office hours

See the website of Mirko Maraldi

See the website of Antonello Pesce

See the website of Cosimo Rota