# Scienze Ambientali | MATHEMATICS 2

## Scienze Ambientali MATHEMATICS 2

 0512700009 DEPARTMENT OF CHEMISTRY AND BIOLOGY "ADOLFO ZAMBELLI" EQF6 ENVIRONMENTAL SCIENCES 2022/2023

 OBBLIGATORIO YEAR OF COURSE 2 YEAR OF DIDACTIC SYSTEM 2016 AUTUMN SEMESTER
SSD CFU HOURS ACTIVITY TYPE OF ACTIVITY MAT/05 5 40 LESSONS BASIC COMPULSORY SUBJECTS MAT/05 1 8 EXERCISES BASIC COMPULSORY SUBJECTS
 SALVATORE MORETTA T
Objectives
KNOWLEDGE AND UNDERSTANDING:
UNDERSTANDING THE TERMINOLOGY USED IN MATHEMATICAL ANALYSIS; KNOWLEDGE OF DEMONSTRATION METHODS; KNOWLEDGE OF THE FUNDAMENTAL CONCEPTS OF MATHEMATICAL ANALYSIS. KNOWLEDGE RELATED TO: INTEGRAL FUNCTIONS OF A VARIABLE, NUMERICAL SERIES, SEQUENCES AND SERIES OF FUNCTIONS, DIFFERENTIAL EQUATIONS, NUMERICAL METHODS FOR SOLVING EQUATIONS, DEFINED INTEGRALS AND ORDINARY DIFFERENTIAL EQUATIONS.
APPLYING KNOWLEDGE AND UNDERSTANDING – ENGINEERING ANALYSIS
APPLYING THE THEOREMS AND THE RULES STUDIED TO SOLVE PROBLEMS. BUILDING METHODS AND TROUBLESHOOTING PROCEDURES. KNOW HOW TO PROCESS AND COMMUNICATE INFORMATION USING A FORMAL LINGUISTIC LOG. APPLYING KNOWLEDGE OF THE CONCEPTS AND METHODS OF CALCULUS AND MATHEMATICAL TOOLS TO SOLVE DIFFERENTIAL EQUATIONS, INTEGRAL, PERFORM SERIES AND INTEGRAL CALCULATIONS, APPLYING NUMERICAL METHODS FOR SOLVING EQUATIONS, DEFINED INTEGRALS AND ORDINARY DIFFERENTIAL EQUATIONS
APPLYING KNOWLEDGE TO DEVELOP DEMONSTRATIONS OF CERTAIN THEOREMS CONSISTENTLY
APPLYING KNOWLEDGE AND UNDERSTANDING – ENGINEERING DESIGN
APPLYING KNOWLEDGE TO FIND THE MOST APPROPRIATE METHODS TO SOLVE A MATH PROBLEM. BE ABLE TO FIND OPTIMIZATIONS IN THE PROCESS OF SOLVING A MATH PROBLEM.
MAKING JUDGMENTS - ENGINEERING PRACTICE:
APPLYING THE ACQUIRED KNOWLEDGE TO CONTEXTS DIFFERENT FROM THOSE PRESENTED DURING THE COURSE
COMMUNICATION SKILLS – TRANSVERSAL SKILLS:
LEARNING SKILLS – TRANSVERSAL SKILLS:
LEARN HOW TO DECIPHER THE TOPICS DISCUSSED USING TEACHING MATERIALS OTHER THAN THOSE PROPOSED DURING THE COURSE. DEVELOP A POSITIVE ATTITUDE TOWARD MATHS BASED ON RESPECT FOR TRUTH AND AVAILABILITY TO SEEK MOTIVATION AND TO CLARIFY ITS VALIDITY.

Prerequisites
THE BASIC NOTIONS OF THE MATHEMATICS 1 COURSE ARE REQUIRED, IN PARTICULAR THOSE RELATING TO THE CONCEPT OF FUNCTION, LIMIT, CONTINUITY AND DIFFERENTIABILITY.
IT IS THEREFORE REQUIRED TO PASS THE MATHEMATICS 1 EXAM IN ORDER TO TAKE THE MATHEMATICS 2 EXAM

Contents
REVIEW OF DERIVATIVES AND DIFFERENTIALS - lectures 2 hours

INDEFINITE INTEGRALS - lectures 6 hours exercises 1 hours

DEFINITE INTEGRALS AND IMPROPER INTEGRALS - lectures 5 hours exercises 1 hours

DIFFERENTIAL EQUATIONS (WITH SEPARABLE VARIABLES, HOMOGENEOUS, LINEAR OF 1ST AND 2ND ORDER, BERNOULLI ) - lectures 6 hours exercises 1 hours

APPROXIMATE RESOLUTION METHODS FOR EQUATIONS (BISECTION, SECANT, NEWTON-RAPHSON) - lectures 3 hours exercises 1 hours

NUMERICAL INTEGRATION (RECTANGLE, TRAPEZOID, CAVALIERI-SIMPSON METHOD) - lectures 3 hours exercises 1 hours

SEQUENCES AND NUMERICAL SERIES - lectures 6 hours exercises 1 hours

FUNCTION SERIES- lectures 6 hours exercises 1 hours

NUMERICAL METHODS FOR SOLVING EXPLICIT AND IMPLICIT ORDINARY DIFFERENTIAL EQUATIONS (EULER, RUNGE-KUTTA, CRANK-NICHOLSON) - lectures 3 hours exercises 1 hours
Teaching Methods
FRONTAL LECTURE
GUIDED EXERCISE
PROBLEM SOLVING

ATTENDANCE OF CLASSROOM LESSONS AND EXERCISES IS NOT MANDATORY, BUT IT IS STRONGLY RECOMMENDED
Verification of learning
THE EXAM CONSISTS OF A WRITTEN AND AN ORAL TESTTHE EXAM CONSISTS OF A WRITTEN AND AN ORAL TEST

TO TAKE THE ORAL TEST IT IS NECESSARY TO PASS A WRITTEN TEST DURING THE SAME EXAM SESSION.

THE MINIMUM MARK FOR PASSING THE WRITTEN TEST IS 18/30 AND IS AWARDED BY CORRECTLY SOLVING THE HALF OF THE PROPOSED QUESTIONS

THE MINIMUM MARK FOR PASSING THE EXAM IS 18/30, AND IS AWARDED WHEN THE STUDENT, AFTER PASSING THE WRITING, SHOWS A KNOWLEDGE OF THE BASIC CONCEPTS NOT SUPPORTED BY KNOWLEDGE OF THE DEMONSTRATIONS
THE MAXIMUM VOTE (30) IS AWARDED WHEN THE STUDENT SHOWS A COMPLETE AND IN-DEPTH KNOWLEDGE OF CONCEPTS SUPPORTED BY KNOWLEDGE OF THE DEMONSTRATIONS
THE PRAISE MAY BE ATTRIBUTED TO STUDENTS WHO REACH THE MAXIMUM VOTE OF 30/30, SUPPORTED BY A SOLID RESULT IN THE WRITTEN TEST AND WHO PROVE THAT THEY ARE ABLE TO APPLY AUTONOMOUSLY KNOWLEDGE AND SKILLS ACQUIRED EVEN IN THEIR CONTEXTS.
Texts
MATERIALS PROVIDED BY THE TEACHER