65965 - Mathematics, Statistics and Physics

Course Unit Page

SDGs

This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.

Quality education

Academic Year 2021/2022

Learning outcomes

Mathematics: The students will be able to operate with real numbers, to understand the algebraic calculation and the basic properties of the geometrical figures. The student will be able in general to: use the mathematical knowledge and the mathematical tools; to set and solve problems; to learn new concepts on the base of its experience and the previous knowledge. In Statistics the student will learn the main methods and tools for the qualitative and quantitative inferential and descriptive  analysis. In particular: interpret and critically evaluate the statistical information; produce and process raw data; apply the statistical approach to the natual and social sciences topics related to animal production.

In Physics: the student will learn the meaning of the different units of measure; the meaning of the basic physics terms; the basic principls of physics; the student will then be able to follow the successive courses of physiology, food technology, animal production related buildings and machinery.

Course contents

Module 1 Mathematics

Introduction: motivations and examples

Review of basic concepts: numerical sets; functions; order relations; powers and logarithms; analytical geometry; trigonometry: basic trigonometric functions and identities.

Limits and continuous functions: neighborhoods and accumulation points; definition of limit and continuous function; theorems on limit of sum, product, ratio, and composition of functions; limit of basic functions and indeterminate forms; comparison theorems; limit of sequences and Napier’s number; special limits and computational rules.

Differential calculus: differentiable functions and derivatives; theorem on the derivative of the sum, product, ratio, composition of functions; derivative of basic functions; higher order derivatives; main theorems of differential calculus: Fermat, mean-value, monotonicity and convexity intervals; study of a function.

Riemann’s integration: integral defined on an interval; properties of the integrals and of the integrable functions; integral of a continuous function; mean-value theorem; fundamental theorem of calculus; integration methods: by parts, substitution, rational functions; improper integral.

Module 2 Statistics

Theory 

Introduction: Definition and goal of statistics. Structure of Statistics. Definition of Universe, collective, population, sample. Classification.

Classification schemes: omograde and eterograde classes, numerosity,intensity and frequence. Graphical representations in statistics.

Measures of central tendency: Arithmetic and geometric mean, central value, median and mode.

Measures of statistical dispersion: standard deviation, variance, coefficient of variation.

Probability: Definiiton and assioms of probaility.Binomial and normal distribution.Standardized normal distribution. Theory of errors.

Sampling: general features and meaning.

Statistical inference: sample sum and mean, interval of confidence, Hypothesis test. chi-square test.Covariance correlation and linear regression.analysis of Variance.

Group work:application of descriptive and inferential statistical techniques to simple cases related to the animal production sector

 

Module 3 Physics

MEASUREMENT AND UNITS OF MEASURE: physical quantities, symbols and units of measure; measuring instruments, systems of units of measure: SI system, c.g.s. system, fundamental and derived units.

VECTORS: vectors and scalars; vector algebra: sum, product of a scalar and a vector, scalar product, vector product.

KINEMATICS: material point kinematics, position, displacement, mean and instantaneous velocity, mean and instantaneous acceleration; uniform rectilinear motion, uniform circular motion, uniformly accelerated motion.

DYNAMICS: mass and force; examples of forces: gravitational force, weight force, elastic force. Centre of mass. Newton’s Laws. Mechanical equilibrium and stability (in brief). Examples: mathematical pendulum, inclined plane. Friction. Mechanical work and potential energy; kinetic energy; conservation law for mechanical energy. Examples: work done by the gravitational force and by an elastic force.

FLUID MECHANICS: Eulerian and Lagrangian description (in brief). Density and pressure. Fluid Statics laws, pressure measurement, Pascal’s law, Archimedes’ law. Examples: hydraulic ram, floating bodies. Fluid Dynamics: continuity equation, Bernoulli’s equation.

THERMODYNAMICS: temperature and heat. The Laws of Thermodynamics. Heat capacity, specific heat, latent heat. Examples of thermodynamic processes: adiabatic, isochoric, isobaric, isothermal, cyclic processes, free expansion. Entropy and its relevance; reversible and irreversible processes; the arrow of time. Ideal gas law. Heat transfer: conduction, convection, radiation. Machines Carnot’s cycle, efficiency; refrigeration cycle and its efficiency.

After each unit, exercises will be solved in class to better analyse and acquire the course conten.

 

Readings/Bibliography

Module 1 (Mathematics)

Slides

Lecture notes

Further bibliographic references will be provided in class

Module 2 (Statistics)

Teacher notes and slides

Internet + other material provided during the class

Module 3 (Physics)

Lecture 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

Ageno M., Elementi di Fisica. Bollati Boringhieri

Further references will be discussed during the classes

Teaching methods

Classroom lessons and group works on case studies

Assessment methods

The final mark of the integrated course will be calculated as an arithmetic mean of the three different modules.

Concerning the module on Mathematics, the exam includes a written and an oral test. The written one is further divided into two parts: the first is a brief quiz to assess the knowledge of basic concepts, and the second part is a more thorough examination that includes the resolution of some exercises. The oral test is optional, though it is necessary in order to achieve a final grade higher than 28.

The module Staitstics will involve a written test with both multiple choice quesitons and open quesitons.

Ther module Physics involves an oral examination (approximate duration: 30 minutes) during which the understanding of the Mechanics of the material point, of the Fluid Mechanics, and of the Thermodynamics will be assessed.

  The marks in each module will be valid for 3 years. That is after the first module exam results the student will have three years to finalize the exams for the remaining two modules of  the integrated course

Teaching tools

Mathematics: 

slides and electronic board. Tutoring for the resolution of exercises.

Statistics: online and offline statistical software, slides and papers

Phyisics: papers and slides

Office hours

See the website of Cesare Zanasi

See the website of Stefano Pagliarani

See the website of Mirko Maraldi