15968 - Physics and Mathematics

Learning outcomes

Physics. 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.
Mathematics. 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.

 

Course contents

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.
Mathematics.
Elements of set theory.
Definition of set. Operations between sets. Set of real numbers
Functions
Concept of relation. Functions of a variable. Continuous functions.
Theory of limits.
Limits for functions.
Derivatives.
Definition of incremental ratio. Derivative of a function. Properties of derivatives. Derivative rules.
Integrals.
Infinitesimal and differential. Indefinite integral. Integral properties. Integration by substitution. Integration for parts. Defined integral. Improper integral.
Introduction to functions study.
Asymptotes, maximum and minimum points, inflection points.

Readings/Bibliography

Physics:
Desmond M. Burns, Simon G.G. MacDonald - Ed. Zanichelli (Bologna)
Principi di fisica - Ezio Ragozzino - Ed. EdiSES (Napoli)
Electronic exercises book available from the web page: http://www.bo.infn.it/ctf/eser
Mathematics: 
The files with the lesson teaching material will be stored in AMSCampus.

Teaching methods

Physics. Lectures and samples of problems using the electronic exercise book.
Mathematics. The course will cover the topics of the program through classroom teaching, both for lectures and for exercises.

Assessment methods

Physics:
1 hour and half written exam of 6 exercises, regarding the course contents. The exam is passed whether 3 exercises are correctly carried out, also taking into account the correct exercise pieces.
Mathematics:
The exam is done through a final exam with a written test and eventually an oral examination, both with grades expressed in thirtieths.
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.

The final evaluation, which requires the 2 exams both passed, is their average.

Teaching tools

Overhead projector, PC, projector. Tutors will carry out preliminary lessons to allow all students to acquire the same basic knowledge at the beginning of the courses.
Physics: for the contents see the web page http://www.bo.infn.it/ctf/eser 
Mathematics: PC and video projector.

Links to further information

http://ishtar.unibo.it/did/corsi.html

Office hours

See the website of Tiziano Rovelli

See the website of Claudio Caprara