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).
1st BLOCK (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.
Power, square root, exponential, logarithm, trigonometric and inverse trigonometric functions. Absolute value function.
Limit of a function. Limits theorems. Computing limits. List of common limits.
Continuous function. Classification of discontinuities. Weirstrass theorem (statment). Bolzano theorem (statment).
2st BLOCK (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.
3rd BLOCK (24 hours)
Primitives of a function. Definition of indefinite integral and definite integral.
Vectors, operations with vectors and their properties. Linear dipendence and independence of vectors. Matrices, operations with matrices. Determinant of a square matrix . Rank of a matrix. Linear systems.
Introduction to real functions of two variables
First and second order partial derivatives. Hessian matrix. Maxima and minima of functions of two variables. Economic applications.
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.
Specific topics (economic applications) can be found in the following book:
L. Peccati, S. Salsa, A. Squellati. Matematica per l’economia e l’azienda, Terza Edizione, Egea Editore, Milano, 2004.
- Robert A. Adams (2013), Christopher Essex. Calculus: A Complete Course. Pearson Education Canada.
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), an exercise concerning linear algebra (6 points), calculus of an integral (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.