PRINCIPLES OF MATHEMATICS
cod. 13137

Academic year 2007/08
1° year of course - Second semester
Professor
Academic discipline
Analisi matematica (MAT/05)
Field
Formazione scientifica di base
Type of training activity
Basic
120 hours
of face-to-face activities
8 credits
hub:
course unit
in - - -

Learning objectives

<br />BASIC KNOWLEDGE OF CALCULUS AND MATHEMATICAL ANALYSIS FOR FUNCTIONS DEPENDING ON ONE REAL VARIABLE.<br /> 

Prerequisites

<br />NO PREREQUISITES ARE REQUIRED.<br />THE PRELIMINARY PART: ALGEBRAIC CALCULUS, ANALYTIC GEOMETRY, LOGIC AND SET THEORY, GENERAL FUNCTION THEORY, IS TEACHED DURING THE FIRST SEMESTER.<br /> 

Course unit content

<br />PRELIMINARY PART: ALGEBRAIC CALCULUS, POLYNOMIAL AND RATIONAL DISEQUATIONS.<br />ANALYTIC GEOMETRY IN THE PLANE.<br />ELEMENTS OF LOGIC AND SET THEORY.<br />BASIC FUNCTION THEORY. MONOTONIC, EVEN AND ODD FUNCTIONS.ABSOLUTE VALUE. POWERS AND ROOTS. IRRATIONAL DISEQUATIONS. TRIGONOMETRIC FUNCTIONS AND DISEQUATIONS.<br />REAL NUMBERS AND LEAST UPPER BOUND. CONTINUITY AXIOM.<br />LIMITS OF FUNCTIONS. PROPERTIES AND OPERATIONS.<br />CONTINUOUS FUNCTIONS. WEIERSTRASS THEOREM.<br />DERIVATIVES. PROPERTIES AND OPERATIONS.FERMAT, ROLLE AND LAGRANGE'S THEOREMS. QUALITATIVE STUDY OF GRAPHS OF FUNCTIONS.<br />INDETERMINATE FORMS AND ASYMPTOTICS: DE L`HOPITAL AND TAYLOR'S THEOREMS AND APPLICATION TO LIMITS OF FUNCTIONS.<br />INTEGRATION THEORY. MEASURE OF SETS. RIEMANN INTEGRAL. OPERATIONS WITH INTEGRALS. THE FUNDAMENTAL THEOREM OF THE CALCULUS. PRIMITIVES, INTEGRAL FUNCTIONS. INTEGRATIION BY PARTS AND CHANGE OF VARIABLES FORMULAS. GENERALIZED INTEGRALS.<br />SEQUENCES AND LIMITS. SERIES: CONVERGENCE CRITERIA. HARMONIC, GEOMETRIC AND EXPONENTIAL SERIES. LEIBINIZ CRITERIUM.<br /> 

Full programme

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Bibliography

E. ACERBI G.BUTTAZZO MATEMATICA PREUNIVERSITARIA DI BASE' . PITAGORA EDITRICE, BOLOGNA.<br /><br />E. ACERBI G.BUTTAZZO 'ANALISI MATEMATICA ABC' VOL.1: FUNZIONI DI UNA VARIABILE REALE . PITAGORA EDITRICE, BOLOGNA.<br /><br />D. MUCCI 'ANALISI MATEMATICA ESERCIZI' VOL.1: FUNZIONI DI UNA VARIABILE REALE . PITAGORA EDITRICE, BOLOGNA.<br />

Teaching methods

<br />FRONTAL LECTURES OF THEORY AND APPLICATIONS.<br />WRITTEN TESTS ARE ORGANIZED DURING THE PERIOD OF THE COURSE. <br />THE CROSS EXAMINATION CONSISTS IN BOTH WRITTEN AND ORAL PARTS.<br /> 

Assessment methods and criteria

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Other information

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