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.
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.
Finally, 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
BASIC CALCULUS
Course unit content
- LINEAR FUNCTIONS AND MODELS.
- SYSTEMS OF LINEAR EQUATIONS AND MATRICES. MATRIX ALGEBRA AND APPLICATIONS.
- NON-LINEAR MODELS.
- THE DERIVATIVE. TECHNIQUES OF DIFFERENTIATION. APPLICATIONS OF THE DERIVATIVE.
- THE INTEGRAL. TECHNIQUES OF CALCULUS AND APPLICATIONS.
- FUNCTIONS IN SEVERAL VARIABLES.
- eCONOMIC APPLICATIONS.
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, 2018.
FOR SOME IN-DEPTH STUDY, LECTURE NOTES WILL BE MADE AVAILABLE ON ELLY.
Teaching methods
Oral and practical lessons.
Classes will be online by means of Teams and Elly. In particular, lectures will be given in streaming and/or published on the Elly platform.
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 exam online by means of Teams and Elly.
The exam will be a multiple choice test.
During the exam, the student can use a scientific calculator. Graphic calculators, smartphone, tablet, laptops and smartwatches, different from the machine used for the exam, are not allowed.
The knowledge and comprehension will be tested with three questions related to the course prerequisites (1), three short problems (2) and three
theoretic/practical questions (3).
The quality of learning, skills and ability to apply knowledge to practical problems will be checked through the problem (2) to solve which the student must identify an appropriate mathematical model, finally getting the solution using the analytical tools learned in the course.
The maximum score achievable through the problems is 15 points.
The knowledge of the appropriate technical language will be assessed through three open-ended questions (3) on the topics covered by the syllabus.
The maximum score achievable through the open questions is 12 points.
A further oral examination may be requested by the teacher, if necessary.
The honors will be awarded by oral examination to those particularly deserving students who, in addition to having complied with the requisites necessary to obtain the full evaluation, have overall demonstrated an appreciable systematic knowledge of the topic, an excellent ability to apply the knowledge acquired to the specific problem in question, a considerable autonomy of judgment, as well as a particular care in the formal drafting of the exam.
The examinations will be through Teams, Elly and
Respondus.
The guidelines are published at the addresses:
http://selma.unipr.it/
http://selma.unipr.it/wp-content/uploads/Guida-Respondus.pdf
https://elly.(nome dip.).unipr.it
Before the examination, the student will send, through OneDrive, his/her identity document and will declare, through Elly, to accept the Honour Code and the video-recording conditions. The student who does not carry out these operations within the indicated deadlines will not be admitted to the exam.
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
The teachers could modify some indications, in particular concerning exams in the summer session, according to the pandemic evolution and to possible techical problems which could arise.
The Syllabus, the detailed program and the previous exam tests are uploaded on Elly.
