# MATHEMATICS I AND PRACTICAL EXERCISE cod. 1001383

1° year of course - First semester
Professor
Matematiche complementari (MAT/04)
Field
Discipline matematiche, informatiche e fisiche
Type of training activity
Basic
48 hours
of face-to-face activities
6 credits
hub: -
course unit
in ITALIAN

Integrated course unit module: MATHEMATICS

## Learning objectives

Mathematics I  and  Exercitations gives first year student the main notions of Mathematics.<br />
Mathematics II  and Exercitations completes the mathematical work begun in the Mathematics I course, providing students additional skills useful in understanding how mathematics may be applied to the other subjects in the degree course.

## Prerequisites

Course aims: To give first year students the main basic notions of Mathematics; other basic notions will be given in Mathematics II course. Mathematics I and Mathematics II are courses with only one integrated examination.<br />
9. Prerequisiti:<br />
Rational and irrational numbers. Powers and radicals. Logarithms, exponentials. Basic notions of geometry in plane and of trigonometry.

## Course unit content

Mathematics I gives first year student the main notions of Mathematics.<br />
Mathematics II completes the mathematical work begun in the Mathematics I course, providing students additional skills useful in understanding how mathematics may be applied to the other subjects in the degree course.<br />
9. Prerequisiti:<br />
Rational and irrational numbers. Powers and radicals. Logarithms, exponentials. Basic notions of trigonometry. Basic notions of geometry in plane.<br />
10. Contenuti del corso:<br />
Mathematics I : Complex numbers. Binomial coefficients, binomial theorem. Matrices. Systems of linear equations. Basic notions in vector algebra. Basic notions of geometry in plane (lines, conics in canonic form) and in space (planes, lines, quadrics in canonic form). Sequences, series. Functions, composed functions, one to one functions and their inverse functions. Computations of limits. Differential calculus: definition of derivative, geometrical interpretation. Differentiation and continuity. Main theorems about the derivative (Fermat's theorem, Lagrange's theorem and its inferences, De l'Hospital's theorem). Applications of derivatives to the graphical study of functions. Taylor's formula. Integral calculus: primitives. Integration rules. Definite integrals. The fundamental theorem of integral calculus. Improper integrals. Functions of two or more variables: limits, continuity, first and second order partial derivatives. Directional derivatives. Differentiable functions. Taylor's formula. Local maxima and minima for functions of two variabiles. Mathematics II : Implicit functions. Dini's theorem. Ordinary differential equations. Linear first order diffential equations. Initial-value problems. Linear differential equations with constant coefficients. Simple numerical methods of integration. Parametric representations of curves and surfaces. Regular curves and surfaces. Line integrals. Vector fields. Conservative fields and potential functions. Language of differential forms. Double integrals, triple integrals and surface integrals. Flow of a vector field through a surface. Divergence theorem. Power series. Complex exponential function. Euler's formulas. Vector spaces. Linear transformations. Eigenvalues and eigenvectors. Diagonalisation of square matrices.

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## Bibliography

Recommended textbooks: M. Bramanti, C.D. Pagani, S. Salsa, MATEMATICA (Calcolo Infinitesimale e Algebra Lineare), Zanichelli Editore, Bologna<br />
Other usefull textbooks:<br />
G. Prodi, Istituzioni di Matematiche, McGrow-Hill, Milano.<br />
A.Zaccagnini, M.G.Rinaldi, Esercizi per i corsi di Istituzioni di Matematiche, Azzali, Parma.<br />
<br />
G.De Marco, Analisi 0, Zanichelli, Bologna<br />
12. Metodologia d'insegnamento: Oral lesson<br />
13. Metodi di valutazione: Joined oral written exam<br />
Descrizione Metodi di Insegnamento e Valutazione:<br />
Frontal lectures and exercises .<br />
The exam consists of written and oral tests.<br />
14. Lingua d'insegnamento: ITALIANO

## Teaching methods

13. Metodi di valutazione: Joined oral written exam<br />
Descrizione Metodi di Insegnamento e Valutazione:<br />
Frontal lectures and exercises .<br />
The exam consists of written and oral tests.<br />
14. Lingua d'insegnamento: ITALIANO

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