Ateneo - UPO

Basic mathematics, functions, derivatives, integrals. Some elements of descriptive statistics. Basic knowledge of the fundamental laws of classical physics and some elements of modern.

Slides of the lectures published on the course web page. In addition for the module of Mathematics the book Sergio Invernizzi, Maurizio Rinaldi, Federico Comoglio, Moduli di Matematica e Statistica con l'uso di R, Zanichelli Editore, Bologna 2018.

The aim of the course is to give the students the knowledge and tools of Mathematics (differential and integral calculus) and the basic elements of Physics preparatory to the other courses of the Degree Course and to introduce students to the methodologies of analysis of experimental data (for example presentation and numerical and graphical synthesis of simple series of data).
The student is expected
to become able to use the knowledge acquired also in multidisciplinary field.
It is expected that the student is able to apply the learned methods even in different situations and if required has the tools to expand his
knowledge in an autonomous way. The student will have to acquire the ability to express the concepts
fundamentals learned in a simple but clear and effective way.

During the course the student should acquire the ability to
study and learn by choosing your path with originality and will have to
be able to choose resources, possibly even online, useful
to his study.

The student should have the basic knowledge of the subject that can be acquired in a normal high school. In particular: arithmetic operations, powers, Cartesian plane, equation of the line, parabola and circumference, angles, measured in degrees and radians, circular functions, fundamental formulas of plane and solid geometry.

Classroom lectures plus online material

The exam consists of two final tests. A computer test aimed primarily at the verification of mathematical skills (possible combined with homework or oral examination) and a physics test consisting of a written and an oral exam where the student's ability to apply the knowledge of physics acquired during the course is evaluated.Upon reaching the sufficiency in both tests based on their outcome, the overall grade is formulated.

Numbers.Equation and inequalities. The Cartesian plane. Straight lines and simple curves. Linear systems. Angles and their measures: radian. Concept of mathematical functions. Domain and codomain. Image. Function composition. Invertible function and inverse function. Cosine, Sine and tangent and their inverse functions. Logarithms and exponential functions. Geometric meaning of the Derivative. Graphic computation of the derivative through repeated zooms. Approximation of the derivative at a point via Newton quotient. Three point rule. Derivative for tabulated functions. Derivative function. Differentiation rules Derivative of the sum, of the product, of the composite function, of the reciprocal and of the quotient. Derivative of the inverse function. Applications of the derivatives. Increasing and decreasing functions, Minima and maxima of functions. Computation of maxima and minima with the help of the derivative. Second derivative and study of concavity-convexity of a graph. Netwon’s method. Numerical Integration Definite integral for positive functions over finite intervals, Computation. Numerical integration with the rectangle methods and trapezoid method. Stochastic integration with the Montecarlo methods. Exact integration The Fundamental Theorem of Calculus. Indefinite integral and antiderivatives. Computation of antiderivatives. Area between two curves. Extensions of the Integral Integrals for non positive functions. Inversions of integration endpoints. . Basic elements of Statistics. Statistical data and their representations. Population and samples. Variables and observations. Graphical representations: bar charts, histograms and box-plot. Numerical representations and statistical indices. Scatter plot. Linear regression. Variable transformations to reduce to a linear relationship.Measure and vectors, motonion in one dimension- motion in a plane. The laws of the Dynamic. Work, energy and energy conservation. Conservative and non conservative forces. Rotational kinematics and dinamics. Elastic properties of materials. Static. Waves, stationary waves. Acoustics. Fluids, static and dynamics of fluids. Ideal fluids and real fluids. Surface phenomena. Temperature, Heat Propagation. Kinetic theory of gases. The Laws of Thermodynamics, thermal machines. Entropy. Electric field, Electrical current in solids, liquids, gases, Electrical circuits, Magnetic field, electromagnetic induction. Electromagnetic waves. Geometric optics, optical instruments and the eye, Elements of Physical Optics.

Knowledge of some basic concepts and methods of mathematics, in particular: real numbers and their representations, main elementary functions, derivative and its geometric interpretation, simple integrals, calculation of areas and basic elements of Statistics. Ability at applying these concepts and methods in the modelisation of simple problems in which there are numerical and graphical presentations and synthesis of simple series of experimental data. Ability at communicating problem solutions in a clear and complete fashion. Ability in choosing the mathematical resources useful to deal with simple problems where it is required to interpret and use modeling of natural phenomena. Knowledge and understanding": Acquisition of a deep knowledge of physical phenomena, knowledge of the concepts and applications of the fundamental laws of classical physics, acquisition of appropriate scientific language.
"Knowledge and understanding of applied skills": knowing how to identify the data necessary to characterize a physical phenomenon; ability to interpret data and understand orders of magnitude, ability to apply the fundamental principles and laws of physics to solve problems and describe natural phenomena. Ability to use the teaching material for a critical and reasoned study.