Learning objectives
In an ever increasing number of contexts it is
advisable that a graduate in economic disciplines is
able to use quantitative measurements and tools.
The main objective of the course is to allow the
student to "take
possession" of these tools in order to separate the
structure of a problem from the context so that
he/she can understand and communicate as
effectively as possible what is needed to take
informed and justified economic decisions.
In an ever increasing number of contexts it is
advisable that a graduate in economic disciplines is
able to use quantitative measurements and tools.
The main objective of the course is to allow the
student to "take possession" of these tools in order
to separate the structure of a problem from the
context so that he/she can understand and
communicate as effectively as possible what is
needed to take informed and justified economic
decisions.
Furthermore, at the end of the course:
- as far as concerns knowledge and understanding:
the student should understand and properly treat the
main models presented in the course;
- as far as concerns applying knowledge and
understanding: the student should be able to solve
practical problems;
- as far as concerns making judgements: the student
should show good skills in making judgement,
developing reasoning and critical capacities;
- as far as concerns communication skills: the
student should clearly communicate what he/she
has learned;
- as far as concerns learning skills: the student
should update and consolidate his/her quantitative
knowledge and relate this knowledge and
competence to other disciplines in the degree
course.
Furthermore, the student should be able to formalize
in quantitative terms some economic problems, by
individuating initial data and the more adequate
mathematical instruments in order to obtain an
efficient and rigorous solution and to provide an
economic interpretation of the obtained results.
Prerequisites
First and second order equations and inequalities.
Course unit content
Linear functions and models.
Linear systems and matrices. Economic
applications.
Non-linear models.
Differential Calculus and economic applications.
Integrals. Economic applications.
Functions in several variables.
Full programme
Functions and Linear Models
The concepts of function and mathematical model.
Representation of a function.
Common types of function. Examples of mathematical economic models.
Linear functions.
Linear economic models.
Systems of linear equations and matrices
Systems of linear equations.
The reduction algorithm of Gauss-Jordan.
Economic applications of linear systems.
Linear algebra and applications
Concept of matrix and vector.
Matrix operations.
Matrix form of a linear system.
Inverse matrix and its use for the resolution of a linear system.
Determinant of a matrix calculation for arrays of size 2x2.
Non-linear models
General aspects: bounded functions, monotone functions, maxima and minima, infimum and supremum, even functions and odd functions, composite functions, inverse function, concave and convex functions (definition only).
Quadratic functions, exponential and logarithmic functions.
Economic models: quadratic, exponential and logarithmic.
The derivative
Average (or quotient) and instantaneous (or derivative) rate of change.
The derivative as the slope. Link between sign of the derivative and growth / decreasing function. Derivation rules.
Marginal analysis.
Limits: definition and examples of calculation. Continuity.
Techniques of differentiation
Rule of derivation of the product and ratio.
Rule of derivation of composite functions.
Derivatives of logarithmic and exponential functions.
Applications of the derivative
Maxima and minima. Applications.
Second derivative and study the graph.
Elasticity of demand.
The integral
The indefinite integral.
Integration by substitution.
Definite Integral.
The fundamental theorem of calculus.
Integrals: techniques and applications
Integration by parts.
Generalized integrals (notes).
Functions of several variables
Functions of several variables.
Notes on the graphs of functions of two variables.
Sections and contours.
Partial derivatives.
Maxima and minima.
Free and constrained optimization.
Bibliography
S. Waner, S.R. Costenoble, Strumenti quantitativi per la gestione
aziendale, Apogeo, Milano, 2019.
Teaching methods
1) Knowledge and understanding: teacher-fronted
sessions.
2) Applying knowledge and understanding: practice
sessions.
3) Making judgements: teacher-fronted sessions
and practice sessions.
4) Communication skills: practice sessions.
5) Learning skills: teacher-fronted sessions and
practice sessions
Assessment methods and criteria
Written examination (60 minutes).
During the exam, the student can use a scientific
calculator. Graphic calculators, smartphone, tablet,
laptops and smartwatch are not allowed.
The knowledge and the skill in comprehension will
be tested through three questions about elementary
mathematics and five theoretic/practical questions.
The quality of learning, the skill in the applications of
the concepts and the independence of judgement
will be verified through economic problems: the
student will individuate an opportune mathematical
model, obtaining the solution through the analytical
tools presented in Course.
The use of an appropriate technical language will be
checked through open questions about the theoretic
subjects of the Course.
Marks:
first part: 3/30
second part: 28/30
If the exam, possibly integrated by an oral exam, is
excellent, it will be valuated with full marks cum
laude.
The teacher reserves the right to complete the exam
with an oral test, if necessary.
The University will send to the students an email
message to their University email address with the
result of the exam (through Essetre system). The
students can reject the result in a week, through an
online procedure, clearly described in the message.
Other information
Further teaching materials, the Syllabus, the
detailed program of the
course and the exams already assigned will be
published on Elly.
