Gianluca FRASCA CACCIA | NUMERICAL COMPUTING AND PROGRAMMING FOR DATA ANALYSIS

cod. 0522300062

NUMERICAL COMPUTING AND PROGRAMMING FOR DATA ANALYSIS

	0522300062
	DEPARTMENT OF CHEMISTRY AND BIOLOGY "ADOLFO ZAMBELLI"
	EQF7
	CHEMISTRY
	2024/2025

CURRICULUM BIOMOLECULAR CHEMISTRY

	YEAR OF COURSE 2
	YEAR OF DIDACTIC SYSTEM 2016
	AUTUMN SEMESTER

TEACHING UNITS

	SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
	MAT/08	6	48	LESSONS	SUPPLEMENTARY COMPULSORY SUBJECTS

PROFESSORS

	GIANLUCA FRASCA CACCIA T Curriculum
	DAJANA CONTE Curriculum

	Objectives
	GENERAL OBJECTIVE THE COURSE IS ORGANIZED IN CLASSROOM LESSONS AND LABORATORY AND EXERCISE SESSIONS. IT IS AIMED AT PROVIDING STUDENTS WITH SUFFICIENT THEORETICAL BACKGROUND AND PRACTICAL TOOLS FOR THE NUMERICAL SOLUTION OF MATHEMATICAL PROBLEMS THAT ARISE IN VARIOUS APPLICATIONS OF CHEMISTRY, BY USING COMPUTATIONAL SOFTWARES. KNOWLEDGE AND UNDERSTANDING THE MAIN KNOWLEDGE ACQUIRED WILL BE: - KNOWLEDGE OF THE RELEVANT NUMERICAL METHODS IN THE FOLLOWING TOPICS: NUMERICAL SOLUTION OF LINEAR SYSTEMS BY DIRECT AND ITERATIVE METHODS, APPROXIMATION OF DATA AND FUNCTIONS, NUMERICAL SOLUTION OF NON-LINEAR EQUATIONS, NUMERICAL INTEGRATION, NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS AND PARTIAL DIFFERENTIAL EQUATIONS - KNOWLEDGE OF THE BASIC PRINCIPLES OF PROCEDURAL PROGRAMMING IN MATLAB ENVIRONMENT (OR IN PYTHON LANGUAGE) - BASIC KNOWLEDGE OF THE MATLAB (OR PYTHON) COMPUTING ENVIRONMENT AND THE RELATED SCIENTIFIC COMPUTING FUNCTIONS ABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING THE MAIN SKILLS WILL BE: - SOLVING SCIENTIFIC COMPUTING PROBLEMS BY DEVELOPING MATHEMATICAL SOFTWARE USING THE MATLAB (OR PYTHON) COMPUTING ENVIRONMENT - SOLVING (IN MATLAB OR PYTHON) EXERCISES THAT REQUIRE THE NUMERICAL SOLUTION OF LINEAR SYSTEMS, THE APPROXIMATION OF DATA AND FUNCTIONS, THE NUMERICAL SOLUTION OF NON-LINEAR EQUATIONS, NUMERICAL INTEGRATION, THE NUMERICAL SOLUTION OF ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS AUTONOMY OF JUDGEMENT STUDENTS WILL BE ABLE TO: - CHOOSE SUITABLE NUMERICAL METHODS FOR THE PROBLEM UNDER CONSIDERATION THROUGH THE ANALYSIS OF THE CHARACTERISTICS OF THE PROBLEM ITSELF - EVALUATE THE EFFICIENCY OF THE ALGORITHMS AND THE RELIABILITY OF THE SOLUTIONS OBTAINED - PROVIDE THEORETICAL JUSTIFICATIONS FOR THE EFFECTIVENESS OF DIFFERENT METHODS FOR THE SOLUTION OF THE PROBLEMS AT HAND, PROVING CAPABILITY OF CORRECTLY INTERPRET THE RESULTS. COMMUNICATION SKILLS STUDENTS WILL BE ABLE TO: - DESCRIBE THE RESULTS OBTAINED USING GRAPHS AND TABLES - COMMUNICATE THE KNOWLEDGE ACQUIRED IN WRITTEN AND ORAL FORM BY USING PROPER TECHNICAL-SCIENTIFIC TERMINOLOGY LEARNING ABILITY STUDENTS WILL BE ABLE TO: - UPDATE THEIR KNOWLEDGE OF NUMERICAL COMPUTING FOR THE SOLUTION OF PROBLEMS ARISING IN APPLICATIONS BY USING MATLAB (OR PYTHON) COMPUTING ENVIRONMENT - UNDERSTAND AND INTERPRET BIBLIOGRAPHIC TEXTS ON NUMERICAL COMPUTING FOR THE APPLICATIONS AND ON CODING IN MATLAB ENVIRONMENT (OR IN PYTHON LANGUAGE)

