15968 - Physics and Mathematics

Learning outcomes

MATHEMATICS (Teaching Unit 1, Prof. Caprara)

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, Dott. Zaniboni)

The course introduces some basic 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, Prof. Caprara)

Elements of set theory (4 h)

Definition of set. Operations between sets. Set of real numbers

Functions (4 h)

Concept of relation. Functions of a variable. Continuous functions.

Theory of limits (4 h)

Limits for functions.

Derivatives (6 )

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

Functions study (12 h)

Asymptotes, maximum and minimum points, inflection points.

 

PHYSICS (Teaching Unit 2, Dott. Zaniboni)

Measurement

Scientific method, measurement of a physical quantity, systems of units, dimensions and units, conversions, significant figures, rounding and truncation, scientific and normalized notation, order of magnitude, measuring instruments, 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, fundamental forces, Third Newton’s law.

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.

Readings/Bibliography

MATHEMATICS (Teaching Unit 1, Prof. Caprara)

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.

 

PHYSICS (Teaching Unit 2, Dott. Zaniboni)

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

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

The slides shown during class will be available on the online institutional platform for teaching support (Insegnamenti OnLine) in few days.

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.

Assessment methods

MATHEMATICS (Teaching Unit 1, Prof. Caprara)

The exam is done through a final exam with a written test and eventually an oral examination, both with grades expressed in thirtieths.

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

The written exam include a function study.

The exercises for which only the result is provided without indicating the methodology adopted and the intermediate steps of the calculation will be considered unresolved (grade 0).

The written test is passed with a grade between 18 and 30.

The student who fails the written examination must repeat the examination at the next session.

The student who passes the written test can choose to:

- Refuse the grade and take the examination at the next session;

- Accept the grade without the oral examination and in this case the test is passed with a grade corresponding to that of the only written test;

- Try to improve the grade of the written test with an oral examination, in the awareness that, according to the oral examination, the grade of the written test may increase or decrease.

 

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 passes 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 no expiration date.

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

 

FINAL EVALUATION

The aggregated evaluation of the course will be given by the average of the two tests, rounded up.

It is required to pass both exams, which means that both grades must be at least 18.

NB: the grade registration will be accomplished only under the explicit acceptance of the final grade by the student to the teacher responsible of 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.

Teaching tools

PC and video projector.

Office hours

See the website of Filippo Zaniboni

See the website of Claudio Caprara