Antonio VITOLO | MATHEMATICS

cod. 0512500006

MATHEMATICS

	0512500006
	DIPARTIMENTO DI CHIMICA E BIOLOGIA "ADOLFO ZAMBELLI"

	ENVIRONMENTAL MONITORING AND ASSESSEMENT
	2015/2016

PERCORSO COMUNE

	OBBLIGATORIO
	YEAR OF COURSE 1
	YEAR OF DIDACTIC SYSTEM 2010
	ANNUALE

TEACHING UNITS

	SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
	MAT/05	12	96	LESSONS	BASIC COMPULSORY SUBJECTS

PROFESSORS

	ANTONIO VITOLO T Curriculum
	CRISTINA COPPOLA Curriculum
	VERONICA GAVAGNA Curriculum
	FRANCESCO SAVERIO TORTORIELLO Curriculum

	Objectives
	1. KNOWLEDGE AND UNDERSTANDING: THE AIM OF THE COURSE IS TO PROVIDE THE STUDENTS WITH THE MATHEMATICAL LANGUAGE, THE BASIC MATHEMATICAL NOTIONS AND THE GRAPHICAL REPRESENTATION WITH SPECIAL REGARD TO THE FOLLOWING SUBJECTS: ANALYTIC GEOMETRY, DIFFERENTIAL AND INTEGRAL CALCULUS, SEQUENCES AND SERIES, LINEAR ALGEBRA. 2. APPLYING KNOWLEDGE AND UNDERSTANDING: THE STUDENT WILL BE ABLE TO FORMULATE MATHEMATICALLY AND TO SOLVE SIMPLE PROBLEMS OF THE APPLIED SCIENCES, WITH SPECIAL REGARD TO THE ENVIRONMENTAL SCIENCES. IN PARTICULAR, THE STUDENT WILL BE ABLE TO CALCULATE LIMITS, DERIVATIVES AND INTEGRALS, TO STUDY AND DRAW THE GRAPH OF A FUNCTION, TO COMPUTE LENGHTS, AREAS AND VOLUMES, TO ESTABLISH THE CONVERGENCE OF A SERIES, TO SOLVE DIFFERENTIAL EQUATIONS, TO COMPUTE RANK AND DETERMINANT, TO SOLVE SYSTEMS OF LINEAR EQUATIONS. 3. MAKING JUDGEMENTS: THE STUDENT WILL BE ABLE TO CHOOSE THE MOST APPROPRIATE MATHEMATICAL MODEL IN DIFFERENT SITUATIONS, TO ESTABLISH THE PLAUSIBILITY OF A RESULT AND TO CHECK IT WITH NUMERICAL TEST, EVENTUALLY USING CALCULUS SOFTWARE. 4. COMMUNICATION SKILLS: THE STUDENT WILL BE ABLE TO EXPRESS WITH THE SUITABLE TECHNICAL LANGUAGE AND TO REPRESENT GRAPHICALLY THE LEARNED NOTIONS AND TECHNIQUES, AND TO INTEGRATE THEM WITH THOSE ONES OF OTHER SCIENTIFIC DISCIPLINES. 5. LEARNING SKILLS: THE STUDENT WILL GET A MATHEMATICAL BACKGROUND WHICH ALLOWS HIM TO LEARN MORE ADVANCED MATHEMATICAL CONCEPTS AND MORE GENERALLY SCIENTIFIC SUBJECTS WHICH USE MATHEMATICAL TOOLS.

