Dajana CONTE | MATHEMATICAL METHODS FOR CHEMISTRY
Dajana CONTE MATHEMATICAL METHODS FOR CHEMISTRY
cod. 0512400033
MATHEMATICAL METHODS FOR CHEMISTRY
| 0512400033 | |
| DEPARTMENT OF CHEMISTRY AND BIOLOGY "ADOLFO ZAMBELLI" | |
| EQF6 | |
| CHEMISTRY | |
| 2023/2024 |
| OBBLIGATORIO | |
| YEAR OF COURSE 1 | |
| YEAR OF DIDACTIC SYSTEM 2023 | |
| SPRING SEMESTER |
| SSD | CFU | HOURS | ACTIVITY | |
|---|---|---|---|---|
| MAT/08 | 2 | 16 | LESSONS | |
| MAT/08 | 4 | 48 | EXERCISES |
| Objectives | |
|---|---|
| THE TEACHING 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 AND APPLY (IN SUITABLE CALCULUS ENVIRONMENTS) SOME MATHEMATICAL METHODS FOR THE RESOLUTION OF SCIENTIFIC COMPUTATION PROBLEMS. KNOWLEDGE AND UNDERSTANDING: THE MAIN ACQUIRED KNOWLEDGE WILL BE: •KNOWLEDGE OF MATHEMATICAL METHODS CONCERNING THE FOLLOWING SUBJECTS: SOLUTION OF LINEAR SYSTEMS, EIGENVALUES COMPUTATION, APPROXIMATION OF DATA AND FUNCTIONS, ELEMENTS OF PROBABILITY AND STATISTICS. •KNOWLEDGE OF THE BASIC PRINCIPLES OF PROCEDURAL PROGRAMMING. •KNOWLEDGE OF THE MATLAB COMPUTATIONAL ENVIRONMENT AND ITS SCIENTIFIC COMPUTATION FUNCTIONS. APPLYING KNOWLEDGE AND UNDERSTANDING: THE MAIN CAPABILITIES WILL BE: •PERFORM EXERCISES RELATED TO THE SOLUTION OF LINEAR SYSTEMS, CALCULATION OF EIGENVALUES, APPROXIMATION OF DATA AND FUNCTIONS, CALCULATION OF PROBABILITY. •TO SOLVE PROBLEMS OF SCIENTIFIC COMPUTING BY USING MATHEMATICAL SOFTWARE AND SUITABLE CALCULUS ENVIRONMENTS. •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. •TO ESTIMATE THE ACCURACY OF THE OBTAINED RESULTS. |
| Prerequisites | |
|---|---|
| BASIC KNOWLEDGE ACQUIRED THROUGH HIGH SCHOOL COURSES. |
| Contents | |
|---|---|
| MATRICES AND LINEAR SYSTEMS. DETERMINANT AND RANK. INVERTIBLE MATRICES AND COMPUTATION OF THE INVERSE. LINEAR SYSTEMS RESOLUTION: ROUCHÉ-CAPELLI THEOREM, CRAMER; SCALE REDUCTION AND GAUSS METHOD. (20 HOURS) VECTOR SPACES. LINEAR DEPENDENCE AND INDEPENDENCE. BASES AND COMPONENTS. DIMENSION. VECTOR SUB-SPACE OF THE SOLUTIONS OF A HOMOGENEOUS LINEAR SYSTEM. NORM. ORTHOGONAL VECTORS. ORTONORMAL BASES. LINEAR APPLICATIONS AND MATRICIAL REPRESENTATION. (12 HOURS) EIGENVALUES AND DIAGONALISATION: CHARACTERISTIC POLYNOMIAL. AUTOSPACES AND RELATED PROPERTIES. ALGEBRAIC AND GEOMETRIC MULTIPLICITY. DIAGONALIZATION. DIAGONALIZATION OF SYMMETRICAL MATRICES. (10 HOURS) EVENTS. PROBABILITY: AXISOMS OF PROBABILITY, CLASSICAL AND FREQUENTISTIC DEFINITION, CONDITIONAL PROBABILITY, INDEPENDENCE, BAYES FORMULA, LAW OF ALTERNATIVES. COMBINATORY CALCULATION ELEMENTS. DISCRETE ALEATORY VARIABLES, AVERAGE AND VARIANCE, BINOMIAL DISTRIBUTION AND LAW OF LARGE NUMBERS. CONTINUOUS ALEATORY VARIABLES, DISTRIBUTION FUNCTIONS AND PROBABILITY DENSITY, AVERAGE AND VARIANCE. UNIFORM DISTRIBUTION, NORMAL DISTRIBUTION, CENTRAL LIMIT THEOREM. (12 HOURS) BASIC PRINCIPLES OF PROCEDURAL PROGRAMMING; WRITING AND ANALYSIS OF ALGORITHMS AND PROGRAMS IN THE MATLAB PROGRAMMING LANGUAGE. RESOLUTION OF SCIENTIFIC COMPUTING PROBLEMS, WITH THE APPLICATION OF THE METHODS STUDIED IN THE THEORY LESSONS, BY USING THE MATLAB ENVIRONMENT AND ITS RELEVANT SCIENTIFIC CALCULATION FUNCTIONS. (10 HOURS) |
