Dajana CONTE | MATHEMATICAL METHODS FOR CHEMISTRY
Dajana CONTE MATHEMATICAL METHODS FOR CHEMISTRY
cod. 0512400016
MATHEMATICAL METHODS FOR CHEMISTRY
| 0512400016 | |
| DEPARTMENT OF CHEMISTRY AND BIOLOGY "ADOLFO ZAMBELLI" | |
| EQF6 | |
| CHEMISTRY | |
| 2017/2018 |
| OBBLIGATORIO | |
| YEAR OF COURSE 2 | |
| YEAR OF DIDACTIC SYSTEM 2016 | |
| SECONDO SEMESTRE |
| SSD | CFU | HOURS | ACTIVITY | |
|---|---|---|---|---|
| MAT/08 | 3 | 24 | LESSONS | |
| MAT/08 | 2 | 24 | EXERCISES |
| Objectives | |
|---|---|
| KNOWLEDGE AND UNDERSTANDING: THE COURSE IS MADE OF FRONTAL LECTURES IN THE CLASSROOM AND LECTURES AND EXERCITATIONS IN LABORATORY. ITS AIM IS TO MAKE THE STUDENTS ACQUIRE THE THEORETICAL KNOWLEDGE AND TO LEARN TO CRITICALLY ANALYZE THE MAIN MATHEMATICAL METHODS CONCERNING THE FOLLOWING SUBJECTS: SOLUTION OF LINEAR SYSTEMS, EIGENVALUES COMPUTATION, APPROXIMATION OF DATA AND FUNCTIONS, COMPUTATION OF DEFINITE INTEGRALS, ELEMENTS OF PROBABILITY AND STATISTICS, AND USAGE OF ENVIRONMENTS FOR THE SCIENTIFIC COMPUTATION. THE AIM OF THE LABORATORY LECTURERS IS TO MAKE THE STUDENTS CAPABLE TO SOLVE PROBLEMS OF SCIENTIFIC CALCULUS IN THE CHOSEN CALCULUS ENVIRONMENT, BY ALSO ESTIMATING THE ACCURACY OF THE OBTAINED RESULTS. APPLYING KNOWLEDGE AND UNDERSTANDING: THE AIM OF THE COURSE IS TO MAKE THE STUDENT CAPABLE TO SOLVE PROBLEMS OF SCIENTIFIC COMPUTING BY USING MATHEMATICAL SOFTWARE AND SUITABLE CALCULUS ENVIRONMENTS, TEACHING HIM TO CHOOSE THE MORE APPROPRIATE NUMERICAL METHOD TO SOLVE THE PROBLEM UNDER EXAMINATION, BY MEANS OF THE ANALYSIS OF THE CHARACTERISTICS OF THE PROBLEM ITSELF. |
| Prerequisites | |
|---|---|
| IT IS REQUIRED THE KNOWLEDGE OF THE BASIC TOPICS OF MATHEMATICS, TREATED IN THE COURSES OF MATHEMATICS OF THE FIRST YEAR. |
| Contents | |
|---|---|
| ELEMENTS OF LINEAR ALGEBRA: VECTORIAL SPACES, MATRICES AND LINEAR TRANSFORMATIONS, MATRICIAL ALGEBRA, DETERMINANTS, INVERTIBLE MATRICES, EIGENVALUES, SIMILITUDE TRANSFORMATIONS AND DIAGONALIZATION, SYSTEMS OF LINEAR EQUATIONS. MATHEMATICAL MODELS AND ERROR SOURCES. FLOATING POINT ARITHMETICS. ERRORS IN DATA REPRESENTATIONS AND IN MACHINE OPERATIONS. DISASTROUS CONSEQUENCES OF ROUNDING ERRORS: 0.1 AND THE FAILING OF PATRIOT MISSILE. ILL CONDITIONING OF PROBLEMS AND STABILITY OF NUMERICAL ALGORITHMS. MAIN NUMERICAL METHODS FOR THE SOLUTION OF LINEAR SYSTEMS, COMPUTATION OF EIGENVALUES, APPROXIMATION OF DATA AND FUNCTIONS (INTERPOLATIONS AND LEAST SQUARES), COMPUTATION OF DEFINITE INTEGRALS, NUMERICAL SOLUTION OF NONLINEAR EQUATIONS. EXPERIMENTAL AND SIMULATED DATA, ABSOLUTE AND RELATIVE FREQUENCIES. PROBABILITY, CONDITIONED PROBABILITÀ, INDEPENDENCY. FINITE RANDOM VARIABLES, EXPECTED VALUE AND VARIANCE, LARGE NUMBERS RULE, SIMULATION AND DISTRIBUTION FUNCTIONS. STATISTICAL ESTIMATES AND TEST. SOLUTION OF SCIENTIFIC CALCULUS PROBLEMS BY APPLYING THE METHODS STUDIED IN THE THEORY LECTURES, BY MEANS OF THE USAGE OF MATLAB ENVIRONMENT AND ITS SCIENTIFIC COMPUTATIONS FUNCTIONS. BASIC PRINCIPLES OF PROCEDURAL PROGRAMMING; WRITING AND ANALYSIS OF ALGORITHMS AND PROGRAMS IN MATLAB LANGUAGE. |
| Teaching Methods | |
|---|---|
| THE COURSE IS CONSTITUTED BY SOME THEORETICAL LECTURES FOR THE TRANSFER OF NECESSARY KNOWLEDGE FOR THE USAGE OF MATHEMATICAL METHODS IN THE PROBLEMS OF SCIENTIFIC COMPUTATION, AND SOME LABORATORY LECTURES AND EXERCITATIONS IN ORDER TO USE THE STUDIED MATHEMATICAL METHODS AND TO MAKE THE ANALYSIS OF THE OBTAINED RESULTS. THE TOOL WHICH WILL BE USED IN LABORATORY FOR THE SOLUTION OF SCIENTIFIC PROBLEMS IS THE MATLAB ENVIRONMENT. NAMELY THE COURSE CONSISTS OF 48 TEACHING HOURS, SUBDIVIDED IN 24 HOURS OF CLASSROOM LESSONS, CORRESPONDING TO 3 CFUS OF 8 HOURS EACH, AND 24 HOURS OF LABORATORY LESSON, CORRESPONDING TO 2 CFUS OF 12 HOURS EACH. |
| Verification of learning | |
|---|---|
| THE EXAM TEST EVALUATES THE ACQUIRED KNOWLEDGE AND THE ABILITY TO APPLY THEM TO THE RESOLUTION OF SCIENTIFIC CALCULUS PROBLEMS, BY USING THE MATLAB ENVIRONMENT AND THE PROGRAMS DEVELOPED DURING LABORATORY LESSONS. IT IS DIVIDED INTO TWO TRIALS: A PRACTICAL TEST, IN WHICH THE MATHEMATICAL SOFTWARE DESIGNED AND CONSTRUCTED DURING THE COURSE IS USED TO SOLVE SYSTEMS OF LINEAR EQUATION, APPROXIMATION OF DATA AND FUNCTIONS, NONLINEAR EQUATION RESOLUTION, CALCULATION OF EIGENVALUES OF MATRICES AND DEFINITE INTEGRALS; AN ORAL INTERVIEW, FOR THE PURPOSE OF ASSESSING THE THEORETICAL KNOWLEDGE PRESENTED IN THE THEORETICAL LESSONS. |
| Texts | |
|---|---|
| - G. MONEGATO - FONDAMENTI DI CALCOLO NUMERICO - ED. CLUT - S.INVERNIZZI, M.RINALDI, A.SGARRO, MODULI DI MATEMATICA E STATISTICA. ZANICHELLI. - A. QUARTERONI, F.SALERI, INTRODUZIONE AL CALCOLO SCIENTIFICO: ESERCIZI E PROBLEMI RISOLTI CON MATLAB, SPRINGER |
| More Information | |
|---|---|
| DAJCONTE@UNISA.IT |
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