C8898 - MATEMATICA E FISICA CON ELEMENTI DI INFORMATICA E STATISTICA

Learning outcomes

At the end of the course, the student acquires: the basic skills of the main tools for mathematical analysis (limits, derivatives) and the study of functions; the basic skills of classical physics (measurement and uncertainty, kinematics, dynamics), fluid mechanics with applications in the physiological and biological fields; basic elements of computer science: use of operating systems, main spreadsheets applications; basic knowledge of the main techniques of statistical analysis: statistical indices, dispersion indices.

Course contents

MATHEMATICS

1. Functions. Definition and properties of functions, domain and codomain of a function, composite function, domain of elementary and composite functions.

2. Limits. Around a point, accumulation point, limits for functions, continuous functions, infinite limit, right limit and left limit, properties of limits, limits of elementary functions, notable limits.

3. Derivatives. Definition of incremental ratio, derivative of a function, properties of derivatives, derivative of elementary functions, derivatives of composite and inverse functions, second derivative, increasing and decreasing functions, monotony, concavity, stationary points (maximum, minimum, inflected), De L'Hopital's theorem.

4. Study of Function. Domain, intersections with axes, vertical, horizontal and oblique asymptotes, maximum and minimum points, inflection points, concavities.

PHYSICS

1. Measurement and Errors. Systems of units of measurement, dimensions and units of measurement, conversions between units of measurement, significant digits, truncation and rounding, scientific and normalized notation, precision and accuracy, law of large numbers, average value.

2. Carriers. Vectors and scalars, notation and representation of vectors, vector algebra, components of a vector, scalar and vector product.

3. Kinematics. Rectilinear motion, uniform rectilinear motion, average and instantaneous velocity, average and instantaneous acceleration, uniformly accelerated rectilinear motion, circular motion.

4. Dynamics. The Forces, Newton's First Law, Newton's Second Law, the Law of Universal Gravitation, Acceleration of Gravity, Mass and Weight, Elastic Force, the Simple Pendulum, Centripetal Force, Fundamental Forces.

5. Energy and Work. Work of a constant force, work of the weight force, work of the elastic force, Kinetic energy and theorem of living forces, power, conservative forces, potential energy, Law of conservation of mechanical energy, gravitational and elastic potential energy.

6. Fluid mechanics. Density, pressure, Stevin's law, Pascal's law, atmospheric pressure, Archimedes' thrust, fluid dynamics, ideal fluids, continuity equation, Bernoulli's theorem, real fluids, laminar flow, Poiseuille's law, turbulent flow, Reynolds' number.

ELEMENTS OF COMPUTER SCIENCE

Introduction to Excel: structure of spreadsheets, relative and absolute references, main functions, filters, examples of charts.

ELEMENTS OF STATISTICS

Statistical indices (mean, mode, median), dispersion indices (standard deviation, variance, standard deviation).

Readings/Bibliography

The slides shown in class will be made available in advance by the teacher on the institutional teaching support platform (https://virtuale.unibo.it/).

They will contain, in a schematic way, all the material necessary for the performance of the exams. Students who wish to integrate the material made available, or deepen some topic considered of particular interest, can rely on the volumes indicated below.

MATHEMATICS

Carlo Sbordone, Francesco Sbordone, “Matematica per le Scienze della Vita”. EdiSES s.r.l. – Napoli, ISBN: 978-88-7959-829-3.

Vinicio Villani, Graziano Gentili, “Matematica”. McGraw-Hill Education (Italy) s.r.l. – Milano, ISBN: 978-88-3865-493-0.

A series of exercises (and related solutions) will be made available on the Virtuale platform, divided by topic.

Also of note is the online resource, available to all students enrolled at the University of Bologna https://almaorienta.unibo.it/it/almamathematica

PHYSICS

Ezio Ragozzino, “Principi di fisica”. EdiSES s.r.l. – Napoli, ISBN: 978-88-7959-378-6.

Alessandro Lascialfari, Ferdinando Borsa, Anna Maria Gueli, “Principi di Fisica per indirizzo biomedico e farmaceutico”. EdiSES Università s.r.l – Napoli, ISBN: 978-88-3623-020-4.

