The course aims to provide the basic knowledge of mathematics and the most suitable computing techniques to address the application of mathematics to economics, finance and statistics.
Expected learning outcomes.
Knowledge and understanding
The student will demonstrate knowledge of the mathematical tools to model and solve economic financial and business problems.
Applying Knowledge and understanding
The student has to be able to apply the mathematical techniques to real economic, business and financial problems. In particular, the student has to be able to solve optimization problems.
The student has to be able to formulate a problem in a mathematical approach to describe a real phenomenon.
The student has to be able to answer the oral test questions, showing his ability to express and formalize mathematical concepts. He has to be able to explain the techniques learned to solve the questions of the written exam.
Lifelong learning skills
The student has to develop the ability to use mathematical tools to solve application problems.
Set theory. Naturals, integers, rational and real numbers. Equations and inequalities of the 1st and 2nd degree. Elements of analytical geometry (equation of a line, parallel and perpendicular lines). Parthenope University of Naples provides beginners with pre-courses of Mathematic (in September).
Part I (24 hours)
Injective, surjective and bijective or invertible functions. Composition of functions.
Global maxima and minima of a function. Supremum and infimum of a function. Monotone functions. Graphic. Domain.
Linear function. Absolute value function. Power, square root, exponential, logarithm.
Limit of a function. List of common limits.
Continuous function. Weirstrass theorem (statment). Bolzano theorem (statment).
Part II (24 hours)
Derivability of a function on a point and its geometric meaning. Elementary derivatives and derivative rules.
Applications of differential calculus
Test of monotonicity. Local maxima and minima of a function. Convex and concave functions. Test for convexity/concavity. De l’Hopital theorem (statment). Asymptotes of a function. Study of the graphic of a function.
Supply and Demand. Price elasticity of demand. Market equilibrium.
Part III (24 hours)
Real functions of two variables
First and second order partial derivatives. Hessian matrix. Maxima and minima of functions of two variables.
Economic applications: profit maximization, cost minimization.
Primitives of a function. Definition of indefinite integral.
Vectors. Matrices, operations with matrices. Determinant of a square matrix. Rank. Linear systems.
The course includes frontal and exercises aimed at the use of mathematical methods studied, with students interaction.
P. Marcellini, C. Sbordone. Matematica generale, Liguori Editore, Napoli, 2007.
P. Marcellini, C. Sbordone. Esercitazioni di Matematica 1, parte I e II, Liguori Editore, Napoli, 1991.
- Robert A. Adams (2018), Christopher Essex. Calculus: A Complete Course. Pearson Education Canada.
- Patrick Roger (2013). Analysis and Linear Algebra for Finance, Part I, bookboon.com
The assessment is based on written examination and an oral examination. The written text (duration 90 minutes) is composed of exercises in order to assess the achievement by the student of the learning objectives. It is divided into 4 exercises related to the topics of the program: study of function (12 points), global maxima and minima of a function (6 points), resolution of a linear system of equations (6 points), partial derivatives of a function of two variables and critical points (6 points). The oral exam focuses on the theoretical topics dealt with during the course and it is designed to evaluate the student's ability to express and formalize mathematical concepts.
Only those who have passed the written test with a minimum vote of 18/30 can hold the oral test. The vote of the examination is results of written and oral examination.
During the examination, the use of notes, books and informatics devices (smartphone, tablet, pc, ecc.) is not allowed.