Gianluca FRASCA CACCIA | MATHEMATICAL METHODS FOR CHEMISTRY

cod. CB12400004

MATHEMATICAL METHODS FOR CHEMISTRY

	CB12400004
	DEPARTMENT OF CHEMISTRY AND BIOLOGY "ADOLFO ZAMBELLI"
	EQF6
	CHEMISTRY
	2025/2026

PERCORSO CHEMISTRY

	OBBLIGATORIO
	YEAR OF COURSE 1
	YEAR OF DIDACTIC SYSTEM 2025
	SPRING SEMESTER

TEACHING UNITS

SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
MAT/08	2	16	LESSONS	BASIC COMPULSORY SUBJECTS
MAT/08	4	48	EXERCISES	BASIC COMPULSORY SUBJECTS

PROFESSORS

	GIANLUCA FRASCA CACCIA T Curriculum
	DAJANA CONTE Curriculum

	Objectives
	GENERAL OBJECTIVE THE TEACHING, CONSISTING OF CLASSROOM LECTURES, LABORATORY LESSONS AND EXERCISES, IS AIMED AT PROVIDING STUDENTS WITH THEORETICAL KNOWLEDGE AND SKILLS TO CRITICALLY ANALYZE AND APPLY (IN APPROPRIATE COMPUTING ENVIRONMENTS) MATHEMATICAL METHODS FOR SOLVING PROBLEMS OF SCIENTIFIC COMPUTING. KNOWLEDGE AND UNDERSTANDING THE MAIN KNOWLEDGE ACQUIRED WILL BE: - KNOWLEDGE OF THE RELEVANT MATHEMATICAL METHODS IN THE FOLLOWING TOPICS: SOLUTION OF LINEAR SYSTEMS, COMPUTATION OF EIGENVALUES, APPROXIMATION OF DATA AND FUNCTIONS, ELEMENTS OF PROBABILITY AND STATISTICS - KNOWLEDGE OF THE BASIC PRINCIPLES OF PROCEDURAL PROGRAMMING - BASIC KNOWLEDGE OF MATLAB COMPUTING ENVIRONMENT AND RELATED SCIENTIFIC COMPUTING FUNCTIONS. ABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING THE MAIN SKILLS WILL BE: - SOLVING RELEVANT PROBLEMS THAT REQUIRE THE SOLUTION OF LINEAR SYSTEMS, CALCULATION OF EIGENVALUES, APPROXIMATION OF DATA AND FUNCTIONS, PROBABILITY THEORY - SOLVING SCIENTIFIC COMPUTING PROBLEMS THROUGH THE DEVELOPMENT OF MATHEMATICAL SOFTWARE USING MATLAB COMPUTING ENVIRONMENT AUTONOMY OF JUDGEMENT THE STUDENT WILL BE ABLE TO: - CHOOSE THE MOST SUITABLE NUMERICAL METHOD FOR THE PROBLEM UNDER CONSIDERATION THROUGH THE ANALYSIS OF THE CHARACTERISTICS OF THE PROBLEM ITSELF - ESTIMATE THE ACCURACY OF A NUMERICAL METHOD BY CRITICALLY INTERPRETING THE RESULTS OBTAINED - PROVIDE THEORETICAL JUSTIFICATIONS FOR THE EFFECTIVENESS OF DIFFERENT METHODS FOR THE SOLUTION OF THE PROBLEM AT HAND. COMMUNICATION SKILLS THE STUDENT WILL BE ABLE TO: - BE ABLE TO DESCRIBE THE RESULTS OBTAINED USING GRAPHS AND TABLES - COMMUNICATE THE KNOWLEDGE ACQUIRED IN WRITTEN AND ORAL FORM USING A PROPER TECHNICAL-SCIENTIFIC LANGUAGE LEARNING ABILITY THE STUDENT WILL BE ABLE TO: - UPDATE THEIR KNOWLEDGE OF MATHEMATICAL METHODS AND PROGRAMMING IN THE MATLAB ENVIRONMENT - UNDERSTAND AND INTERPRET BIBLIOGRAPHIC TEXTS OF BASIC MATHEMATICAL METHODS FOR APPLICATIONS.

