Calculus

A.Y. 2023/2024
8
Max ECTS
88
Overall hours
SSD
MAT/05
Language
Italian
Learning objectives
The course aims to deal with some mathematical concepts and tools, developing the instrumental aspects of analysis and calculation for an effective use in the subsequent teachings of the degree course.
Expected learning outcomes
The student will have adequate capacity of execution of the calculus procedures.At the end of the course students will acquire the ability to solve computational exercises related to the topics covered in the course.
Single course

This course can be attended as a single course.

Course syllabus and organization

Single session

Responsible
Lesson period
First semester
Course syllabus
Numerical sets: N, Z, Q, and R. Absolute value and nth roots. The Cartesian plane: lines, parabolas, circles. Elementary functions and their graphs: powers, roots, hyperbolas, exponentials, logarithms. Equations, inequalities, and systems of algebraic and irrational inequalities. Real functions: notion of a function, domain, range, injectivity and surjectivity, composite functions, inverse functions, invertibility, geometrical transformations of elementary functions. Limits: geometrical meaning of limits, computing limits, comparison of infinites and infinitesimals, indeterminate forms, continuity, horizontal, vertical, and oblique asymptotes. Differential calculus: first derivative, tangent line, monotonicity, global and local maxima and minima. Second derivative: convexity and concavity, inflection points. Integral calculus. Computation of areas in the plane.
Prerequisites for admission
Integers, rational and real numbers. Literal calculus. Eponentials and logarithms. Algebraic equations and inequalities, exponential and logaritmic inequalities. Systems of inequalities. Fractional inequalities. Basic analytic geometry (coordinates and lines)
Teaching methods
Lectures, exercises, group work with tutoring
Teaching Resources
Annaratone S. "Matematica sul campo" E. Pearson (II edition) with related digital platform
Weekly exercises sheets uploaded on MyAriel
Assessment methods and Criteria
The exam consists of a compulsory written test, lasting 2:30 hours, with a grade up to 30/30, followed by a compulsory oral test to which only students who have obtained a grade greater than or equal to 16/30 in the written test have access. Students who, having passed the written test, do not show up to take the oral test will be rejected.
The written test consists of some immediate-response questions and some open-response questions, the solution of which must be explicitly explained. The purpose of this test is to assess whether the student possesses the minimum required skills and has acquired the computational tools practiced during the course.
The oral test consists of a short interview on the topics of the program aimed at completing the assessment of the tools acquired by the student in the study of mathematics.
The final evaluation is expressed by a grade in thirtieths and will take into account both tests. The exam is passed if the final grade is greater than or equal to 18/30. To take the exam, it is necessary to register by the deadline on UNIMIA (http://www.unimi.it/). The grade is communicated to each individual student by an automated e-mail from the university's verbalization system.
Students also have the option of taking an optional test during the semester that consists of a written test covering the minimum required skills and topics covered in the first weeks of class. This test allows for a grade of up to 10/10 and is passed with a grade of 6/10 or higher. Students who have passed the test may use the grade obtained as a grade for part of the written test. Students can use this option only in the first written exam they will attempt after the test and only in the January-February exam session.
Student with DSA and with disabilities are kindly requested to contact the instructor via email at least 10 days before the scheduled exam date to discuss any necessary individualized measures. In the email addressed to the instructor, it is necessary to CC the respective University Services: [email protected] (for students with Specific Learning Disabilities - DSA) and [email protected] (for students with disabilities).
MAT/05 - MATHEMATICAL ANALYSIS - University credits: 8
Practicals: 48 hours
Lessons: 40 hours
Professors: Carai Luca, Luoni Maria
Educational website(s)
Professor(s)
Reception:
By appointment (to be scheduled via email)
Department of Mathematics, via C. Saldini 50, second floor, office 2090
Reception:
To plan a meeting with the professor, please write an email