1. KNOWLEDGE AND UNDERSTANDING: THE AIM OF THE COURSE IS TO PROVIDE THE STUDENTS WITH THE MATHEMATICAL LANGUAGE, THE BASIC MATHEMATICAL NOTIONS AND THE GRAPHICAL REPRESENTATION WITH SPECIAL REGARD TO THE FOLLOWING SUBJECTS: ANALYTIC GEOMETRY, DIFFERENTIAL AND INTEGRAL CALCULUS, SEQUENCES AND SERIES, LINEAR ALGEBRA. 2. APPLYING KNOWLEDGE AND UNDERSTANDING: THE STUDENT WILL BE ABLE TO FORMULATE MATHEMATICALLY AND TO SOLVE SIMPLE PROBLEMS OF THE APPLIED SCIENCES, WITH SPECIAL REGARD TO THE ENVIRONMENTAL SCIENCES. IN PARTICULAR, THE STUDENT WILL BE ABLE TO CALCULATE LIMITS, DERIVATIVES AND INTEGRALS, TO STUDY AND DRAW THE GRAPH OF A FUNCTION, TO COMPUTE LENGHTS, AREAS AND VOLUMES, TO ESTABLISH THE CONVERGENCE OF A SERIES, TO SOLVE DIFFERENTIAL EQUATIONS, TO COMPUTE RANK AND DETERMINANT, TO SOLVE SYSTEMS OF LINEAR EQUATIONS. 3. MAKING JUDGEMENTS: THE STUDENT WILL BE ABLE TO CHOOSE THE MOST APPROPRIATE MATHEMATICAL MODEL IN DIFFERENT SITUATIONS, TO ESTABLISH THE PLAUSIBILITY OF A RESULT AND TO CHECK IT WITH NUMERICAL TEST, EVENTUALLY USING CALCULUS SOFTWARE. 4. COMMUNICATION SKILLS: THE STUDENT WILL BE ABLE TO EXPRESS WITH THE SUITABLE TECHNICAL LANGUAGE AND TO REPRESENT GRAPHICALLY THE LEARNED NOTIONS AND TECHNIQUES, AND TO INTEGRATE THEM WITH THOSE ONES OF OTHER SCIENTIFIC DISCIPLINES. 5. LEARNING SKILLS: THE STUDENT WILL GET A MATHEMATICAL BACKGROUND WHICH ALLOWS HIM TO LEARN MORE ADVANCED MATHEMATICAL CONCEPTS AND MORE GENERALLY SCIENTIFIC SUBJECTS WHICH USE MATHEMATICAL TOOLS.

	Prerequisites
	SET THEORY. REPRESENTATIONS OF REAL NUMBERS AND OPERATIONS. FIRST AND SECOND DEREE EQUATIONS. TRIGONOMETRY. DECIMAL LOGARITHM.

	Contents
	PART 1. 1. REAL NUMBERS. REAL LINE. ANALYTICAL GEOMETRY OF THE PLANE. TRIGONOMETRY. LINES AND CONICS. ELEMENTARY, COMPOSITE AND INVERSE FUNCTIONS. 2. LIMITS AND CONTINUITY. ESTREME VALUE THEOREM AND INTERMEDIATE VALUE THEOREM. 3. DERIVATIVES. MEAN VALUE THEOREM. MONOTONICITY. PRIMITIVES. MAXIMA AND MINIMA. TAYLOR FORMULA. CONVEXITY AND CONCAVITY. GRAPHICS. 4. DEFINITE INTEGRATION. FUNDAMENTAL THEOREM OF CALCULUS. CALCULATION OF AREAS. PART 2. 1. APPLICATIONS OF INTEGRATION TO THE CALCULATION OF LENGTHS, AREAS AND VOLUMES. MASSES AND MOMENTS. IMPROPER INTEGRALS. DISCRETE AND CONTINUOUS PROBABILITY. GAUSS DISTRIBUTION. 2. NUMERICAL SEQUENCES AND SERIES. CONVERGENCE CRITERIA. POWER SERIES. TAYLOR SERIES. COMPLEX NUMBERS. EULER FORMULA. 3. DIFFERENTIAL EQUATIONS. SEPARATION OF VARIABLES. LINEAR EQUATION WITH CONSTANT COEFFICIENTS. THE VARIATION OF CONSTANTS METHOD. SHORT NOTES ABOUT FUNCTIONS OF TWO OR SEVERAL VARIABLES. CAUCHY PROBLEMS. 4. LINEAR ALGEBRA. VECTOR SPACES. SCALAR PRODUCTS. MATRICES. DETERMINANT. RANK. LINEAR MAPS. LINEAR SYSTEMS. EIGENVALUES AND EIGENVECTORS.

