MATHEMATICAL MODELS FOR ECONOMIC ANALYSIS
The aim of the course is to provide the main mathematical methods
• for studying of optimization problems,
• for modeling and solving economic, financial and corporate problems.
Expected learning outcomes
Knowledge and understanding: The student should be able to prove knowledge of mathematical tools and ability to identify those suitable for modeling and solving economic, financial and corporate issues.
Applying knowledge and understanding: the student should be able to apply the acquired knowledge in order to resolve the assigned problems.
Making judgements: the student should be able to use the acquired knowledge also in an autonomous way, by also applying them to specific issues related to optimization problems.
Communication: the student should be able to answer in a clear and thorough way to the questions of the written examination and to those of the oral examination.
Lifelong learning skills: the student should be able to show a good learning ability, by widening, for example, his/her knowledge with use of relevant bibliographic references.
Contents of the course of Calculus I
Functions of several variables: Limits and Continuity. Partial Derivatives. Higher Order Derivatives: Schwarz Theorem. Gradient vector and Differentiability. Directional Derivatives. Quadratic Forms. Convex Functions. Local and Global Maxima and Minima. Constrained Maximization Problems. (28 ore)
Curves: introduction. Tangent vector to a Curve. Orientation of a curve. Rectifiable curve: length of a curve (4 ore)
Ordinary Differential Equations: Existence and Uniqueness: the Cauchy problem, Linear First Order Equations, Linear Second Order Equations, Separable Equations, Bernoulli Equations. Systems of Differential Equations. (16 ore)
The course includes frontal lessons, during which the themes of the
program are discussed, and exercises in attendance.
P.Marcellini, C.Sbordone: Esercitazioni di Matematica Due, prima parte e seconda parte, Zanichelli Editore, 2017.
C.P. Simon - L.E. Blume, Matematica 2 per l’Economia e le scienze sociali, Università Bocconi editore.
The assessment is based on written examination and an oral interview. The vote of the examination is expressed in scale from 0 to 30, and it is results of written and oral examination. The laude can be assigned if the student shows, in his/her answers, a particular ability to deepen the topics mentioned in the examination’s questions.