GENERAL OBJECTIVE
THE COURSE IS ORGANIZED IN CLASSROOM LESSONS AND LABORATORY AND EXERCISE SESSIONS. IT IS AIMED AT PROVIDING STUDENTS WITH SUFFICIENT THEORETICAL BACKGROUND AND PRACTICAL TOOLS FOR THE NUMERICAL SOLUTION OF MATHEMATICAL PROBLEMS THAT ARISE IN VARIOUS APPLICATIONS OF CHEMISTRY, BY USING COMPUTATIONAL SOFTWARES.
KNOWLEDGE AND UNDERSTANDING
THE MAIN KNOWLEDGE ACQUIRED WILL BE:
- KNOWLEDGE OF THE RELEVANT NUMERICAL METHODS IN THE FOLLOWING TOPICS: NUMERICAL SOLUTION OF LINEAR SYSTEMS BY DIRECT AND ITERATIVE METHODS, APPROXIMATION OF DATA AND FUNCTIONS, NUMERICAL SOLUTION OF NON-LINEAR EQUATIONS, NUMERICAL INTEGRATION, NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
- KNOWLEDGE OF THE BASIC PRINCIPLES OF PROCEDURAL PROGRAMMING IN MATLAB ENVIRONMENT (OR IN PYTHON LANGUAGE)
- BASIC KNOWLEDGE OF THE MATLAB (OR PYTHON) COMPUTING ENVIRONMENT AND THE RELATED SCIENTIFIC COMPUTING FUNCTIONS
ABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING
THE MAIN SKILLS WILL BE:
- SOLVING SCIENTIFIC COMPUTING PROBLEMS BY DEVELOPING MATHEMATICAL SOFTWARE USING THE MATLAB (OR PYTHON) COMPUTING ENVIRONMENT
- SOLVING (IN MATLAB OR PYTHON) EXERCISES THAT REQUIRE THE NUMERICAL SOLUTION OF LINEAR SYSTEMS, THE APPROXIMATION OF DATA AND FUNCTIONS, THE NUMERICAL SOLUTION OF NON-LINEAR EQUATIONS, NUMERICAL INTEGRATION, THE NUMERICAL SOLUTION OF ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS
AUTONOMY OF JUDGEMENT
STUDENTS WILL BE ABLE TO:
- CHOOSE SUITABLE NUMERICAL METHODS FOR THE PROBLEM UNDER CONSIDERATION THROUGH THE ANALYSIS OF THE CHARACTERISTICS OF THE PROBLEM ITSELF
- EVALUATE THE EFFICIENCY OF THE ALGORITHMS AND THE RELIABILITY OF THE SOLUTIONS OBTAINED
- PROVIDE THEORETICAL JUSTIFICATIONS FOR THE EFFECTIVENESS OF DIFFERENT METHODS FOR THE SOLUTION OF THE PROBLEMS AT HAND, PROVING CAPABILITY OF CORRECTLY INTERPRET THE RESULTS.
COMMUNICATION SKILLS
STUDENTS WILL BE ABLE TO:
- DESCRIBE THE RESULTS OBTAINED USING GRAPHS AND TABLES
- COMMUNICATE THE KNOWLEDGE ACQUIRED IN WRITTEN AND ORAL FORM BY USING PROPER TECHNICAL-SCIENTIFIC TERMINOLOGY
LEARNING ABILITY
STUDENTS WILL BE ABLE TO:
- UPDATE THEIR KNOWLEDGE OF NUMERICAL COMPUTING FOR THE SOLUTION OF PROBLEMS ARISING IN APPLICATIONS BY USING MATLAB (OR PYTHON) COMPUTING ENVIRONMENT
- UNDERSTAND AND INTERPRET BIBLIOGRAPHIC TEXTS ON NUMERICAL COMPUTING FOR THE APPLICATIONS AND ON CODING IN MATLAB ENVIRONMENT (OR IN PYTHON LANGUAGE)

	Prerequisites
	KNOWLEDGE AND SKILLS IN ELEMENTS OF MATHEMATICAL ANALYSIS AND LINEAR ALGEBRA.

