# 15968 - Physics and Mathematics

### SDGs

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

## Learning outcomes

MATHEMATICS (Teaching Unit 1)

At the end of the course, the student knows the technical mathematical tools and their use for the quantitative study of phenomena. The student is then able to set up and solve problems and to assimilate new concepts from the experience and previous knowledge.

PHYSICS (Teaching Unit 2)

The course introduces some base elements of classical mechanics, fluid mechanics, and thermodynamics, with the relative methodologies and applications in the fields of physiology, biology, and chemistry.

## Course contents

MATHEMATICS (Teaching unit 1)

Elements of set theory

Definition of set. Operations between sets. Set of natural, integer, rational, irrational, and real numbers.

Functions

Concept of relation. Properties of relations. Definition and properties of functions. Functions of a variable. Continuous functions. Composite functions. Domain of a function.

Theory of limits

Neighborhood of a point, accumulation points. Limits for functions. Properties of limits. Examples of limit calculation.

Derivatives

Definition of incremental ratio. Derivative of a function. Properties of derivatives. Second derivative. Derivative rules.

Functions study

Exponential function, logarithmic function, power function. Intersections with the axes, asymptotes, maximum and minimum points, inflection points.

Elements of statistics and data analysis

Aritmethic and geometric mean, median, fashion. Root mean square, variance, standard deviation. Covariance, correlation, linear regression, least square method.

PHYSICS (Teaching Unit 2, Dott. Zaniboni)

Measurement

Measurement of a physical quantity, dimensions and units, conversions, significant figures, rounding and truncation, scientific and normalized notation, precision and accuracy, experimental errors, law of averages, mean value.

Vectors

Vectors and scalars, notation and representation of vectors, vectorial algebra, vector components, dot and cross product.

Kinematics

Motion and reference system, rectilinear motion, uniform motion, average and instantaneous velocity, average and instantaneous acceleration, uniformly accelerated motion, circular motion, harmonic motion.

Dynamics

Forces, First Newton’s law, inertial systems, Second Newton’s law, universal gravity law, gravity acceleration, mass and weight, elastic force, normal force, friction force, centripetal force, simple pendulum, overview on wave phenomena.

Energy and Work

Work of a constant force, work of gravity and elastic force, Kinetic energy, efficiency, power, conservative forces, potential energy, conservation law of mechanic energy, gravitational and elastic potential energy, harmonic motion energy, dissipative forces, moment of a force, static equilibrium.

Fluid Mechanics

Density, pressure, Stevin’s law, fluids properties, atmospheric pressure, Pascal’s law, buoyancy, fluid dynamics, ideal fluids, continuity equation, Bernoulli’s theorem, Torricelli’s law, real fluids, Poiseuille’s law, turbulent flow, Reynolds number, Stokes’ law, sedimentation, centrifugation, superficial tension, capillarity.

Thermodynamics

Temperature and its scales, kinetic theory of gas, laws of gases, Avogadro’s number and mole, Dalton’s law, humidity, heat and work, thermal capacity and specific heat, the first principle of thermodynamics, change of phase, latent heat, propagation of heat.

The slides shown during class, both for Mathematics and Physics, will be available on the online institutional platform for teaching support (https://virtuale.unibo.it/) in few days.

These will contain, in a schematic way, all the teaching material necessary to perform the exam. The students willing to integrate their knowledge, or deepen some specific topics, can refer to the following volumes.

When available, the students can refer to the volumes of Mathematics and Physics used at the high school. In this case, they should be checked by the teacher in order to verify the coverage of the course topics.

MATHEMATICS (Teaching unit 1)

Claudio Caprara, “Mathematics for Agricultural and Life Sciences: Principles of Calculus with Solved Problems”, Nova Science Publishers, Inc., New York, USA. ISBN: 978-1-53618-027-5.

Carlo Sbordone, Francesco Sbordone, "Matematica per le Scienze della Vita", Ed. EdiSES s.r.l. (Napoli). ISBN: 978-88-7959-829-3.

The online resource, available for all students of University of Bologna: https://almaorienta.unibo.it/it/almamathematica

PHYSICS (Teaching Unit 2)

Ezio Ragozzino, Principi di fisica, Ed. EdiSES (Napoli)

Alessandro Lascialfari, Ferdinando Borsa, Anna Maria Gueli, Principi di Fisica per indirizzo biomedico e farmaceutico, Ed. EdiSES (Napoli).

Electronic exercises book available from the web page: http://ishtar.df.unibo.it/Uni/bo/farmacia/all/navarria/stuff/eser/eser.html

## Teaching methods

The course will cover the topics of the program through classroom teaching, both for lectures and for exercises.

For the latter, it is possible to contact the course tutor to organize additional classes for exercises, revision and exam simulations.

## Assessment methods

To pass the exam and achieve the final evaluation (that is one for the two teaching units), the two tests (Mathematics and Physics) should be passed, separately.

The single tests will be passed with a minimum evaluation of 18/30.

The aggregated evaluation of the course will be given by the average of the two tests, rounded up. The achievement of 30/30 in both tests provides a final evaluation of 30 and laudation.

The grade registration will be accomplished only under the explicit acceptance of the final grade by the student to the teacher responsible for the course. This can be fulfilled by e-mail as well (sent to filippo.zaniboni@unibo.it), by reporting in the text the date and grades of the two exams, the final evaluation, and an explicit acceptance of the latter.

In lack of this consent, the final evaluation won’t be recorded.

In the following, the details on the single tests are reported.

MATHEMATICS (Teaching unit 1)

The exam is done through a written test, with grades expressed in thirtieths.

The test consists of a set of closed-ended questions, concerning the topics listed in the Course Contents section, that should be completed in 90 minutes unless specific derogation which has to be agreed upon before the exam.

Some questions, with variable evaluation, will be asked for each topic, with simple calculation procedures.

For the written test no notebooks, tablets, smartphones, or pocket calculators are allowed.

The written test is passed with a grade higher or equal to 18. It has not expiration date.

The student who passes the written test can choose to refuse the grade and take the examination at the next session.

Should a new test be delivered, the previous evaluation will be invalidated.

PHYSICS (Teaching Unit 2, Dott. Zaniboni)

2 hours written test made of 6 exercises concerning the course contents.

For the test, the use of books, personal notes, class slides, and a calculator is admitted. It is strictly forbidden the use of communication devices (smartphone, tablet, notebook).

The test will be passed should the evaluation reach at least 18. Three correct exercises (numerical result included) will be evaluated 6 points each, and are then sufficient to pass the written test; further correct exercises will be scored 4 points each.

Correct exercise pieces are accounted for as well.

The grade has not expiration date.

The test can be repeated, but the delivery of a new trial will invalidate the previous grade.

## Teaching tools

PC and video projector.

Spreadsheet software (Microsoft Excel or open-source equivalent) for examples of data analysis and visualization.

## Office hours

See the website of Filippo Zaniboni