The course aims, through the study of elements of basic mathematical analysis and classical physics, to introduce the basic logical and conceptual methodologies to lead learners to a correct approach to the scientific problems they may encounter in their studies and professional activity. The objectives concern the correct use of abstraction procedures, formalisation of the quantitative language and understanding of the experimental method.

Elements of Mathematics

• Concepts of set theory. Numerical sets. Limited sets: major and minor, upper and lower extremes, maxima and minima. Intervals and surrounds. (4 hours)
• Functions: definition and properties. Real functions of real variables, increasing and decreasing, absolute and relative maxima and minima, even and odd functions. (2 hours)
• Limits. Uniqueness of limit and permanence of sign theorem. Operations between limits. Uncertain forms and remarkable limits (6 hours)
• Continuity of a function. Weierstrass theorem and the theorem of zeros. (2 hours)
• Derivatives, derivability and the derivative function. Derivation rules. Remarkable derivatives. Fermat's theorem on the maxima and minima of a function. Rolle's theorem and Lagrange's theorem. Monotonous functions and sign of the derivative. Definition of concavity and second derivative. Study of the probable graph of a function (6 hours)
• Integrability according to Riemann. Geometric meaning of integral as the area of the epigraph. Properties of integrals. The mean value theorem. (4 hrs.)
• Integral function and the primitive function. The fundamental theorem of calculus. Definition of indefinite integral. Torricelli's theorem. Remarkable primitives. Derivation by substitution. Generalised immediate integrals. Rule of derivation by parts. (4 hours)

Physics

• The scientific method.  Physical quantities and units of measurement. Scalars and vectors. Measurement and uncertainties. (2 hours)
• Kinematics. Quantities of kinematics. Kinematics of unidimensional motion. Motions in bidimensional plane. (4 hours)
• The laws of dynamics and the fundamental forces. The weight force and the motions in free fall and on a inclined plane. Constraining forces and friction. The elastic force and the harmonic motion. (6 hours)
• Work and kinetic energy. Conservative forces and potential energy. The energy balance and the conservation of energy. (6 hours)
• Momentum. Systems of bodies and the centre of mass. The laws of dynamics for systems of bodies. Mechanically isolated systems and conservation of momentum. Impacts in one and two dimensions. The rotation of rigid bodies. The angular momentum. The torque (6 hours)
• Fluid dynamics of incompressible fluids. Pascal's principle. Stevino's law and the hydrostatic pressure. Torricelli's experiment to measure the atmospheric pressure. The Archimedes' principle. (4 hours)
• Ideal fluids in laminar motion. The law of continuity. Bernulli's law. Real fluid dynamics. Viscosity and resistance. Hagen Poiseuille's law.  (4 hours)

• Kinetic theory and thermodynamics of ideal gases. Microscopic and macroscopic quantities.Energy equipartition theorem. Definition of temperature; Celsius and Kelvin thermometric scales. Variables of state; equation of state of perfect gases. Work, heat and internal energy.The I principle of thermodynamics; thermodynamic transformations.. The second principle of thermodynamics. Thermal engines. Clausius and Kelvin's enunciations. The variation of entropy and the II principle. Statistical interpretation of entropy. Spontaneous transformations, enthalpy and Gibbs' free energy. (12 hours)

• The electrostatic force and Coulomb's law. The electric field. Field lines (sources and sinks). The electric dipole. The flow of the electric field and The Gauss's law. Field effects on a charge, the motion of a charge in an electric field. Effect of the field on a dipole (6 hrs)
• The potential difference. Capacitors and electrical capacitance. Conductors and insulators. The intensity of current. Ohmic conductors and Ohm's law, electrical resistance. Electric current density. Microscopic Ohm's law. Electrical circuits, the voltage generator. The power dissipated on a resistor. The elements of the circuit: nodes, branches and meshes. Kirchhoff's laws. RC circuits in transient regime. AC circuits. The average power. (8 hours)
• The Lorentz force and the definition of magnetic field. The sources of the magnetic field. Biot-Savart's law. Ampere's law. Effects of the magnetic field on currents. Ampere's definition. Magnetic moment and torque. Magnets. Ferromagnetic materials. (6 hours)
• The Faraday-Lentz law of induction. The circuitry of the electric field. The circuitry of the magnetic field and the displacement current. Maxwell's laws.  Electromagnetic waves and their propagation. The speed of electromagnetic waves. The electromagnetic spectrum (4 hours)

None

Knowledge and ability to understand: students should know the basics of infinitesimal analysis, in particular the concept of function and the operations of limit, derivative and definite and indefinite integral. Furthermore, they must know the main laws of physics, in particular in the fields of mechanics of the material point, of the rigid body and of fluids. They should have learned the basics of electrostatics, magnetism and electrodynamics. They will know the basics of modern physics for a first understanding of atomic and nucleus physics.
Applied knowledge and understanding: the students should be able to study the behaviour of a function, identifying trends and characteristics. They should be able to apply the laws of physics to real problems, and solve simple problems both qualitatively and quantitatively.
Autonomy of judgement: the students should be able to autonomously assess the plausibility of the result of a calculation, both on the basis of the correctness of the units of measurement and through analogical and common-sense scientific considerations.
Communication skills: the students shall acquire correct scientific language, including the appropriate use of units of measurement.
Ability to learn: the students will be able to investigate specific concepts, not presented during the course, in non-specialist scientific texts.

The teaching material prepared by the lecturer in addition to recommended textbooks (such as for instance slides, lecture notes, exercises, bibliography) and communications from the lecturer specific to the course can be found inside the Moodle platform › blended.uniurb.it

Teaching

Lectures with tutorials.

Weekly reception by appointment.

Attendance

The student must be able to apply basic mathematical concepts studied in high school, such as algebra, geometry and trigonometry.

Course books

Mathematics: any text on Institutions of Mathematics

As an example: 

Mat&matica, M.C. Patria, G. Zanghirati, Pitagora

Physics: a text of your choice from the following:

Fondamenti di fisica, Vol 1 (Meccanica, Termodinamica, Onde, Elettromagnetismo), P.R. Kesten, D.L.Tauck, Zanichelli

Fondamenti di Fisica, Meccanica Termologia Elettrologia Magnetismo Ottica, D. Halliday, R. Resnick, J. Walker, CEA

Assessment

Written and oral tests.

The written test consists of solving physics and mathematics problems. The test is considered passed if a score of 10/20 for Physics and 5/10 for Mathematics is achieved or exceeded.

The oral test consists of a discussion of the written test and the presentation of topics relating to the course.

Disability and Specific Learning Disorders (SLD)

Students who have registered their disability certification or SLD certification with the Inclusion and Right to Study Office can request to use conceptual maps (for keywords) during exams.

To this end, it is necessary to send the maps, two weeks before the exam date, to the course instructor, who will verify their compliance with the university guidelines and may request modifications.

Teaching

It is advisable to contact the lecturer. The teaching materials and assessment methods are the same for both attending and non-attending students.

Attendance

The same for both attending and non-attending students.

Course books

The same for both attending and non-attending students.

Assessment

The same for both attending and non-attending students.

Disability and Specific Learning Disorders (SLD)

Students who have registered their disability certification or SLD certification with the Inclusion and Right to Study Office can request to use conceptual maps (for keywords) during exams.

To this end, it is necessary to send the maps, two weeks before the exam date, to the course instructor, who will verify their compliance with the university guidelines and may request modifications.