15968 - Physics and Mathematics

Learning outcomes

The course introduces some base elements of mathematics and general physics, with the relative methodologies and applications in the fields of physiology, biology and chemistry.

Course contents

Mathematics: Real numbers. Algebraic calculus. Elements of plane analytical geometry. Functions. Graphical representation and characteristics of elementary functions: linear, polynomials, exponential, logaritmic, trigonometrical, with absolute value. Limits: concept and definition of limit, algebra of limits, fundamental results; continuity of a function. Differential calculus: derivative, geometrical meaning of derivative. Fundamental derivatives. De l'Hopital's rule. Increasing and decreasing functions, maxima and minima, convexity and concavity, inflections. Asimptotes. Study of a function. Integral calculus: primitive functions, indefinite integral. Definite integral. Fundamental theorem of integral calculus.Integration methods: integration by parts and by substitution. Areas and volumes. Combinatorial calculus. Physics: Measurement of a physical quantity. Unit of measurements. Systems of units. Experimental errors. Significant figures. Vectors and vectorial algebra. The forces. Newton's laws. The moment of a force. Static equilibrium. The levers. Friction. Rectilinear and circular motion. Uniform motion and uniformly accelerated motion. Energy. Power. Kinetic and potential energy. Conservation of energy. Elasticity of materials and Hooke's law. Density. Pressure. Hydrostatic pressure. Surface tension. Capillary phenomena. Continuity equation. Bernoulli's theorem. Poiseuille's law. Reynold's number. Sedimentation and centrifugation. Diffusion phenomena. Thermal equilibrium. Temperature. Law of gases. Heat. Specific heats. The first principle of thermodynamics. Real gases. Change of phase. Latent heats. Propagation of heat. The electric charge. Coulomb's law. The electric field. The electrical potential. The electric current. The electrical resistance. The magnetic field. The Lorentz force. Sources of the magnetic field. Periodic and harmonic motions. The simple pendulum. The waves motion. Speed of the waves. Superimposition and polarization of the waves. Interference and diffraction of the waves. Reflection and refraction phenomena. Mirrors. Convergent and divergent lenses. Lenses' aberrations. The microscope.

Readings/Bibliography

Mathematics: Vinicio Villani – MATEMATICA PER DISCIPLINE BIO-MEDICHE quarta edizioneMcGraw-Hill – Milano. Physics: Copies of the lectures
Principi di fisica - Ezio Ragozzino - Ed. EdiSES (Napoli)
Fisica - Desmond M. Burns, Simon G.G. MacDonald - Ed. Zanichelli (Bologna)
Electronic exercise book available from the web page: http://www.bo.infn.it/ctf/eser

Teaching methods

Lectures and samples of problems using (Physics) the electronic exercise book

Assessment methods

Mathematics: Written and oral test. Physics: Written test, complemented with an optional oral test.

Teaching tools

Mathematics and Physics: Overhead projector,PCprojector.
Physics: For the contents, seethe web page
http://www.bo.infn.it/ctf/eser

Office hours

See the website of Francesco Luigi Navarria

See the website of Milva Arcangeli

See the website of Niccolò Moggi