	Contents
	1. ARITHMETIC, ERRORS. MATHEMATICAL MODELS AND SOURCES OF ERROR. FLOATING-POINT ARITHMETIC: ERRORS IN DATA REPRESENTATION AND MACHINE OPERATIONS, MACHINE ACCURACY. DISASTROUS CONSEQUENCES OF THE ROUNDING ERROR: 0.1 AND THE FAILURE OF THE PATRIOT MISSILE. MALCONDITIONING PROBLEMS AND STABILITY OF NUMERICAL ALGORITHMS. (6 HOURS) 2. NUMERICAL METHODS FOR SOLVING LINEAR SYSTEMS: SOLVING SYSTEMS OF LINEAR EQUATIONS: GAUSSIAN ELIMINATION METHOD AND STABILITY. CONDITIONING A MATRIX, PIVOTING AND SCALING. ITERATIVE METHODS: CONVERGENCE, ERROR ESTIMATION AND STOPPING CRITERIA. APPLICATIONS: BALANCING OF CHEMICAL REACTIONS. (10 HOURS) 3. APPROXIMATION OF DATA AND FUNCTIONS. CHOICE OF THE CLASS OF APPROXIMATING FUNCTIONS. POLYNOMIAL INTERPOLATION: METHOD OF INDETERMINATE COEFFICIENTS, LAGRANGE INTERPOLATION FORMULA, ERROR REPRESENTATION. APPROXIMATION OF DATA AND FUNCTIONS USING LEAST SQUARES. INTERPOLATION AND LEAST SQUARES IN MATLAB ENVIRONMENT. APPLICATIONS: REPRESENTATION OF EXPERIMENTAL DATA ON PRESSURE AS A FUNCTION OF TEMPERATURE IN A LIQUID; ON THE SPECIFIC HEAT VERSUS TEMPERATURE. (8 HOURS) 4. NUMERICAL RESOLUTION OF NONLINEAR EQUATIONS SOLVING EQUATIONS (NEWTON'S METHOD AND FIXED POINT METHOD). CONVERGENCE AND ERROR ESTIMATION. APPLICATIONS: CHEMICAL EQUILIBRIA IN HOMOGENEOUS AND HETEROGENEOUS PHASE. CALCULATION OF THE NODAL POINTS OF THE HYDROGENOID ORBITALS. (4 HOURS) 5. NUMERICAL INTEGRATION QUADRATURE FORMULAS, NEWTON-COTES FORMULAS, GAUSSIAN QUADRATURES, COMPOUND FORMULAS. APPLICATIONS: CALCULATION OF THE ENTROPY OF A PURE SUBSTANCE FROM CALORIMETRIC DATA. 6. NUMERICAL SOLUTION OF CAUCHY PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS BASIC DEFINITIONS AND CONCEPTS. LOCAL TRUNCATION ERROR, GLOBAL ERROR. CONSISTENCY, STABILITY, CONVERGENCE OF METHODS. EXPLICIT ONE-STEP METHODS: EULER-CAUCHY METHOD, HEUN METHOD, RUNGE KUTTA METHODS. CONVERGENCE OF EXPLICIT ONE-STEP METHODS. SYSTEMS OF FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS. STIFF PROBLEMS. APPLICATIONS: CHEMOSTAT, CHEMICAL KINETICS. (10 HOURS) 7. NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS GENERALITIES ON THE NUMERICAL TREATMENT OF LINEAR PARTIAL DIFFERENTIAL EQUATIONS OF THE SECOND ORDER. FINITE DIFFERENCE METHODS FOR ELLIPTIC, PARABOLIC AND HYPERBOLIC EQUATIONS. LINE METHOD FOR EQUATIONS OF PARABOLIC TYPE. (6 HOURS) FOR EACH TOPIC WE WILL DEAL WITH WRITING AND ANALYZING ALGORITHMS AND PROGRAMS IN THE MATLAB PROGRAMMING LANGUAGE (OR PYTHON), BY SOLVING SCIENTIFIC CALCULATION PROBLEMS, WITH THE APPLICATION OF THE METHODS STUDIED IN THE THEORY LESSONS, THROUGH THE USE OF THE MATLAB (OR PYTHON) CALCULATION ENVIRONMENT AND THE RELATED SCIENTIFIC CALCULATION FUNCTIONS;

