MATHEMATICS I
- Overview
- Assessment methods
- Learning objectives
- Contents
- Full programme
- 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.
The exam takes place IN PRESENCE and the 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.
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). The overall number of Quiz will vary between 7 and 10 for a total of 10 points. Each correct answer will be worth 1 or 2 points. Whenever the total score obtained in the first part is less than 5, the test will be considered insufficient, and the second part will not be evaluated. There is no penalty for incorrect answers.
Part 2: The second part will consist of theoretical questions and more complex exercises, for a total of 22 points. The complete solutions of the second part will be reported in a white paper. Each theoretical question and exercise in this part is worth up to a maximum of 10 points. The duration of the total exam (Part 1+Part2) is 90 minutes.
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 5 (five) points in the first part. Scores above 30 are entitled to praise.
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, for a total of 16 points and will consists of 10/12 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 second partial) 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 3 points to be able to access the second part. There is no penalty for incorrect answers. The second part (of the second partial) 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 duration of the second partial test is 60 minutes.
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.
Note: At each exam session there is the possibility of an additional interview, at the discretion of the teacher.
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 session of the exam 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;
• Solve 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. (12h)
Sequences. (2h)
Real valued functions of a real variable. (9h)
Limits of a real valued function. (4h)
Continuous functions. (4h)
Differential calculus for real functions of a real variable. (16h)
Integral calculus. (10h)
Series. (10h)
Function of multiple variables. (6h)
Numeric sets and their properties.
Sup/inf, internal. Maximum and minimum points.
Linear Algebra.
Algebra of vectors and matrices, determinant, inverse matrix, transposed, rank, linear systems (solution study and resolution).
Real functions of real variable. Function definition. Elementary functions, graph, geometric transformations, graphically resolvable inequalities. Domain, bounded function, composition of functions, monotonicity, invertibility, concavity / convexity.
Sequences. Limit of sequences.
Limits of a function in a variable. 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. Weierstrass theorem, Zero values theorem, intermediate values theorem.
Differential calculus for functions in a real variable.
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.
Integral Calculation.
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.
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).
Functions of multiple variables.
Definition, domain, chart, and contour lines. Extremely free. Partial derivatives and Fermat's theorem. Optimization. Constraint optimization.
Basically, the course is organized in lectures. Occasionally, active teaching methods may be adopted (such as cooperative learning, peer education, flipped classroom). Tutoring sessions will also be offered.
The office hours for the first semester are available on the University’s Professor personal page. Students who need to speak with the lecturer can send an email at elisa.mastrogiacomo@uninsubria.it (partition A-G) e paolo.leonetti@uninsubria.it (partition H-Z)