Calculus

A.Y. 2020/2021
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.
Course syllabus and organization

Single session

Lesson period
First semester
Teaching methods

Lessons will be provided both in synchronous and in asynchronous mode during class hours (see official timetable). The synchronous will be delivered through Google Meet platform. The asynchronous lessons will consist of very short recorded videos with self evaluations tests attachments and they will be avaliable through Ariel platform. Also some meetings to test students understandings of the main proposed topics will be arranged if the emergency situation will allow.

Program and reference material

Program and reference material will not be affected.

Verification methods and assessment criteria

Online exams will will be composed of a written and an oral part. Both of them will be provided through Google Meet platform. Written tests will consist of six very short open-ended questions. Students have 5 minutes to answer to each question and very simple calculations are requested. If at least 4 questions over six are answered correctly then students can take the oral exam
The oral exam consists of five multiple choice questions and three open-ended questions. If more than two of the multiple choice questions are not answered correctly, the entire exam is failed
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
Teaching Resources
Annaratone S. "Matematica sul campo" E. Pearson with related digital platform
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.
MAT/05 - MATHEMATICAL ANALYSIS - University credits: 8
Practicals: 48 hours
Lessons: 40 hours