Mathematics
A.Y. 2024/2025
Learning objectives
The main objective of the course is to provide students with the basics of the Differential and Integral Calculus for real functions of a real variable and of Linear Algebra
Expected learning outcomes
At the end of the course the student will be able to study some types of real functions of real variables (rational functions, exponential and logarithmic functions) and calculate simple limits and areas delimited by curves and lines. He will be able to draw the graph of these functions and calculate the required areas. He will know the principles underlying linear equation systems and will be able to solve simple systems of linear equations and calculate real eigenvalues and eigenvectors of a real and symmetric matrix. Will develop skills to be able to address the scientific subjects of the course of study.
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
Responsible
Lesson period
First semester
Course syllabus
Sets and Real Numbers: Elementary properties of real numbers, infimum and supremum. Functions: Main properties and elementary functions. Limits and Their Properties. Continuity and Fundamental Properties of Continuous Functions: Uniform continuity; Weierstrass, Heine-Cantor, Intermediate Value, and Darboux theorems. Derivative of a Real Function and Its Properties: Rolle's, Lagrange's, Cauchy's, and L'Hôpital's theorems. Taylor polynomials. Integral Calculus: Definite integrals, integration of continuous functions. Integral functions. First and Second Fundamental Theorem of Calculus. Indefinite integrals. Integration by parts and substitution. Linear Algebra: Real vector spaces. Matrices and linear applications. Determinant. Solution of linear equation systems.
Prerequisites for admission
Preliminary Knowledge: Basic high school level mathematics knowledge as required by the admission tests. Elementary algebra: monomials, polynomials, and operations with polynomials. Trigonometry: definition of sine, cosine, and tangent; their properties and relationships; unit circle. Analytical geometry: equations of a line, circle, ellipse, parabola, hyperbola. Exponential functions and logarithms.
Prerequisite Exams: None.
Prerequisite Exams: None.
Teaching methods
Mode of Delivery: Lectures, classroom exercises.
Availability of Teaching Materials: All teaching materials will be available on MyAriel.
Contribution of Teaching Methods to Achieving Expected Results: Theoretical lessons will provide the conceptual foundations, while exercises will help consolidate knowledge through practice.
Availability of Teaching Materials: All teaching materials will be available on MyAriel.
Contribution of Teaching Methods to Achieving Expected Results: Theoretical lessons will provide the conceptual foundations, while exercises will help consolidate knowledge through practice.
Teaching Resources
Main Reference Text: G. Aletti, G. Naldi, L. Paeschi, Calcolo differenziale e algebra lineare - McGraw-Hill Education (Italy) srl
Teaching Materials: The teaching materials used in class are uploaded to the course website.
Teaching Materials: The teaching materials used in class are uploaded to the course website.
Assessment methods and Criteria
Mode: Written exam.
Type: The exam takes place in one day with the following format:
- At least 20 minutes to complete the first part (true/false theory questions, limit exercise, function domain exercise). The first part is passed with half of the available points (75/150).
- At least one hour to complete the second part (linear algebra exercise and function study, open-ended questions).
Duration: At least 20 minutes for the first part, at least 60 minutes for the second part.
Evaluation Criteria: Correctness of answers, ability to apply concepts.
Grading: In thirtieths.
Number of Exam Sessions: Six sessions per year.
Verification Methods for DSA Students: Personalized, mainly extended time.
Midterm Exams: Not provided.
Final Grade Communication: Personalized communication through official channels.
Use of Calculators: Allowed only if not connected to the internet and without function plotting capabilities.
Type: The exam takes place in one day with the following format:
- At least 20 minutes to complete the first part (true/false theory questions, limit exercise, function domain exercise). The first part is passed with half of the available points (75/150).
- At least one hour to complete the second part (linear algebra exercise and function study, open-ended questions).
Duration: At least 20 minutes for the first part, at least 60 minutes for the second part.
Evaluation Criteria: Correctness of answers, ability to apply concepts.
Grading: In thirtieths.
Number of Exam Sessions: Six sessions per year.
Verification Methods for DSA Students: Personalized, mainly extended time.
Midterm Exams: Not provided.
Final Grade Communication: Personalized communication through official channels.
Use of Calculators: Allowed only if not connected to the internet and without function plotting capabilities.
MAT/01 - MATHEMATICAL LOGIC
MAT/02 - ALGEBRA
MAT/03 - GEOMETRY
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS
MAT/05 - MATHEMATICAL ANALYSIS
MAT/06 - PROBABILITY AND STATISTICS
MAT/07 - MATHEMATICAL PHYSICS
MAT/08 - NUMERICAL ANALYSIS
MAT/09 - OPERATIONS RESEARCH
MAT/02 - ALGEBRA
MAT/03 - GEOMETRY
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS
MAT/05 - MATHEMATICAL ANALYSIS
MAT/06 - PROBABILITY AND STATISTICS
MAT/07 - MATHEMATICAL PHYSICS
MAT/08 - NUMERICAL ANALYSIS
MAT/09 - OPERATIONS RESEARCH
Practicals: 32 hours
Lessons: 56 hours
Lessons: 56 hours
Professor:
Aletti Giacomo
Educational website(s)
Professor(s)
Reception:
on appointment
office 2099