Unit ELEMENTS OF MATHEMATICS AND PHYSICS

PRINCIPLES OF PHYSICS

Code	GP004371
CFU	3
Teacher	Igor Neri
Teachers	Igor Neri
Hours	21 ore - Igor Neri
Learning activities	Base
Area	Formazione chimica e fisica di base
Academic discipline	FIS/03
Type of study-unit	Obbligatorio (Required)
Language of instruction	Italian
Contents	Introduction to the experimental method. Elements of mechanics: kinematics and dynamics of the material point. Elements of thermodynamics. Elements of electrostatics
Reference texts	Walker, Fondamenti di Fisica (Pearson)
Educational objectives	To provide the student with basic information on the main topics of classical physics with particular reference to the 'physical sense'. Students must acquire the ability to reason logically and critically analyze what they will encounter in subsequent courses. They must be able to ask the right questions to face unforeseen situations and avoid gross errors from a logical-practical point of view. Ability to solve basic physics exercises and problems. More specifically, and with reference to the Dublin Descriptors for learning objectives (D1 knowledge and understanding; D2 applying knowledge and understanding; D3 making judgments; D4 communication skills; D5 learning skills), the student will acquire the basic notions of classical physics (D1) to be able to correctly interpret the theoretical principles on which some analysis equipment, diagnostic tools, and biological phenomena are based (D2). During the course, analytical and problem-solving skills will be developed by proposing numerical exercises that allow the application of acquired theoretical notions and through the collaborative discussion of some physiological phenomena from a physical point of view (D3 and D4). The skills acquired (both in terms of knowledge and methodological approach) will be fundamental in the autonomous study of related disciplines and, more generally, in continuous professional development (D5).
Prerequisites	Basic notions of algebra and geometry, manipulation of numerical and literal expressions, solution of first and second degree equations, notions of trigonometry
Teaching methods	Lectures in the classroom with the aid of slide projections and videos.
Other information	For information on support services for students with disabilities and/or learning disabilities (DSA), visit the page http://www.unipg.it/disabilita-e-dsa
Learning verification modality	The assessment method consists of a written and oral exam. The oral exam involves discussing the written test, with a request to delve deeper into the related theory, with the aim of ascertaining the degree of knowledge and mastery of the fundamental concepts and their application in physics problems.
Extended program	Course presentation. Physical quantities and the International System of Units. Motion in one dimension. Position vector, velocity, and acceleration. One-dimensional kinematics. Motion in two and three dimensions. Forces and Newton's laws. Work, power, and kinetic energy. Conservative forces and potential energy. Conservation of mechanical energy. Momentum. Impulse and momentum. Conservation of momentum. Collisions between two bodies. Temperature, macroscopic and microscopic viewpoints. Thermal equilibrium, concept of temperature, and temperature measurement. Kinetic theory of gases and equations of ideal gases. Heat, work, and internal energy. Conservation of energy and the first law of thermodynamics. Carnot's theorem and the second law of thermodynamics. Entropy. Electric charges: forces and fields. Electric potential and electric potential energy. Electric current and direct current circuits.

