MATHEMATICS AND COMPUTER SCIENCE + PHYSICS
Academic year and teacher
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- Versione italiana
- Academic year
- 2016/2017
- Teacher
- ALBERTO CALABRI
- Credits
- 12
- Didactic period
- Secondo Semestre
Training objectives
- MATHEMATICS AND COMPUTER SCIENCE
Knowing.
The student will learn basic knowledges with respect to:
- the main functions and their features;
- the concepts of limit and continuity;
- the derivative of relevant functions and its geometric significance;
- calculation and geometric interpretation of the integral of relevant functions and their simple compositions;
- probabilistic interpretation of events, probability calculation in discrete cases;
- calculation of linear regression, Gauss function, and related properties.
Skills.
The student will acquire the ability to:
- study the graphic of a function;
- apply the concepts of limit, derivative, integral;
- provide the probabilistic interpretation of events;
- calculate probability in discrete cases;
- calculate linear regressions;
- create a Gauss function.
PHYSICS
Knowing.
The student will learn basic knowledges with respect to:
- dynamic and thermodynamic;
- waves;
- Ohm’s law;
- lens
Skills.
The student will acquire the ability to:
- apply the dynamical principles to simple systems;
- apply thermodynamical principles to simple transformations;
- discriminate between transversal and longitudinal waves;
- apply the Ohm’s law to simple circuits;
- discriminate between convergent and divergent lens. Prerequisites
- Symbolic computations, math symbols, set operations, sets of numbers and their properties, equations and inequalities of the first and the second degree, Cartesian plane, systems of coordinates, equations of lines in the plane.
Course programme
- Physics module syllabus:
Introduction to the course, definition of units, scalar and vector quantities, coordinate systems (2 hours).
Mechanics: Kinematics and motion equations, dynamics and Newton's laws, force and mass, momentum conservation law, the force of universal gravitation , frictional forces, work and energy, potential energy and conservation of mechanical energy, uniform circular motion (10 hours)
Exercises on the topics of Mechanics (2 hours)
The oscillatory motion: restoring forces and Hooke's law, equation of harmonic motion (2 hours)
The fluids: pressure and density, Pascal's principle and buoyancy, fluid dynamics, continuity equation, Bernoulli's equation, viscosity and surface tension (6 hours)
Mechanical waves: explanation of wave phenomena, interference phenomena, equation of a wave, elements of acoustics, Doppler effect (4 hours)
Thermology and Thermodynamics: temperature and heat, ideal gases, equilibrium of a thermodynamic system and state functions, thermodynamic processes, the concept of entropy, reversible and irreversible processes, cyclic processes and Carnot engine (6 hours)
Exercises on the topics of Thermodynamics (2 hours)
Electromagnetism: electric charge, Coulomb force, electric field and electric potential, electric capacity and capacitors, electric current and Ohm's law, magnetic phenomena and definition of magnetic field, Lorentz force, field generated by an electrical wire, Ampere's Law, Faraday's law (6 hours)
Exercises on the topics of Electromagnetism (2 hours)
Introduction to electromagnetic waves, the light and the electromagnetic spectrum, geometrical optics, reflection and refraction, the lens, the human eye. (2 hours)
Basics of radiation physics: ionizing radiation, absorbed dose, radiation-matter interaction, the radioactive decay (2 hours)
Exercises on the whole programme of the course and conduct of examinations (2 hours)
Mathematics and Computer Science syllabus:
Recalls on numbers and units of measurement, operations, scientific notation, approximations, equalities and inequalities, error propagation, percentages, intuitive set theory, elementary logic (6 hours).
Discrete probability: events, probability distributions, relative frequencies, axioms of probability, independent events, the Hardy-Weinberg law, conditional probability, diagnostic tests (8 hours).
Representations of data: functions, Cartesian coordinates, equations and inequalities, Cartesian diagrams, histograms, mean, median and mode, variance (6 hours).
Algebraic functions: linear functions, linear programming, quadratic functions, the least squares method, regression line, polynomial functions, power functions, rational functions, limits and continuity (6 hours).
Transcendental functions: exponential and logarithmic functions (4 hours).
Differential calculus: derivative, calculation of derivative: algebraic and transcendental functions, maximum and minimum, qualitative study of functions, the rule of de l'Hôpital (6 hours).
Integral calculus: definition of integral, properties of the integral, indefinite integral, integration by parts, integration by substitution, improper integrals (6 hours).
Continuous probability: random variables, the mean and variance of random variables, continuous random variables, distribution function, uniform distribution, exponential distribution, normal distribution (6 hours). Didactic methods
- Lectures; exercises
Learning assessment procedures
- The score is the arithmetic mean between the score in Physics and the score in Mathematics & Computer Science.
Physics:
Written examination with five exercises having the same weight as far as the final score is concerned: the proposed exercises will be similar to the ones explained during the course and there will be always 2 exercises regarding Mechanics and 1 regarding Electromagnetism. The written examination is considered positive if the student gets at least 18 (eighteen) with at least 1 exercise about Mechanics and 1 exercise about Electromagnetism correctly done. The student will be asked for a short oral examination if clarifications about the written exam are needed.
Mathematics & Computer Science:
Written examination with five exercises: one about probability (6 points), one about statistics (6 points), one about the study of a real function (10 points), one about the least squares method (6 points) and one about integrals and continuous random variables (6 points). The student is admitted to the oral examination with a rating greater than or equal to 17 (seventeen).
Oral examination with one or two questions about the written exam or about theoretical arguments of the course: the written score can be raised up to 4 or 5 points in the case of very good oral or lowered by 4 or 5 points in the case of bad oral. The oral examination is considered positive if the student gets at least 18 (eighteen). Reference texts
- Physics:
Giancoli, Fisica, Casa Editrice Ambrosiana
Halliday - Resnick - Walker, Fondamenti di Fisica, Casa Editrice Ambrosiana
Serway - Jewett, Principi di Fisica, EdiSES
Mathematics & Computer Science:
The text of the course is
Marco Abate, Matematica e Statistica. Le basi per le scienze della vita, 2nd edition, McGraw-Hill Libri, Milano, 2013.
Other useful references are:
Maria Cristina Patria & Gaetano Zanghirati, Mat&matica. Corso di base per discipline bio-farmaceutiche, Pitagora Editrice, Bologna, 2003.
Vinicio Villani, Graziano Gentili, Matematica. Comprendere e interpretare fenomeni delle scienze della vita, McGraw-Hill Libri, Milano, 2012.