It is also possible to consult high school Mathematics and Physics textbooks, if they are available: in this case the student can show it to the teacher to verify the adequate coverage of the teaching program.

As for Physics, an online workbook is available at the web address: http://ishtar.unibo.it/Uni/bo/farmacia/all/navarria/stuff/eser/eser.html

Teaching methods

The course will deal with the topics of the program through lectures in the classroom, with projection and commentary of PowerPoint presentations related to the various topics listed. At the end of each lesson, the recording will be made available on the Virtuale platform.

For the exercises, support is also provided through the course tutors, who can be contacted to carry out (optional) lessons, to be agreed outside the official teaching hours, in which to carry out exercises, revision and possibly simulations of exam tests.

The topics covered in the statistics and computer science lessons will be the subject of an exercitation that will be carried out in the computer rooms, of which an outline will be provided with the indications of the activity to be carried out, and whose results must be reported in a short report to be sent to the teacher before the final exam. Attendance at this exercitation is mandatory, except for working students.

Assessment methods

To pass the exam and achieve the final grade (the same for the different subjects covered in the course), two conditions must be met, which will be detailed below:

- Pass the Mathematics and Physics written test

- Obtain the approval by the teacher of the report of the activity carried out in the computer room

The registration of the final evaluation will take place only after an explicit message of acceptance by the student. In the absence of this communication, the grade (which has no time limit) will remain valid but will not be recorded. The test can be retried in subsequent sessions, but the delivery of a new paper automatically invalidates the grade obtained previously. Failure to pass the test does not preclude further attempts in subsequent sessions.

For students with SLD or temporary or permanent disabilities: it is recommended to contact the competent University Office (https://site.unibo.it/studenti-con-disabilita-e-dsa/en) in time. It will be the responsibility of proposing any adaptations to the students concerned, which must in any case be submitted, at least 15 days in advance, to the approval of the teacher, who will evaluate the opportunity also in relation to the educational objectives of the course.

WRITTEN TEST OF MATHEMATICS AND PHYSICS

The test will consist of 10 exercises in total. Of these, 6 will concern Mathematics: an exercise related to the domain of a function (worth 3 points); two exercises on limits (one of 3 and one of 4 points); two on derivatives (one of 3 and one of 4 points), for a total of 20 points; a simple function study (3 points). The remaining 4 exercises, each worth 3 points, will concern Physics, one for each topic: kinematics, dynamics, energy and work, fluid mechanics, for a total of 12 points.

The available time for the exam is two hours, except for specific exceptions (e.g. for students with SLD) which must be requested before the test.

The test will be considered passed if at least 10/20 points in Mathematics and 6/12 points in Physics are obtained. Partial exercises will also be considered valid. If one of these two thresholds is not exceeded, the entire test must be repeated. If a score higher than 30 is obtained, a 30 cum laude evaluation will be assigned.

For the test, the use of books, notes, slides shown in class is allowed. The use of the calculator is allowed, but it must not include CAS (Computer Algebra System) functions, allowing the resolution of limits and derivatives. This device will be checked on the day of the exam. The use of external communication equipment (smartphones, tablets, notebooks) is not allowed in any way.

The exam will be carried out in person except for the health/flooding situation of the country, areas at risk as per the new legislation and/or fragility of the student (assessment by the SLD service). The cases will be evaluated individually and, if they fall within the requirements, they can be carried out via the TEAMS platform.

REPORT ON THE ACTIVITY CARRIED OUT IN THE COMPUTER ROOM

A short report, of a few pages, relating to the activity and results obtained in the computer room, concerning the topics of computer science and statistics, is required. This report must be sent to the teacher and approved by him.

Students who do not attend the laboratory will still have to carry out the planned activity following the instructions in the appropriate track, which will be uploaded on the Virtuale platform, and draw up the report.

Without the approval of the report by the teacher, the exam will not be considered passed and the recording of the final evaluation will not be carried out. This approval has no time limit and does not have to be obtained again if the written test of Mathematics and Physics is not passed.

The use of AI is prohibited. Any use constitutes a violation of academic integrity.

Teaching tools

PC and Video projection system.

Computer room with PC for the use of Excel.

Office hours

See the website of Filippo Zaniboni