GENERAL OBJECTIVE
THE TEACHING, CONSISTING OF CLASSROOM LECTURES, LABORATORY LESSONS AND EXERCISES, IS AIMED AT PROVIDING STUDENTS WITH THEORETICAL KNOWLEDGE AND SKILLS TO CRITICALLY ANALYZE AND APPLY (IN APPROPRIATE COMPUTING ENVIRONMENTS) MATHEMATICAL METHODS FOR SOLVING PROBLEMS OF SCIENTIFIC COMPUTING.
KNOWLEDGE AND UNDERSTANDING
THE MAIN KNOWLEDGE ACQUIRED WILL BE:
- KNOWLEDGE OF THE RELEVANT MATHEMATICAL METHODS IN THE FOLLOWING TOPICS: SOLUTION OF LINEAR SYSTEMS, COMPUTATION OF EIGENVALUES, APPROXIMATION OF DATA AND FUNCTIONS, ELEMENTS OF PROBABILITY AND STATISTICS
- KNOWLEDGE OF THE BASIC PRINCIPLES OF PROCEDURAL PROGRAMMING
- BASIC KNOWLEDGE OF MATLAB COMPUTING ENVIRONMENT AND RELATED SCIENTIFIC COMPUTING FUNCTIONS.
ABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING
THE MAIN SKILLS WILL BE:
- SOLVING RELEVANT PROBLEMS THAT REQUIRE THE SOLUTION OF LINEAR SYSTEMS, CALCULATION OF EIGENVALUES, APPROXIMATION OF DATA AND FUNCTIONS, PROBABILITY THEORY
- SOLVING SCIENTIFIC COMPUTING PROBLEMS THROUGH THE DEVELOPMENT OF MATHEMATICAL SOFTWARE USING MATLAB COMPUTING ENVIRONMENT
AUTONOMY OF JUDGEMENT
THE STUDENT WILL BE ABLE TO:
- CHOOSE THE MOST SUITABLE NUMERICAL METHOD FOR THE PROBLEM UNDER CONSIDERATION THROUGH THE ANALYSIS OF THE CHARACTERISTICS OF THE PROBLEM ITSELF
- ESTIMATE THE ACCURACY OF A NUMERICAL METHOD BY CRITICALLY INTERPRETING THE RESULTS OBTAINED
- PROVIDE THEORETICAL JUSTIFICATIONS FOR THE EFFECTIVENESS OF DIFFERENT METHODS FOR THE SOLUTION OF THE PROBLEM AT HAND.
COMMUNICATION SKILLS
THE STUDENT WILL BE ABLE TO:
- BE ABLE TO DESCRIBE THE RESULTS OBTAINED USING GRAPHS AND TABLES
- COMMUNICATE THE KNOWLEDGE ACQUIRED IN WRITTEN AND ORAL FORM USING A PROPER TECHNICAL-SCIENTIFIC LANGUAGE
LEARNING ABILITY
THE STUDENT WILL BE ABLE TO:
- UPDATE THEIR KNOWLEDGE OF MATHEMATICAL METHODS AND PROGRAMMING IN THE MATLAB ENVIRONMENT
- UNDERSTAND AND INTERPRET BIBLIOGRAPHIC TEXTS OF BASIC MATHEMATICAL METHODS FOR APPLICATIONS.

	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)

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.

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 SOLVE 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 OUT OF 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. EXCELLENCE WILL BE ACHIEVED BY THOSE STUDENTS ABLE TO APPLY THE ACQUIRED KNOWLEDGE AND SKILLS WITH CRITICAL SENSE AND ORIGINALITY. DURING THE COURSE, A MID-TERM TEST WILL BE CARRIED OUT, ACCORDING TO THE SAME RULES OF THE FINAL EXAM.

Verification of learning

THE EXAMINATION TEST ASSESSES THE ACQUIRED KNOWLEDGE AND ABILITY TO SOLVE 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 OUT OF 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.

EXCELLENCE WILL BE ACHIEVED BY THOSE STUDENTS ABLE TO APPLY THE ACQUIRED KNOWLEDGE AND SKILLS WITH CRITICAL SENSE AND ORIGINALITY.

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, GFRASCACACCIA@UNISA.IT

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Gianluca FRASCA CACCIA | MATHEMATICAL METHODS FOR CHEMISTRY