Mathematic and Physics
A.Y. 2025/2026
Learning objectives
The course aims to provide the student with an understanding of basic mathematics and physics (equations, inequalities, systems, limits, derivatives, mechanics, thermodynamics, wave phenomena, electricity and magnetism), illustrating their relevance with concrete examples in order to solve simple exercises in which these principles are applied to specific problems.
Expected learning outcomes
1. Knowledge and Understanding: By the end of the course, the student will be expected to demonstrate knowledge of the basic rules and theoretical concepts outlined in the course syllabus.
2. Ability to Apply Knowledge and Understanding: The student must demonstrate the ability to apply theoretical knowledge to practical scenarios. They should be able to solve exercises based on the rules and methods covered during the lessons.
3. Critical Thinking and Judgment Skills: The student should be able to critically discuss and analyze the information acquired. Specific lessons and exercises focused on all parts of the course syllabus aim to develop these skills.
4. Ability to Communicate What Has Been Learned: The student will need to demonstrate the ability to express themselves using scientifically appropriate terminology, particularly concerning the course content. Lessons and exercises are designed to enhance the ability to communicate clearly and engage in scientific discussions with peers.
5. Lifelong Learning Skills: The student will be expected to show the ability to use the acquired knowledge to interpret new situations, laws, and exercises. This includes effectively utilizing available knowledge sources and maintaining strong organizational skills
2. Ability to Apply Knowledge and Understanding: The student must demonstrate the ability to apply theoretical knowledge to practical scenarios. They should be able to solve exercises based on the rules and methods covered during the lessons.
3. Critical Thinking and Judgment Skills: The student should be able to critically discuss and analyze the information acquired. Specific lessons and exercises focused on all parts of the course syllabus aim to develop these skills.
4. Ability to Communicate What Has Been Learned: The student will need to demonstrate the ability to express themselves using scientifically appropriate terminology, particularly concerning the course content. Lessons and exercises are designed to enhance the ability to communicate clearly and engage in scientific discussions with peers.
5. Lifelong Learning Skills: The student will be expected to show the ability to use the acquired knowledge to interpret new situations, laws, and exercises. This includes effectively utilizing available knowledge sources and maintaining strong organizational skills
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Lesson period
First semester
Course syllabus
For the Mathematics and Statistics part (48 h):
· Numeric sets;
· Operations on sets;
· Direct and inverse proportionality;
· Percentages;
· Radicals;
· Logarithms;
· Exponentials;
· First degree integer and fractional equations;
· Whole and fractional second degree equations;
· Equations of degree higher than the second;
· Integer and fractional systems of first degree equations;
· Integer and fractional systems of second degree equations;
· Whole and fractional first degree inequalities;
· Whole and fractional second degree inequalities;
· Systems of first degree integer and fractional inequalities;
· Systems of integer and fractional second degree inequalities;
· Elements of trigonometry;
· Limits;
· Derivatives;
· Elements of mathematical logic;
· Elements of Descriptive Statistics;
For the Physics part (32h):
· Preliminary elements: physical quantities; unit of measure; scientific notation and orders of magnitude; significant figures; scalar and vector quantities; operations with vectors (addition, subtraction, scalar product and vector product, decomposition).
· Kinematics: speed and acceleration (average and instantaneous); uniform rectilinear motion; uniformly accelerated motion; uniform circular motion and harmonic motion; parabolic motion.
· Dynamics of the material point: the three principles of dynamics (with practical applications); examples of forces: weight force, elastic force, constraint force, friction force; momentum; moment of a force; levers.
· Work and energy: definition of work; mechanical energy; kinetic energy and kinetic energy theorem; conservative forces; gravitational and elastic potential energy; conservation of mechanical energy and its applications.
· States of aggregation of matter: outline of intermolecular forces; qualitative description of the gaseous, liquid and solid states.
· States and dynamics of liquids: pressure; Pascal's law; Stevino's law; Archimedes' principle; scope; Bernoulli's theorem and its applications
· Thermodynamics: heat and temperature; mode of heat transmission; changes of state; thermal capacity and specific heat; particular transformations of a gas (isobar, isochore, isothermal and cyclic); equation of state for ideal gases; work of compression and expansion of a gas; internal energy; first and second law of thermodynamics; thermodynamic cycles; efficiency of a thermal machine.
