MATHEMATICS FOR ECONOMICS
The aim of the course is to provide basic knowledge concerning the theory of functions of several real variables (continuity, differentiability, integrability), of ordinary differential equations and their applications to concrete problems. Eventually, the student will have to prove to have understood both theoretical and applicative parts of the course and to be able to use those methods to solve concrete problems.
Knowledge and understanding: the student must demonstrate knowledge and understanding of the fundamental tools of mathematical analysis, with particular regard to the logical understanding of definitions and theorems and the identification of examples and counter-examples.
Ability to apply knowledge and understanding: the students must demonstrate the ability to use their acquired knowledge in solving the main problems regarding the study of functions of several variables. This will involve the ability to identify appropriate theoretical tools
suitable to the particular problem under study by applying correctly the tools of the infinitesimal calculus.
Autonomy of judgment: Students must be able to know how to establish the logical veracity of affirmations and properties regarding the functions of several variables.
Communication Skills: students 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.
Learning Skills: The student must be able to update and deepen the discussed topics, also by identifying the appropriate tools among those available on the web.
Knowledge of basic concepts of mathematical analysis treated in the course of Matematica I.
Integration: definite and indefinite integrals; table of integrals ; integration by parts, integrations by substitution (8 hours)
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. (16 hours)
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. Economic applications (32 hours)
Curves: introduction. Tangent vector to a Curve. Orientation of a curve. Rectifiable curve: length of a curve. Integration on curves. (8 hours)
Double integrals: normal domains ; change of variable (8 hours)
Lectures and exercises will take place in lecture rooms using black board.
Paolo Marcellini Carlo Sbordone; ESERCITAZIONI DI ANALISI MATEMATICA DUE - prima parte e seconda parte - Zanichelli
C.P. Simon - L.E. Blume, Mathematics for Economists
The assessment is based on a written examination (duration 2 hours) and an oral examination . The written examination will focus on the main topics covered in the course. The oral examination will assess the actual student learning with respect to the objectives. The vote of the examination is expressed in scale from 0 to 30. During the examination, the use of notes, books and informatics devices (smartphone, tablet, pc, ecc.) is not allowed.