Learning objectives
In an ever increasing number of contexts, it is advisable that a graduate student in
Economics is able to use quantitative measurements and tools. The main objective
of this course is to provide the student the basic mathematical instruments to
construct simple models for economic problems and take informed and justified
decisions.
At the end of the course, the student
should:
- understand and properly treat the main models
presented in the course;
- be able to analyze, formalize and solve practical (economical) problems;
- show good skills in making judgement;
- clearly communicate what he/she has learned using an appropriate language.
Prerequisites
First and second order equations and inequalities. Properties of exponentiation.
Course unit content
Linear functions and models. Linar systems and matrices. Economic applications.
Non-linear functions.
Differential Calculus and economic applications.
Integrals. Functions in several variables. Economic applications.
Full programme
Real functions. Graph of a function.
Linear functions and models. Economic applications.
Systems of linear equations.
Linear algebra: vectors and matrices.
Non-linear models: quadratic functions, exponential functions, logarithm.
Limits and continuity of functions. First and second derivatives.
Maxima and minima of functions.
Economic applications.
Integration theory: indefinite and definite integral. Fundamental theorem of calculus.
Integration by parts and by substitution.
Improper integrals.
Introduction to functions of several variables. Partial derivatives of first and second
order. Hessian matrix.
Maxima and minima of functions of two variables.
Constrained optimization:Lagrange's multipliers.
Bibliography
S. Waner, S.R. Costenoble, Strumenti quantitativi per la gestione aziendale,
Maggioli Editore, 2018
Teaching methods
Classes will take place online through the use of the Teams and Elly
platforms. They will be both synchronous (via Teams) and asynchronous
(uploaded on the Elly page of the course). Asynchronous lessons will be
dedicated to a rigourous exposition of the theory, for the acquisition of
knowledge.
Synchrounous classes will be mainly dedicated to the presentation of
examples and exercises. Students will be encouraged
to actively
participate to the discussion, to develop the ability to apply knowledge
and the acquisition of judgements and learning skills.
For the acquisition of technical language, the meaning of the specific
terms used in the course will be illustrated.
On the Elly platform the detailed program and the exams of the previous years will be uploaded at the beginning of the course. To download the material, registration to the online
course is required
The links to the videos will be available on Elly until December 31st, 2020.
Assessment methods and criteria
The summative evaluation of the learning will be done through a written
test evaluated on a 0-33 scale: the test will be a quiz on Elly, with the use
of the Respondus software (alternativley, Teams will be used).
The instructions can be found on the web pages:
http://selma.unipr.it/;
http://selma.unipr.it/wp-content/uploads/Guida-Respondus.pdf;
https://elly2020.sea.unipr.it
The ID will be uploaded on a OneDrive foldere which link will be sent after
the deadline for the registration.
nd will. The student will also declare, through Elly, to accept the Honour Code
and the video-recording conditions. The student who will
not effect the above operations will not attend the
exam.
During the exam, the student can use a scientific
calculator. Graphic calculators, smartphone, tablet,
laptops and smartwatch are not allowed.
The test will consist of 9 multiple choice questions:
three questions about elementary
mathematics (1 point each), three short problems (each worth 5 or 6 point) and three
theoretic/practical questions (each worth 4 or 5 point) for a maximum total score of 31.
Students achieving the maximum score will we rewarded with the laude.
The knowledge and the skill in comprehension will
be tested through all the questions.
The quality of learning, the skill in the applications of
the concepts and the independence of judgement
will be verified through the three economic problems.
In order to solve such problems, the student will
individuate an opportune mathematical model, by
obtaining the solution through the analytical tools
presented in Course.
The knowledge of an appropriate technical language
will be checked through the three questions about the theoretical topics.
In case of return to activity in presence, the exam will be written.
The knowledge and the skill in comprehension will
be tested through three questions about elementary
mathematics (1 point each, a problem (15 points) and three theoretical
questions (4 points each).
The quality of learning, the skill in the applications of
the concepts and the independence of judgement will be verified
through the economic problem. In order to solve
such a problem, the student will individuate an
opportune mathematical model, by obtaining the
solution through the analytical tools presented in
Course.
The use of an appropriate technical language will be
checked through three open questions, about the
theoretic subjects of the Course.
If the exam is excellent (for completeness,
brightness and organization of the answers,
concepts not specifically treated in the course), it is
valuated with full marks cum laude.
The teacher reserves the right to complete the exam
with an oral test, if necessary.
Results will be communicated to the students within 10 days, via Esse3. The solution of the exam will be uploaded on the Elly platform within 7 days.
Other information
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2030 agenda goals for sustainable development
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