Contents

1. ARITHMETIC, ERRORS.
MATHEMATICAL MODELS AND SOURCES OF ERROR. FLOATING-POINT ARITHMETIC: ERRORS IN DATA REPRESENTATION AND MACHINE OPERATIONS, MACHINE ACCURACY. DISASTROUS CONSEQUENCES OF THE ROUNDING ERROR: 0.1 AND THE FAILURE OF THE PATRIOT MISSILE. MALCONDITIONING PROBLEMS AND STABILITY OF NUMERICAL ALGORITHMS. (6 HOURS)
2. NUMERICAL METHODS FOR SOLVING LINEAR SYSTEMS:
SOLVING SYSTEMS OF LINEAR EQUATIONS: GAUSSIAN ELIMINATION METHOD AND STABILITY. CONDITIONING A MATRIX, PIVOTING AND SCALING. ITERATIVE METHODS: CONVERGENCE, ERROR ESTIMATION AND STOPPING CRITERIA.
APPLICATIONS: BALANCING OF CHEMICAL REACTIONS. (10 HOURS)
3. APPROXIMATION OF DATA AND FUNCTIONS.
CHOICE OF THE CLASS OF APPROXIMATING FUNCTIONS. POLYNOMIAL INTERPOLATION: METHOD OF INDETERMINATE COEFFICIENTS, LAGRANGE INTERPOLATION FORMULA, ERROR REPRESENTATION. APPROXIMATION OF DATA AND FUNCTIONS USING LEAST SQUARES. INTERPOLATION AND LEAST SQUARES IN MATLAB ENVIRONMENT.
APPLICATIONS: REPRESENTATION OF EXPERIMENTAL DATA ON PRESSURE AS A FUNCTION OF TEMPERATURE IN A LIQUID; ON THE SPECIFIC HEAT VERSUS TEMPERATURE. (8 HOURS)
4. NUMERICAL RESOLUTION OF NONLINEAR EQUATIONS
SOLVING EQUATIONS (NEWTON'S METHOD AND FIXED POINT METHOD). CONVERGENCE AND ERROR ESTIMATION.
APPLICATIONS: CHEMICAL EQUILIBRIA IN HOMOGENEOUS AND HETEROGENEOUS PHASE. CALCULATION OF THE NODAL POINTS OF THE HYDROGENOID ORBITALS. (4 HOURS)
5. NUMERICAL INTEGRATION
QUADRATURE FORMULAS, NEWTON-COTES FORMULAS, GAUSSIAN QUADRATURES, COMPOUND FORMULAS.
APPLICATIONS: CALCULATION OF THE ENTROPY OF A PURE SUBSTANCE FROM CALORIMETRIC DATA.
6. NUMERICAL SOLUTION OF CAUCHY PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS
BASIC DEFINITIONS AND CONCEPTS. LOCAL TRUNCATION ERROR, GLOBAL ERROR. CONSISTENCY, STABILITY, CONVERGENCE OF METHODS. EXPLICIT ONE-STEP METHODS: EULER-CAUCHY METHOD, HEUN METHOD, RUNGE KUTTA METHODS. CONVERGENCE OF EXPLICIT ONE-STEP METHODS. SYSTEMS OF FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS. STIFF PROBLEMS.
APPLICATIONS: CHEMOSTAT, CHEMICAL KINETICS. (10 HOURS)
7. NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS
GENERALITIES ON THE NUMERICAL TREATMENT OF LINEAR PARTIAL DIFFERENTIAL EQUATIONS OF THE SECOND ORDER. FINITE DIFFERENCE METHODS FOR ELLIPTIC, PARABOLIC AND HYPERBOLIC EQUATIONS. LINE METHOD FOR EQUATIONS OF PARABOLIC TYPE. (6 HOURS)

