Dajana CONTE | 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
	2023/2024

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	OPTIONAL SUBJECTS

PROFESSORS

	DAJANA CONTE T Curriculum
	GIANLUCA FRASCA CACCIA Curriculum

	Objectives
	LEARNING 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 AND PRACTICAL TOOLS TO SOLVE NUMERICALLY, WITH THE AID OF THE CALCULATOR, MATHEMATICAL PROBLEMS THAT ARISE IN VARIOUS APPLICATIONS OF CHEMISTRY. KNOWLEDGE AND UNDERSTANDING: THE MAIN ACQUIRED KNOWLEDGE WILL BE: •KNOWLEDGE OF NUMERICAL METHODS RELATED TO THE FOLLOWING TOPICS: NUMERICAL SOLUTION OF LINEAR SYSTEMS WITH DIRECT AND ITERATIVE METHODS, APPROXIMATION OF DATA AND FUNCTIONS, NUMERICAL SOLUTION OF NON LINEAR EQUATIONS, NUMERICAL INTEGRATION, NUMERICAL SOLUTION OF ORDINARY 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) CALCULATION ENVIRONMENT AND RELATED SCIENTIFIC CALCULATION FUNCTIONS. APPLYING KNOWLEDGE AND UNDERSTANDING: •SOLVING SCIENTIFIC CALCULATION PROBLEMS THROUGH THE DEVELOPMENT OF MATHEMATICAL SOFTWARE AND THE USE OF THE MATLAB CALCULATION ENVIRONMENT (OR THE PYTHON LANGUAGE) •CARRY OUT (IN MATLAB OR PYTHON) EXERCISES RELATED TO THE NUMERICAL SOLUTION OF LINEAR SYSTEMS, TO THE APPROXIMATION OF DATA AND FUNCTIONS, TO THE NUMERICAL SOLUTION OF NON-LINEAR EQUATIONS, TO NUMERICAL INTEGRATION, TO THE NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS AND PARTIAL DIFFERENTIAL EQUATIONS •CHOOSE THE MOST SUITABLE NUMERICAL METHOD FOR THE PROBLEM UNDER CONSIDERATION THROUGH THE ANALYSIS OF THE CHARACTERISTICS OF THE PROBLEM ITSELF •ASSESS THE EFFICIENCY OF THE ALGORITHMS AND THE RELIABILITY OF THE OBTAINED SOLUTIONS

LEARNING 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 AND PRACTICAL TOOLS TO SOLVE NUMERICALLY, WITH THE AID OF THE CALCULATOR, MATHEMATICAL PROBLEMS THAT ARISE IN VARIOUS APPLICATIONS OF CHEMISTRY.

KNOWLEDGE AND UNDERSTANDING:
THE MAIN ACQUIRED KNOWLEDGE WILL BE:
•KNOWLEDGE OF NUMERICAL METHODS RELATED TO THE FOLLOWING TOPICS: NUMERICAL SOLUTION OF LINEAR SYSTEMS WITH DIRECT AND ITERATIVE METHODS, APPROXIMATION OF DATA AND FUNCTIONS, NUMERICAL SOLUTION OF NON LINEAR EQUATIONS, NUMERICAL INTEGRATION, NUMERICAL SOLUTION OF ORDINARY 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) CALCULATION ENVIRONMENT AND RELATED SCIENTIFIC CALCULATION FUNCTIONS.

APPLYING KNOWLEDGE AND UNDERSTANDING:
•SOLVING SCIENTIFIC CALCULATION PROBLEMS THROUGH THE DEVELOPMENT OF MATHEMATICAL SOFTWARE AND THE USE OF THE MATLAB CALCULATION ENVIRONMENT (OR THE PYTHON LANGUAGE)
•CARRY OUT (IN MATLAB OR PYTHON) EXERCISES RELATED TO THE NUMERICAL SOLUTION OF LINEAR SYSTEMS, TO THE APPROXIMATION OF DATA AND FUNCTIONS, TO THE NUMERICAL SOLUTION OF NON-LINEAR EQUATIONS, TO NUMERICAL INTEGRATION, TO THE NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
•CHOOSE THE MOST SUITABLE NUMERICAL METHOD FOR THE PROBLEM UNDER CONSIDERATION THROUGH THE ANALYSIS OF THE CHARACTERISTICS OF THE PROBLEM ITSELF
•ASSESS THE EFFICIENCY OF THE ALGORITHMS AND THE RELIABILITY OF THE OBTAINED SOLUTIONS

	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 A PRACTICAL TEST IN THE LABORATORY RELATING TO THE RESOLUTION OF SCIENTIFIC CALCULATION PROBLEMS USING THE MATLAB/PYTHON CALCULATION ENVIRONMENT AND THE PROGRAMS DEVELOPED DURING THE LABORATORY EXERCISES, AND A COMMENTARY ON THE DEVELOPED PROGRAMS. THE LABORATORY TEST WILL BE IMMEDIATELY FOLLOWED BY THE ORAL EXAM.

	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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Dajana CONTE | NUMERICAL COMPUTING AND PROGRAMMING FOR DATA ANALYSIS