MATHEMATICS I

International Teaching MATHEMATICS I

0612100001
DEPARTMENT OF CIVIL ENGINEERING
EQF6
BSC DEGREE IN CIVIL ENGINEERING
2021/2022

OBBLIGATORIO
YEAR OF COURSE 1
YEAR OF DIDACTIC SYSTEM 2018
PRIMO SEMESTRE
CFUHOURSACTIVITY
990LESSONS
Objectives
LEARNING OUTCOMES:
THE AIM OF THE COURSE IS THE STUDENT LEARNING ABOUT THE BASIC CONCEPTS OF MATHEMATICAL ANALYSIS AND CALCULUS, WITH ELEMENTS OF ANALYTIC GEOMETRY OF THE PLANE AND IN PARTICULAR PHYSICAL APPLICATIONS.

LEARNING OUTCOMES
1. KNOWLEDGE AND UNDERSTANDING: THE COURSE IS FINALIZED TO PROVIDE THE STUDENTS WITH THE MATHEMATICAL LANGUAGE, THE BASIC MATHEMATICAL NOTIONS AND THE GRAPHICAL REPRESENTATION ESPECIALLY ABOUT THE FOLLOWING SUBJECTS: ANALYTICAL GEOMETRY, ONE VARIABLE FUNCTIONS, DIFFERENTIAL AND INTEGRAL CALCULUS, SEQUENCES AND SERIES.
2. APPLYING KNOWLEDGE AND UNDERSTANDING: THE STUDENT WILL BE ABLE TO FORMULATE MATHEMATICALLY AND TO SOLVE SIMPLE PROBLEMS OF THE APPLIED SCIENCES, ESPECIALLY IN THE CIVIL ENGINEERING FRAMEWORK. IN PARTICULAR, THE STUDENT WILL BE ABLE TO CALCULATE LIMITS, DERIVATIVES AND INTEGRALS, TO STUDY AND DRAW THE GRAPH OF ONE VARIABLES FUNCTIONS AND CONIC SECTIONS, TO COMPUTE AREAS, TO ESTABLISH THE CONVERGENCE OF A SERIES, MAKING COMPUTATIONS WITH COMPLEX NUMBERS.
3. MAKING JUDGEMENTS: THE STUDENT WILL BE ABLE TO CHOOSE THE MOST APPROPRIATE MATHEMATICAL MODEL AND METHOD IN DIFFERENT SITUATIONS, TO ESTABLISH THE PLAUSIBILITY OF A RESULT AND TO CHECK ITS VALIDITY.
4. COMMUNICATION SKILLS: THE STUDENT WILL BE ABLE TO EXPRESS WITH THE SUITABLE TECHNICAL LANGUAGE AND TO REPRESENT GRAPHICALLY THE LEARNED MATHEMATICAL 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 COURSE IS FINALIZED TO PROVIDE THE STUDENTS WITH THE MATHEMATICAL LANGUAGE, THE BASIC MATHEMATICAL NOTIONS AND THE GRAPHICAL REPRESENTATION ESPECIALLY ABOUT THE FOLLOWING SUBJECTS: ONE VARIABLE FUNCTIONS, DIFFERENTIAL AND INTEGRAL CALCULUS, SEQUENCES AND SERIES.
2. APPLYING KNOWLEDGE AND UNDERSTANDING: THE STUDENT WILL BE ABLE TO FORMULATE MATHEMATICALLY AND TO SOLVE SIMPLE PROBLEMS OF THE APPLIED SCIENCES, ESPECIALLY IN THE CIVIL ENGINEERING FRAMEWORK. IN PARTICULAR, THE STUDENT WILL BE ABLE TO CALCULATE LIMITS, DERIVATIVES AND INTEGRALS, TO STUDY AND DRAW THE GRAPH OF A FUNCTION, TO COMPUTE AREAS, TO ESTABLISH THE CONVERGENCE OF A SERIES, MAKING COMPUTATIONS WITH COMPLEX NUMBERS.
3. MAKING JUDGEMENTS: THE STUDENT WILL BE ABLE TO CHOOSE THE MOST APPROPRIATE MATHEMATICAL MODEL AND METHOD IN DIFFERENT SITUATIONS, TO ESTABLISH THE PLAUSIBILITY OF A RESULT AND TO CHECK ITS VALIDITY.
4. COMMUNICATION SKILLS: THE STUDENT WILL BE ABLE TO EXPRESS WITH THE SUITABLE TECHNICAL LANGUAGE AND TO REPRESENT GRAPHICALLY THE LEARNED MATHEMATICAL 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
SETS. REPRESENTATIONS OF REAL NUMBERS AND OPERATIONS. FIRST AND SECOND DEGREE EQUATIONS AND INEQUALITIES. TRIGONOMETRY. DECIMAL AND NATURAL LOGARITHM.