| Teaching Methods | |
|---|---|
| THE TEACHING IS COMPOSED OF • THEORETICAL LESSONS, DURING WHICH THE COURSE TOPICS WILL BE PRESENTED THROUGH FRONTAL LESSONS • CLASSROOM EXERCISES, DURING WHICH THE MAIN TOOLS NEEDED FOR THE RESOLUTION OF EXERCISES RELATED TO THE CONTENT OF THE TEACHING • LABORATORY EXERCISES, DURING WHICH SOME OF THE METHODS STUDIED WILL BE CODED IN SCIENTIFIC CALCULATION ENVIRONMENTS, AND TESTED ON CERTAIN PROBLEMS OF INTEREST TESTS. THE INSTRUMENT USED IN THE LABORATORY IS THE MATLAB CALCULATION ENVIRONMENT. IN PARTICULAR THE TEACHING INCLUDES 52 HOURS OF DIDACTICS DIVIDED IN 16 HOURS OF LESSON IN THE CLASSROOM, CORRESPONDING TO 2 CFU OF 8 HOURS EACH AND 36 HOURS OF EXERCISES IN THE CLASSROOM OR LABORATORY, CORRESPONDING TO 3 CFU FROM 12 HOURS EACH. |
| Verification of learning | |
|---|---|
| THE EXAMINATION TEST ASSESSES THE ACQUIRED KNOWLEDGE AND ABILITY TO RESOLVE EXERCISES RELATED TO THE COURSE TOPICS, BOTH BY HAND AND BY USING THE MATLAB ENVIRONMENT. IT IS DIVIDED IN TWO TESTS: A) A WRITTEN TEST THAT PROVIDES FOR THE RESOLUTION OF EXERCISES OF THE TYPE PRESENTED AT THE COURSE B) AN ORAL TEST, DURING WHICH IT WILL BE REQUIRED • TO USE THE MATHEMATICAL SOFTWARE DESIGNED AND REALIZED DURING THE COURSE FOR THE RESOLUTION OF THE MATHEMATICAL PROBLEMS TREATED DURING THE COURSE. THE RESULTS OBTAINED MUST BE COMMENTED IN RELATION TO THE APPLICABILITY, ACCURACY AND EFFICIENCY OF THE USED METHODS. • TO EXPOSE THE THEORETICAL TOPICS PRESENTED IN A LESSON: DEFINITIONS, STATEMENTS AND DEMONSTRATIONS OF THEOREMS, RESOLUTION OF EXERCISES. EACH TEST IS ASSESSED IN THIRTY AND IS INTENDED TO BE PASSED WITH A MINIMUM VOTE OF 18/30. THE FINAL VOTE IS GIVEN BY THE AVERAGE OF THE VOTES REPORTED IN EACH TEST. DURING THE COURSE, A MID-TERM TEST WILL BE CARRIED OUT, ACCORDING TO THE SAME RULES OF THE FINAL EXAM. |
| Texts | |
|---|---|
| - SEYMOUR LIPSCHUTZ, MARC LIPSON, ALGEBRA LINEARE, MCGRAW-HILL - MARCO ABATE – MATEMATICA E STATISTICA, LE BASI PER LE SCIENZE DELLA VITA, MCGRAW-HILL. - G. MONEGATO - FONDAMENTI DI CALCOLO NUMERICO - ED. CLUT - A. QUARTERONI, F.SALERI, SCIENTIFIC COMPUTING WITH MATLAB AND OCTAVE, SPRINGER THE SLIDES OF THE LECTURES WILL ALSO BE PROVIDED, AS A GUIDANCE FOR THE ORGANIZATION OF THE STUDY. |
| More Information | |
|---|---|
| EMAIL OF THE PROFESSORS: DAJCONTE@UNISA.IT, PDIAZDEALBA@UNISA.IT |
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