Contents

PART 1.
1. REAL NUMBERS. REAL LINE. ANALYTICAL GEOMETRY OF THE PLANE. TRIGONOMETRY. LINES AND CONICS. ELEMENTARY, COMPOSITE AND INVERSE FUNCTIONS.
2. LIMITS AND CONTINUITY. ESTREME VALUE THEOREM AND INTERMEDIATE VALUE THEOREM.
3. DERIVATIVES. MEAN VALUE THEOREM. MONOTONICITY. PRIMITIVES. MAXIMA AND MINIMA. TAYLOR FORMULA. CONVEXITY AND CONCAVITY. GRAPHICS.
4. DEFINITE INTEGRATION. FUNDAMENTAL THEOREM OF CALCULUS. CALCULATION OF AREAS.
PART 2.
1. APPLICATIONS OF INTEGRATION TO THE CALCULATION OF LENGTHS, AREAS AND VOLUMES. MASSES AND MOMENTS. IMPROPER INTEGRALS. DISCRETE AND CONTINUOUS PROBABILITY. GAUSS DISTRIBUTION.
2. NUMERICAL SEQUENCES AND SERIES. CONVERGENCE CRITERIA. POWER SERIES. TAYLOR SERIES. COMPLEX NUMBERS. EULER FORMULA.
3. DIFFERENTIAL EQUATIONS. SEPARATION OF VARIABLES. LINEAR EQUATION WITH CONSTANT COEFFICIENTS. THE VARIATION OF CONSTANTS METHOD. SHORT NOTES ABOUT FUNCTIONS OF TWO OR SEVERAL VARIABLES. CAUCHY PROBLEMS.
4. LINEAR ALGEBRA. VECTOR SPACES. SCALAR PRODUCTS. MATRICES. DETERMINANT. RANK. LINEAR MAPS. LINEAR SYSTEMS. EIGENVALUES AND EIGENVECTORS.

	Teaching Methods
	LECTURES AT THE BLACKBOARD. EXERCISE SESSIONS. HOMEWORKS.

	Verification of learning
	THE EXAM CONSISTS OF TWO PARTS: A WRITTEN TEST WITH THEORETICAL AND NUMERICAL EXERCISES; AN ORAL EXAM WITH CONCEPTUAL AND TECHNICAL QUESTIONS CONCERNING THE CONTENTS OF THE COURSE.

	Texts
	1. ROBERT A. ADAMS, CALCOLO DIFFERENZIALE 1, CASA EDITRICE AMBROSIANA. 2. ROBERT A. ADAMS, CALCOLO DIFFERENZIALE 2, CASA EDITRICE AMBROSIANA. 3. M.BRAMANTI, C.D.PAGANI, S.SALSA, MATEMATICA. CALCOLO INFINITESIMALE E ALGEBRA LINEARE, ZANICHELLI

	More Information
	TEACHING MATERIAL IS MADE AVAILABLE THROUGH THE SHARED FOLDER STUDENTI_VCA_MAT ON DROPBOX. TEACHING MATERIAL IS MADE AVAILABLE THROUGH THE SHARED FOLDER STUDENTI_VCA_MAT ON DROPBOX. ACCORDING TO BUDGET CONSTRAINTS, THE COURSE IS SUPPORTED BY SELECTED YOUNG MATHEMATICIANS WHO SERVE AS TUTOR FOR STUDENTS.

BETA VERSION Data source ESSE3 [Ultima Sincronizzazione: 2016-09-30]

Antonio VITOLO | MATHEMATICS