ELEMENTS OF MATHEMATICS

Code	A000248
CFU	3
Teacher	Roberta Filippucci
Teachers	Roberta Filippucci
Hours	21 ore - Roberta Filippucci
Learning activities	Base
Area	Formazione informatica, matematica e statistica di base
Academic discipline	MAT/05
Type of study-unit	Obbligatorio (Required)
Language of instruction	Italian
Contents	Inequalities (first and second degree). Functions: main properties. Limits and continuity. Differentiations of real functions, monotonicuty, concavity and convexity. Graphs of functions. Somo notions on Riemann integration, integral function. Integration techniques. Elements of Descriptive statistic and inferential statistics. Linear regression.
Reference texts	M. Bramanti, F. Confortola, S. Salsa: Matematica per le scienze. Con fondamenti di probabilità e statistica, Ed. Zanichelli, Bologna, 2024
Educational objectives	The student should acquire a basic knowledge in mathematical analysis, descriptive statistic and some notions of inferential statistics. The textbook and the didactics material used during the lessons are rich of examples and counterexamples, and therefore seem to be optimal to achieve a good understanding of the topics starting from exercises, that is from applications. Main knowledge acquired will be: - To know the main topics of mathematical analysis and how to apply them to the natural sciences, - To know several tools to solve elementary and basilar exercises, - To read and understand texts of Mathematical Analysis and Statistics, - To work in teams, but also in autonomy. The skills listed above are set out in the framework of professions related to experts in biotechnological processes operating in industrial/social contexts characterized by the production/use of several categories of products in the field of industrial biotechnology. Main competence (i.e. ability to apply the main knowledge acquired) will be: - To apply the theory to the resolution of exercises or problems based on models developed during lessons - To analyze and treat simple concrete statistical problems by choosing the right statical test to apply, - To solve some easy mathematical problems in the field of applied mathematics, indipendently.
Prerequisites	To better understand the topics covered in the course the student should be familiar with pre-university education notions such as decomposition of simple algebraic expressions, set theory (union, intersection, complement, difference, Venn diagram, algebra of sets), resolution of linear equations and inequalities, manipolation of polynomials. In particular during the first lessons of the course, a short review of the above topics will be performed.
Teaching methods	The course is split in theoretical lessons and practical lessons, in these latter several exercises are carried out in class. The course is organized 21 hours are divided into 9 hours of theory, together with different examples and counterexamples and 12 hours of practical exercises.¿¿ A tablet is used to project lessons for the Mathematical Analysis part , while for the Statistics part a PowerPoint presentation will be used.¿¿ In the tutorial service the students will be followed individually by the teacher.
Other information	The teacher makes available educational materials in UNISTUDIUM , useful for a better understanding of the course, in order to help and to let the students pass easily the exam. ¿¿Furthermore all the previous written tests can be found in UNISTUDIUM, where you can also find the results of the written test and the date of the relative oral exam.
Learning verification modality	The exam is a written exam, by using LibreEol, containing both open answers and multiple choice tests on topics which cover all the programme composed by Mathematical Analysis and Mathematical Statistics. Exercises assigned are modelled on those solved during the lessons. The written exam is designed to assess the ability of solving concrete or teoric problems. The written test is positively concluded if the grade is greater or equal to 18. If possible, the written test can be replaced by progress assessments.¿¿ Furthermore, only under the request of the student, an oral exam can be performed after having concluded positively the written test. In this case the oral exam consists of a discussion on two or three topics on all the programme, mainly starting from exercises, and takes about 20 minutes. The oral test is designed to assess the level of knowledge attained by the student on the theoretical contents and on and counterexamples). Finally, the oral examination allows the teacher to verify the performance of the student and his/her ability to organize the presentation in autonomy.¿¿During the written test the student is allowed to use his/her notes and books. To solve the statistic exercises a calculator is useful. It not possible to use the cellular phone calculator.
Extended program	Quadratic Equations and inequalities. Functions of a single variable. Examples of elementary functions and biological models: exponentials and logarithm.¿Limits, continuous functions, differentiability, increasing and decreasing functions, concave and convex functions. Graphs of functions. Riemann integral: definition and properties. The fundamental theorem of integral calculus. Change of variable in an integral. ¿¿Introduction to Statistic, describing data sets, using statistics to summarize data sets (mean value, median, mode..). variables and normal random variable. Linear regression.

