MATHEMATICS
- Overview
- Assessment methods
- Learning objectives
- Contents
- Full programme
- Bibliography
- Teaching methods
- Contacts/Info
None.
The course starts from the basics and can be profitably attended by possessing the minimum quantitative knowledge common to all high school graduated, regardless their major. It is however advisable to check one's previous skills and knowledge through the self-assessment test provided in the e-learning of the course and the assessment test. In case of difficulty with the concepts contained in these tests, it is recommended to promptly contact the instructors to identify possible ways to recover.
According to University regulations and up to different indications, in the first semester of the academic year 2020/21 the exam will be carried out remotely. The remote exam will be carried out on a specific University platform (e-learning). A student can decide to carry out the exam in two different methods.
METHOD 1 – Total exam:
At the end of the course, during the exam sessions, tests that cover the entire program of the course will be organized. During the total exam (at a distance), the use of calculators, manuals and notes will be allowed.
The test will be divided into two parts and will be designed to evaluate the calculation skills, the knowledge of terminology, the main statements presented during the course and the analytical skills developed by the student.
Part 1: The first part of the exam will be composed by Quiz (multiple choice) delivered through the e-learning platform. The student will have to answer 6 multiple choice or numerical answer questions in 20 minutes. By correctly answering at least 4 questions, students will be admitted to the second part of the exam. Otherwise the exam will be terminated, and the test will be evaluated as insufficient. There is no penalty for incorrect answers. Each correct answer is worth 2 points.
Part 2: The second part will consist of two exercises, composed by several questions. Each exercise is worth up to a maximum of 10 points.
The student will have 40 minutes to solve the exercises on a sheet of paper with black pen and upload a legible image of the paper to the e-learning platform. Further details on how to create and upload the solutions of the exercises will be made available on the e-learning page of the course.
The exam is passed if the sum of the scores obtained in the two parts is not less than 18 (eighteen), with a minimum of 8 (eight) points in the first part. Scores higher than 30 will be registered as 30 with honors.
MODE 2 - Partial exams:
At the end of the first cycle of lessons, in the week of teaching interruption, and at the end of the course in December, two partial exams will be organized mainly concerning the topics of the part of the course just ended.
The first partial exam will last 40 minutes, will be worth 16 points and consists of 12 short questions in the form of quiz (multiple choice question) concerning calculation skills and knowledge of the main definitions and theoretical concepts addressed in class. Students will be admitted to the second partial exam if the score obtained in the quizzes is greater than or equal to 6.
The second partial exam is divided into two parts. The first part of the exam, worth 6 points, is composed of short questions in the form of quiz (multiple choice question). The student must achieve at least 4 points to be able to access the second. The second part of the exam, evaluated 10 points, is composed of more complex exercises, in which the student is required to use the calculation skills and theoretical results presented in the course in an appropriate way to provide the solution to the proposed questions. There is no minimum score for this part.
The second partial exam is also passed with at least 6 points.
The exam is passed if both partial tests are passed and the sum of the points obtained is no less than 18 (eighteen). Honors are awarded to a sum greater than 30.
Students with DSA: Students with DSA are required to contact the disabled service (servizio.disabili@uninsubria.it) to define the individualized Training Project that must be sent to the course holder within 10 days before the exam session that the student intends to sustain.
The course aims to provide students with basic analytical tools to quantitative study of economic and management models.
At the end of the course, the student will be able to:
• Solve problems of a micro-economic nature with one or more decision variable;
• Resolve economic and management problems involving optimization with respect to one decision variable;
• Sketch the graph of functions of a real variable, studying main properties such as monotony, convexity and continuity;
• Understand discrete models, in economic, managerial and financial theory, involving sequences and series;
• Solve systems of linear equations, by means of linear algebra tools;
• Solve problems that require the use of integral calculus in one variable;
• Face the study of more advanced quantitative disciplines;
• Understand mathematical statement and basic mathematical proofs.
Numeric sets. (2h)
Linear Algebra. (11h)
Real valued functions of a real variable. (7h)
Sequences. (2h)
Limits of a real valued function. (9h)
Continuous functions. (5h)
Differential calculus for real functions of a real variable. (16h)
Function of multiple variables. (6h)
Integral calculus. (11h)
Series. (11h)
Linear Algebra. [Ch.16 §§ 1-6]
Algebra of vectors and matrices, determinant (Sarrus rule, Laplace theorem), inverse matrix, transposed, rank, linear systems (solution study and resolution).
Numeric set. [Ch.2 §§ 3; 5 Ch.4 §§ 2-5]
Set R: algebraic, metric structure. Distance, ordering, sup / inf, internal, external, isolated, accumulation, maximum and minimum points
Real functions of real variable. [Ch.2 §§ 3-4; Ch.3; Ch.4 § 6]
Function definition. Elementary functions, graph, geometric transformations, graphically resolvable inequalities. Domain, bounded function, composition of functions, monotonicity, invertibility, concavity / convexity.
Limits of a function in a variable. [Ch.6 §§ 1-4.6; Ch.7 §§3-5]
Theorem of uniqueness of the limit, Theorem of existence of the limit for monotone functions, Theorem of permanence of the sign. Calculation of limits, notable limits, infinities and infinitesimal. The Landau' symbols.
Continuous functions. [Ch.7 §§1-2.6]
Weierstrass theorem, Zero values theorem, intermediate values theorem.
Sequences. [Ch.5 §§1; 3; Ch.6 § 5]
Sequences defined by recurrence, limit of sequences.
Differential calculus for functions in a real variable. [Ch.8, 9]
Incremental ratio, derivative and its geometric meaning, points of non-derivability, calculation of derivatives, derivability and continuity, higher order derivatives, Taylor's theorem (order n), De Hospital's theorem. Rolle's theorem, Lagrange's theorem, Fermat's theorem. Monotonicity of differentiable functions, II test of recognition of stationary points, study of the graph of function.
Functions of multiple variables. [Ch.14 §§ 1-4]
Definition, domain, graph and level curves. Unconstrained extreme points. Partial derivatives and Fermat's theorem.
Integral Calculation. [Ch.10,11]
Undefined integral, immediate primitives, almost immediate, primitives of fractional rational functions, integrations by parts, by substitution. Definite integral, integral function. Mean value Theorem of integral calculus, fundamental theorem of integral calculus. Generalized integrals.
Series. [Ch.12]
Character of a series, geometric series. Necessary condition for convergence. Series with positive terms: generalized harmonic series, criterion of asymptotic comparison, of comparison. Series in terms of any sign: absolute convergence (sketch).
A. Guerraggio, Matematica 2/Ed.
Per gli argomenti di base, si consiglia di consultare
G. Anichini - A. Carbone - P. Chiarelli - G. Conti, Precorso di Matematica 2/Ed.
e-texts available!
The course is based on lectures. Tutoring sessions will also be offered.
During the first semester (a.y. 2020/2021) the office hours will be given through Microsoft Teams. Students needing to speak with the lecturer can send an email at elisa.mastrogiacomo@uninsubria.it (partition A-G) e asmerilda.hitaj@uninsubria.it (partition H-Z)