FOR EACH TOPIC WE WILL DEAL WITH WRITING AND ANALYZING ALGORITHMS AND PROGRAMS IN THE MATLAB PROGRAMMING LANGUAGE (OR PYTHON), BY SOLVING SCIENTIFIC CALCULATION PROBLEMS, WITH THE APPLICATION OF THE METHODS STUDIED IN THE THEORY LESSONS, THROUGH THE USE OF THE MATLAB (OR PYTHON) CALCULATION ENVIRONMENT AND THE RELATED SCIENTIFIC CALCULATION FUNCTIONS;

	Teaching Methods
	THE LECTURES ARE INTENDED TO INTRODUCE AND PRESENT METHODS AND ALGORITHMS THAT WILL BE IMPLEMENTED IN LABORATORY AND TESTED ON A SET OF PROBLEMS. FOR EACH TOPIC, SITUATIONS OF INTEREST IN THE PRACTICE THAT REQUIRE THE EMPLOY OF THE INTRODUCED NUMERICAL TECHNIQUES WILL ALSO BE PRESENTED.

	Verification of learning
	THE EXAM CONSISTS OF AN ORAL TEST ON THE ANALYSIS OF THE COMPUTATIONAL RESULTS OBTAINED BY SOLVING SIMPLE SCIENTIFIC COMPUTING PROBLEMS USING MATLAB/OCTAVE/PYTHON COMPUTING ENVIRONMENT AND THE THEORETICAL ASPECTS OF THE CONSIDERED METHODS. THE ASSESSMENT WILL TAKE INTO ACCOUNT THE CAPACITY OF STUDENTS TO EXPOSE THEIR KNOWLEDGE USING A PROPER SCIENTIFIC TERMINOLOGY WITH CLARITY AND COMPLETENESS. THE ASSESSMENT WILL BE MARKED OUT OF 30 AND THE EXAM WILL BE PASSED WITH A MARK OF AT LEAST 18/30. EXCELLENCE WILL BE ACHIEVED BY THOSE STUDENTS CAPABLE OF APPLY THEIR KNOWLEDGE AND SKILLS WITH CRITICAL SENSE AND ORIGINALITY.

Verification of learning

THE EXAM CONSISTS OF AN ORAL TEST ON THE ANALYSIS OF THE COMPUTATIONAL RESULTS OBTAINED BY SOLVING SIMPLE SCIENTIFIC COMPUTING PROBLEMS USING MATLAB/OCTAVE/PYTHON COMPUTING ENVIRONMENT AND THE THEORETICAL ASPECTS OF THE CONSIDERED METHODS.

THE ASSESSMENT WILL TAKE INTO ACCOUNT THE CAPACITY OF STUDENTS TO EXPOSE THEIR KNOWLEDGE USING A PROPER SCIENTIFIC TERMINOLOGY WITH CLARITY AND COMPLETENESS.

THE ASSESSMENT WILL BE MARKED OUT OF 30 AND THE EXAM WILL BE PASSED WITH A MARK OF AT LEAST 18/30.

EXCELLENCE WILL BE ACHIEVED BY THOSE STUDENTS CAPABLE OF APPLY THEIR KNOWLEDGE AND SKILLS WITH CRITICAL SENSE AND ORIGINALITY.

	Texts
	- A. QUARTERONI, F.SALERI, INTRODUZIONE AL CALCOLO SCIENTIFICO: ESERCIZI E PROBLEMI RISOLTI CON MATLAB, SPRINGER - A. QUARTERONI, MODELLISTICA NUMERICA PER PROBLEMI DIFFERENZIALI, SPRINGER. - QUARTERONI, A., SACCO, R., SALERI, F., GERVASIO, P., MATEMATICA NUMERICA, SPRINGER

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	EMAIL OF PROFESSORS: DAJCONTE@UNISA.IT GFRASCACACCIA@UNISA.IT

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Gianluca FRASCA CACCIA | NUMERICAL COMPUTING AND PROGRAMMING FOR DATA ANALYSIS