MATHEMATICS, FIRST PART
- Overview
- Assessment methods
- Learning objectives
- Contents
- Full programme
- Bibliography
- Delivery method
- Teaching methods
- Contacts/Info
None.
The course will cover the analytical tools necessary to deal with the study of mathematics in economics courses.
It is however recommended students verify their mastery of the basic techniques of:
1. Algebraic calculus: remarkable products, decomposition of polynomials, recollection with common factor, produced between algebraic expressions.
2. Equations: solution of first degree equations in an unknown, second degree in an unknown, fractional rationals, of superior degree the second one by polynomial decomposition. First degree systems of equations.
3. Inequalities: solution of first-degree inequalities in an unknown, second-degree in an unknown, fractional rationals, with a higher degree than the second by polynomial decomposition.
4. Analytical geometry: Cartesian coordinates, line equation, parabola (with vertical axis), equilateral hyperbola with parallel axes, Cartesian axes and circumference (with center in the origin). Intersection problems between curves in the Cartesian plane.
Exam is a written test designed to assess the achievement of each goal of the course. Both theoretical and practical skills are tested. Exercises require both theoretical issues and practical (e.g. calculus) skills.
Students can take the exam with two alternatives:
General Exam.
Partial exams.
At the end of the first part of lectures and at the end of the lectures, students can take part to partial exams, covering mainly the topics of the lectures delivered during the midterm ended.
Please, be advised: students must enroll to attend the exam (partial and/or general)
Students with learning disabilities are required to contact the “servizio disabili” (servizio.disabili@uninsubria.it) to define the individualized training project to be sent within 10 days of each exam session they intend to take.
More details on test structure will be provided at the beginning of the course through the University e-learning system (and on the basis of the state of emergency).
The course aims to provide students with basic analytical tools to address quantitative study of economic and management subjects.
EXPECTED LEARNING OUTCOMES
At the end of the course students will be able to:
• graph elementary functions representing basic models for economic analysis;
• operate with the analytical expression of functions of one and several real variables;
• solve calculus problems with functions of one and several variables;
• solve linear algebra problems, involving matrices and vectors;
• study and solve linear systems, involving real parameters.
Main topics covered are:
• functions of one variable;
• differential calculus in one variable;
• functions of several variables;
• linear algebra.
At the beginning of the course, students will be given, via e-learning repository, a detailed program of each lecture's topics.
Main topics covered are:
Functions of one variable (ch. 2,3,4):
Number sets. Set R: metric structure and topology.
Real functions of real variable, domain, elementary functions, monotonicity, extreme points, concavity and convexity, geometric transformations.
Differential calculus in one variable (ch. 8,9):
Intuitive concept of derivative and its geometrical meaning. Derivatives of elementary functions. Calculus, higher order derivatives. Stationary points, test for monotonicity, convexity's test.
Functions of several variables (ch. 14, 17):
Functions of two variables, domain and level curve.
Partial derivatives, stationary points. First order condition for uncostrained otpimization.
Linear algebra (ch. 15, 16):
Vectors, matrices, matrix calculus and determinant, rank, linear systems.
Angelo Guerraggio, Matematica – Terza edizione, Pearson, Milano, 2020.
However, it is possible to refer to previous editions (2004, 2009).
Detailed references will be provided during classes.
Lectures will discuss both theoretical arguments and solution techniques for most common exercises related to the subject. Additional exercise will be assigned during classes both for individual study and to be solved in the next lecture.
Additional materials will be provided through the e-learning platform