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 will be able to analyze and formalize some economic problems. In particular, she/he will be able to identify the data of the problem and to construct the most suitable model, choosing the appropriate mathematical methods to solve the problem in an efficient and rigorous way. The student will also be able to give an economic interpretazion to the results of her/his analysis.
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, Apogeo, Milano, 2006.
Teaching methods
Oral lectures.
During the classes, a theoretical exposition of the contents of the course will be given.
Then, a great number of examples and exercises will be discussed, with a particular focus on economic applications. The students will be asked to discuss and propose possible solutions to the exercises.
Assessment methods and criteria
Written exam.
The acquisition of knowledge and understanding will be tested by 3 questions about the prerequisites, a problem and 3 questions about the theory.
In particular, 3 initial questions (1 pt each) will be used to test the mastery of the preliminary notions required for the course.
To evaluate the learning ability, the capacity of applying the learned concepts to real problems and the independence of judgement, a problem (value: 15 pt.)will be proposed to the student, who must choose the appropriate mathematical model and method to find a solution and interpret the obtained results.
The acquisition of a technical language will be evaluate through 3 questions (4 pt. each) on theoretical topics covered in the course.
Other information
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