Contents
THE COURSE IS STRUCTURED AS FOLLOWS:
1. PRELIMINARIES: SETS. REAL NUMBERS. REAL LINE. LINEAR, QUADRATIC AND RATIONAL EQUATIONS AND INEQUALITIES (LECTURES/ EXERCISES: 3 H/5 H)
2. ANALYTICAL GEOMETRY OF THE PLANE: CARTESIAN FRAME OF REFERENCE. TRIGONOMETRY. LINES AND CONICS. PLANAR TRANSLATIONS AND ROTATIONS. MATRICES AND DETERMINANTS: AN INTRODUCTION. CONIC SECTIONS: CLASSIFICATION AND REPRESENTATION (LECTURES/ EXERCISES: 7 H/7 H)
3. FUNCTIONS AND GRAPHS: DEFINITIONS AND PROPERTIES. MONOTONICITY. ELEMENTARY FUNCTIONS: POWERS WITH INTEGER AND FRACTIONAL EXPONENTS, SINE, COSINE, EXPONENTIAL, LOGARITHM. OPERATIONS WITH FUNCTIONS. COMPOSITE AND INVERSE FUNCTIONS. IRRATIONAL AND TRANSCENDENTAL EQUATIONS (LECTURES/ EXERCISES: 4 H/4 H)
4. LIMITS AND CONTINUITY: DEFINITIONS AND PROPERTIES. COMPARISON THEOREMS. DISCONTINUITY. EXTREME VALUE THEOREM AND INTERMEDIATE VALUE THEOREM. APPROXIMATE CALCULUS OF SOLUTIONS OF EQUATIONS (LECTURES/ EXERCISES: 6 H/4 H)
5. DIFFERENTIABILITY: DEFINITIONS AND PROPERTIES. DERIVATIVE AND TANGENT LINE. SPEED AND ACCELERATION. COMPUTATION RULES. DIFFERENTIALS. INDEFINITE INTEGRATION. LAGRANGE MEAN VALUE THEOREM. APPLICATIONS: MONOTONICITY, MAXIMA AND MINIMA. HIGHER ORDER DERIVATIVES. TAYLOR FORMULA. CONVEXITY, CONCAVITY AND INFLECTION POINTS. GRAPH OF A FUNCTION. LINEARIZATION AND ERROR ESTIMATE (LECTURES/ EXERCISES: 10 H/10 H)
6. INTEGRATION: THE AREA PROBLEM. DEFINITE INTEGRAL. INTEGRAL MEAN. FUNDAMENTAL THEOREM OF CALCULUS. APPLICATIONS: AREAS, FORCES, WORK. INTEGRATION TECHNIQUES. COMPLEX NUMBERS. IMPROPER INTEGRALS (LECTURES/ EXERCISES: 10 H/10 H)
7. NUMERICAL SEQUENCES AND SERIES: CONVERGENCE OF A SEQUENCE. MONOTONE SEQUENCES. CONVERGENCE AND SUM OF A SERIES. GEOMETRIC AND EXPONENTIAL SERIES. CONVERGENCE CRITERIA (LECTURES/ EXERCISES: 6 H/4 H)
Teaching Methods
THE COURSE CONSISTS OF 46 HOURS OF THEORETIC FRONTAL LECTURES WITH EXAMPLES AND 44 HOURS OF EXERCISE SESSIONS, IN TOTAL 90 HOURS (9 CREDITS).
THE ATTENDANCE IS MANDATORY. THE STUDENT IS REQUIRED TO ATTEND AT LEAST THE 70% OF THE COURSE, USING HIS PERSONAL BADGE.
Verification of learning
THE EXAM CONSISTS OF TWO PARTS: A WRITTEN TEST WITH THEORETICAL AND NUMERICAL EXERCISES FOR APPLYING KNOWLEDGE; AN ORAL EXAM WITH CONCEPTUAL AND TECHNICAL QUESTIONS CONCERNING THE CONTENTS OF THE COURSE TO VERIFY KNOWLEDGE AND UNDERSTANDING AS WELL AS COMMUNICATION SKILLS.
THE FINAL GRADE, EXPRESSED IN THIRTIES, IS THE RESULT OF THE WRITTEN AND ORAL ASSESSMENT.
Texts
ROBERT A. ADAMS, CRISTOPHER ESSEX, CALCULUS, A COMPLETE COURSE, 7TH EDITION, PEARSON.
P. MARCELLINI, C. SBORDONE, ESERCITAZIONI DI MATEMATICA, VOLUME 1, PARTE I, LIGUORI EDITORE
P. MARCELLINI, C. SBORDONE, ESERCITAZIONI DI MATEMATICA, VOLUME 1, PARTE II, LIGUORI EDITORE
LECTURE NOTES.
More Information
TUTORS FOR HELP TEACHING GENERALLY SUPPORT THE COURSE
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