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# Elements of Mathematics

 Degree course FOREST AND ENVIRONMENTAL SCIENCE Curriculum Curriculum unico Learnings UNICO Academic Year 2018/2019 ECTS 6 Scientific Disciplinary Sector MAT/05 Year First year Time unit First semester Class hours 60 Educational activity Basic training activities

## Single group

 Supplying course 14L01L ELEMENTI DI MATEMATICA in SCIENZE E TECNOLOGIE AGRARIE L-25 BONAFEDE SALVATORE Professor Salvatore BONAFEDE Objectives The importance of mathematics as a tool is now an universally accepted fact. Perhaps less obvious is the impression that this discipline can leave in the organization of thought: in the transition from confusion to catalog, from the qualitative to the quantitative, from rational to irrational. That said, the course "Elements of Mathematics" aims, as its main objective to approach the student, in a simple and clear form, in mathematical language, which once limited to physical, now involves a wide variety of human activities, from biology to economics, engineering to finance, from medicine to sociology. Programme Elements of set theory: definition of set. Numerical sets. Subsets of a set. Set of parts. Operations between sets. The numerical sets N, Z, Q, R.Tutorial: Operations between sets.Elements of: Algebraic, fractional, irrational, logarithmic, exponential equations and with the absolute value. Integer and rational powers, powers with base and exponent real. Logarithms. Algebraic, fractional, irrational, logarithmic, exponential inequations and with the absolute value. Inequalities with absolute values. Trigonometry: Measurement of angles and oriented arcs, sine, cosine, tangent and cotangent of an oriented arc. Main relations, addition, double and half angle, Prosthaphaeresis formulas.Tutorial: Solving Equations and inequalities of various kinds.Elements of Analytical Geometry: Lines and oriented segments. X-axis on the line, Cartesian coordinates on the plane. Distance between two points. Midpoint of a segment. Equation of the line, implicit, segmental and explicit form. Slope of a line and its geometrical meaning. Condition of parallelism and perpendicularity of two lines. Distance of a point from a line. Equation of the circle, parabola (*), ellipse (*), hyperbola (*) and related problems. Intersection between circle and line. Intersection of curves.Tutorial: Locating points on the line and on the plane. Calculation of distances between points. Determination of the equation of the line in various forms. Finding the slope. Intersection between two lines, checking if they are parallel or perpendicular (*). Determination of the equation of the circle, parabola, ellipse, with assigned conditions. Recognition of the given geometric locus through his equation. Intersection between circle, parabola and ellipse with a line.Functions of a real variable: definition. Domain and codomain of a function. Operations between functions. Symmetric, periodic functions. Graph of a function. Intervals of the real line. Neighborhood of a point. Surjective, injective and bijective functions. Function composition. Bounded functions: maximum, minimum, supremum and infimum. Monotone functions. The symbols:  oo , + oo. Tutorial: Determination of the domain and possible symmetries of the graph of a real function. Construction of the composite function and identification of its components. Calculating supremum, infimum, maximum and minimum of a bounded function.Limits: Definition of limit of a function at a point: convergence, divergence. One-sided limit. Definition of limit involving infinity. Theorems about limits: uniqueness of the limit, comparison (*). Operations with limits. Limits of special interest (*). Graphical interpretation of the limit.Tutorial: Calculation of limits.Continuous Functions: Definition of continuous function at a point and in an interval. Examples. Points of discontinuity. Continuity of composite function. Properties of continuous functions on a closed, bounded interval: I and II Weierstrasss Theorem (*). Theorem of existence of zeros. Graphical interpretation.Tutorial: Composition of continuous functions. Determination of points of discontinuity. Application of the theorem of existence of zeros to the resolution of algebraic equations of order higher than second.Differential Calculus: Definition of derivative. Continuity of differentiable functions. Geometrical meaning of the derivative. Derivatives of elementary functions. Derivation rules. Higher order derivatives. Derivation of composite functions (*). Fundamental theorems of differential calculus: Rolle's theorem (*), Lagrange's theorem (*) and its corollaries, De L'Hospitals rule. Relative extremes: maximum and minimum. Monotonicity intervals. Concavity and inflection points. Asymptotes. Study of the graph of a function.Tutorial: Calculation of the derivative. Derivation rules. Search the asymptotes of the graph, monotonicity intervals, the relative extremes. Determination of the concavity and inflection points of the graph. Graph of some elementary functions.Integral Calculus: Indefinite Integral. Immediate integrals. Properties of integral. Torricelli's theorem (*). Substitution rule (*). Integration by parts (*). Definite Integral and its geometrical meaning. The fundamental theorem of calculus (*). The area under a curve.Tutorial: Calculation of indefinite integrals of elementary functions. Determination of area of some regions of plane.Of the topics marked with (*) a demonstration is not required. Books 1) S. Bonafede - Elementi di Matematica - dispense delle lezioni.2) S. Bonafede - Analisi Matematica 1  Video - lezioni su www.29elode.it.3) P. Marcellini - C. Sbordone - Elementi di Matematica - Ed. Liguori, Napoli.4) D. Benedetto  M. Degli Espositi  C. Maffei - Matematica per le scienze della vita - Ambrosiana5) P. Marcellini - C.Sbordone - Esercitazioni di Matematica vol. I, parti 1 e 2 - Ed. Liguori, Napoli. Traditional teaching method Yes Distance teaching method No Mandatory attendance No Written examination evaluation Yes Oral examination evaluation Yes Aptitude test evaluation No Project evaluation No Internship evaluation No Evaluation in itinere No Practice Test No

## Further information

Description Document
Corso di Potenziamento (dispensa) Raccolta Compiti d'Esame (dispensa) Raccolta Lezioni (dispensa) Risultati dell'esame di Matematica del 04-07-2019 (varie) Risultati dell'esame di Matematica del 10-09-2019 (varie) Risultati dell'esame di Matematica del 12-06-2019 (varie) Risultati dell'esame di Matematica del 19-07-2019 (varie) Risultati dell'esame di Matematica del 19-09-2019 (varie) Risultati dell'esame di Matematica del 20-09-2018 (varie) Risultati di Elementi di Matematica del 07-02-2019 (varie) Risultati di Elementi di Matematica del 11-04-2019 (varie) Risultati di Elementi di Matematica del 14-03-2019 (varie) Risultati di Elementi di Matematica del 14-05-2019 (varie) Risultati di Elementi di Matematica del 17-01-2019 (varie) Risultati di Elementi di Matematica del 17-01-2019 (prova integrativa) (varie) Risultati di Elementi di Matematica del 21-02-2019 (varie) Risultati di Elementi di Matematica del 21-02-2019 (prova integrativa) (varie) ## Office hours list:

Description News
Office hours by: Salvatore Bonafede
Il ricevimento studenti e' previsto di norma il Giovedi' dalle 9.00 alle 13.00. Solamente nel periodo didattico (dal 3 ottobre al 17 dicembre) il ricevimento sara' il mercoledi' ed il giovedi' dalle 13.00 alle 14.00. Per il ricevimento occorre prenotarsi con il docente via email:
Salvatore.bonafede@unirc.it
• Il ricevimento studenti e' previsto di norma il Giovedi' dalle 9.00 alle 13.00. Solamente nel periodo didattico (dal 3 ottobre al 17 dicembre) il ricevimento sara' il mercoledi' ed il giovedi' dalle 13.00 alle 14.00. Per il ricevimento occorre prenotarsi con il docente via email: Salvatore.bonafede@unirc.it Expiry: 2020-09-30
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