· Electricity: electric charge and Coulomb's law; electric field of a point charge; electric field flux and Gauss' theorem; electric potential and electric potential energy; direct electric current; Ohm's laws; Kirchhoff's laws; solving electrical circuits.
· Magnetism: fundamental magnetic phenomena (wire crossed by current, coil and solenoid).
· Numeric sets;
· Operations on sets;
· Direct and inverse proportionality;
· Percentages;
· Radicals;
· Logarithms;
· Exponentials;
· First degree integer and fractional equations;
· Whole and fractional second degree equations;
· Equations of degree higher than the second;
· Integer and fractional systems of first degree equations;
· Integer and fractional systems of second degree equations;
· Whole and fractional first degree inequalities;
· Whole and fractional second degree inequalities;
· Systems of first degree integer and fractional inequalities;
· Systems of integer and fractional second degree inequalities;
· Elements of trigonometry;
· Limits;
· Derivatives;
· Elements of mathematical logic;
· Elements of Descriptive Statistics;
For the Physics part (32h):
· Preliminary elements: physical quantities; unit of measure; scientific notation and orders of magnitude; significant figures; scalar and vector quantities; operations with vectors (addition, subtraction, scalar product and vector product, decomposition).
· Kinematics: speed and acceleration (average and instantaneous); uniform rectilinear motion; uniformly accelerated motion; uniform circular motion and harmonic motion; parabolic motion.
· Dynamics of the material point: the three principles of dynamics (with practical applications); examples of forces: weight force, elastic force, constraint force, friction force; momentum; moment of a force; levers.
· Work and energy: definition of work; mechanical energy; kinetic energy and kinetic energy theorem; conservative forces; gravitational and elastic potential energy; conservation of mechanical energy and its applications.
· States of aggregation of matter: outline of intermolecular forces; qualitative description of the gaseous, liquid and solid states.
· States and dynamics of liquids: pressure; Pascal's law; Stevino's law; Archimedes' principle; scope; Bernoulli's theorem and its applications
· Thermodynamics: heat and temperature; mode of heat transmission; changes of state; thermal capacity and specific heat; particular transformations of a gas (isobar, isochore, isothermal and cyclic); equation of state for ideal gases; work of compression and expansion of a gas; internal energy; first and second law of thermodynamics; thermodynamic cycles; efficiency of a thermal machine.
· Electricity: electric charge and Coulomb's law; electric field of a point charge; electric field flux and Gauss' theorem; electric potential and electric potential energy; direct electric current; Ohm's laws; Kirchhoff's laws; solving electrical circuits.
· Magnetism: fundamental magnetic phenomena (wire crossed by current, coil and solenoid).
Prerequisites for admission
Basic notions of mathematics are required as prerequisites, such as solving algebraic equations, calculating areas of plane figures and volumes of solids.
Teaching methods
Frontal lessons, practise
Teaching Resources
Serway and Jevett, Principles of Physics, vol. 1 (EdiSES) (for the Physics part)
Assessment methods and Criteria
Written exam (1h + 1h).
The exam consists in carrying out a written test aimed at ascertaining the acquisition, correct understanding and the ability to rework the course contents. The test will be evaluated out of thirty and the mark will take into account the accuracy and quality of the answers.
The final grade of the exam is the arithmetic average of the marks obtained in the mathematics module and in the physics module.
The final result will be visible directly on "SIFA".
The exam consists in carrying out a written test aimed at ascertaining the acquisition, correct understanding and the ability to rework the course contents. The test will be evaluated out of thirty and the mark will take into account the accuracy and quality of the answers.
The final grade of the exam is the arithmetic average of the marks obtained in the mathematics module and in the physics module.
The final result will be visible directly on "SIFA".
FIS/07 - APPLIED PHYSICS - University credits: 4
MAT/02 - ALGEBRA - University credits: 6
MAT/02 - ALGEBRA - University credits: 6
Lessons: 80 hours