Calculus
A.Y. 2022/2023
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.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Lesson period
First semester
TEACHING METHODS
More specific information of the delivery modes of training activities for academic year 2022/2023 will be provided ower the coming months, based on the evolution of the public health situation.
More specific information of the delivery modes of training activities for academic year 2022/2023 will be provided ower the coming months, based on the evolution of the public health situation.
Course syllabus
Numerical sets.: N, Z, Q e R. The coordinate plane: straight lines, parabolas, circles. Elementary functions and their graph. Equations, inequalities and system of algebraic and irrational inequalities. Generalities about real funcion: domain, range, injective and surjective functions, composed functions, inverse functions, geometric transforms of elementary functions. Limits: computing limits, comparison of infinites and infinitesimals, indeterminate forms. Continuity. Asymptotes: vertical, horizontal and slant. Differential calculus: first derivative, tangent line, monotonicity, global and local maxima and minima. Second derivative: convexity and concavity, inflection points. Integral calculus. Computation of plane areas.
Prerequisites for admission
Integers, rational and real numbers. Literal Calculus. Eponential and logarithm. Algebraic equations and inequalities, exponential and logaritmic inequalities. Systems of inequalities. Fractional inequalities. Outline of Analytic geometry (Coordinates and lines)
Teaching methods
Lectures, exercises, teamworks, tutoring, microvideo, online exrcise
Teaching Resources
Annaratone S. "Matematica sul campo" E. Pearson (II edition) with related digital platform
weekly exercises sheets uploaded on Ariel
weekly exercises sheets uploaded on Ariel
Assessment methods and Criteria
The final mark is the outcome of a written and an oral exam that are both compulsory. The written exam (whose mark is at most 30/30) is made of two part, A and B that take place the same day. Part A takes half an hour and it focuses on the prerequisities. It consists in 10 problems to be solved quickly. Only if the student answers correctly at least 8 questions, his part B will be take into consideration. Part B takes two hours and consists of a few open-ended question regarding the exam program.
The oral examination consists of a short conversation about the topics of the program, which aims to establish definitively what tools the student has acquired in the study of mathematics.
Students are supposed to register for the exam on time on the website UNIMIA (http://www.unimi.it/). Students will be rated with marks from 1 to 30. The exam is considered to be passed if the mark is equal or grater than 18. Once passed the exam, the mark will be communicated to the student via e-mail by the automatic University System.
The oral examination consists of a short conversation about the topics of the program, which aims to establish definitively what tools the student has acquired in the study of mathematics.
Students are supposed to register for the exam on time on the website UNIMIA (http://www.unimi.it/). Students will be rated with marks from 1 to 30. The exam is considered to be passed if the mark is equal or grater than 18. Once passed the exam, the mark will be communicated to the student via e-mail by the automatic University System.
MAT/05 - MATHEMATICAL ANALYSIS - University credits: 8
Practicals: 48 hours
Lessons: 40 hours
Lessons: 40 hours
Professor:
Annaratone Silvia Maria Carla