PHYSICS LABORATORY

Code	40998501
CFU	1
Teacher	Igor Neri
Teachers	Igor Neri
Hours	12 ore - Igor Neri
Learning activities	Altro
Area	Altre conoscenze utili per l'inserimento nel mondo del lavoro
Academic discipline	NN
Type of study-unit	Obbligatorio (Required)
Language of instruction	Italian
Contents	Introduction to the experimental method. Introduction to error analysis in the measurement of physical quantities. Simple basic physics experiments with particular reference to the topics covered in the PRINCIPLES OF PHYSICS module.
Reference texts	Walker, Fondamenti di Fisica (Pearson)
Educational objectives	Provide the student with basic information on the main topics of classical physics with particular reference to the 'physical sense'. Students must acquire the ability to reason logically and critically analyze what they will encounter in subsequent courses. They must be able to ask the right questions to face unforeseen situations and avoid gross errors from a logical-practical point of view. Ability to solve basic physics exercises and problems. More specifically, and with reference to the Dublin Descriptors for learning objectives (D1 knowledge and understanding; D2 applying knowledge and understanding; D3 making judgments; D4 communication skills; D5 learning skills), the student will acquire the basic notions of classical physics (D1) to be able to correctly interpret the theoretical principles on which some analysis equipment, diagnostic tools, and biological phenomena are based (D2). During the course, analytical and problem-solving skills will be developed by proposing numerical exercises that allow the application of acquired theoretical notions and through the collaborative discussion of some physiological phenomena from a physical point of view (D3 and D4). The skills acquired (both in terms of knowledge and methodological approach) will be fundamental in the autonomous study of related disciplines and, more generally, in continuous professional development (D5).
Prerequisites	Basic notions of algebra and geometry, manipulation of numerical and literal expressions, solution of first and second degree equations, notions of trigonometry
Teaching methods	Frontal lectures. Laboratory experiments.
Other information	For information on support services for students with disabilities and/or learning disabilities (DSA), visit the page http://www.unipg.it/disabilita-e-dsa
Learning verification modality	The assessment method consists of reporting on laboratory activities and an oral discussion aimed at verifying the degree of knowledge and mastery of the concepts covered.
Extended program	The scientific method. Measurement in physics. The International System (SI) of units of measurement. Multiples and submultiples. Dimensional analysis. Measurement. Methods of measurement: direct measurements and indirect measurements. Measurement and the inevitability of errors. How to represent errors: notation; significant figures; relative error. Precision and accuracy. Types of experimental errors: instrumental resolution errors, random errors, systematic errors. Estimation of instrumental resolution errors. Estimation of errors in repeatable measurements. Statistical analysis of random errors: mean value as the best estimate of the 'true value' of a measured quantity; standard deviation from the mean as the best estimate of the uncertainty of a single measurement (with a 68% confidence level); standard error of the mean as the best estimate of the uncertainty of the mean value (with a 68% confidence level). Gaussian distribution around the mean value of repeated measurements in the case of random and independent errors. How to use errors: assess the consistency or discrepancy of a measured value of a physical quantity with an accepted value or with the result of other measurements; estimate uncertainty in indirect measurements. Error propagation: sums and differences; products and quotients; product with a known quantity; exponentiation. Estimation of the upper limit for propagated error. Best estimate of propagated error in the case of measurements affected by independent and random errors. Simple experiments in basic physics with particular reference to the topics covered in the PRINCIPLES OF PHYSICS module.
Obiettivi Agenda 2030 per lo sviluppo sostenibile

MATHEMATICS LABORATORY FOR DATA MANAGEMENT

Code	A004754
CFU	1
Teacher	Roberta Filippucci
Teachers	Roberta Filippucci
Hours	12 ore - Roberta Filippucci
Learning activities	Altro
Area	Altre conoscenze utili per l'inserimento nel mondo del lavoro
Academic discipline	NN
Type of study-unit	Obbligatorio (Required)
Language of instruction	Italian
Contents	Linear models: linear regression process.
Reference texts	M. Bramanti, F. Confortola, S. Salsa: Matematica per le scienze. Con fondamenti di probabilità e statistica, Ed. Zanichelli, Bologna, 2024
Educational objectives	The student should acquire a basic knowledge in costructing a linear model. Main knowledge acquired will be:¿- To know hoew to build linear models starting form a collection of data and how to apply them to the natural sciences¿¿- To know several tools to develop elementary models - To read and understand simple models in order to made predictions¿- To work in teams, but also in autonomy.¿ The skills listed above are set out in the framework of professions related to experts in biotechnological processes operating in industrial/social contexts characterized by the production/use of several categories of products in the field of industrial biotechnology.
Prerequisites	Basic Word and Excel Skills
Teaching methods	The course is composed by 7 hours of computer laboratory, with the use of Word, Excel and Geogebra.
Other information	The teacher makes available educational materials in UNISTUDIUM , useful for a better understanding of the laboratory course.
Learning verification modality	Oral discussion of the project made during the laboratory experiences supported by computers.
Extended program	How to construct a model. Data collection. The linear regression model. Pearson's coefficient. Graphical representations of data and of the regression line. Prediction.