The aim of the course is to provide the basic
knowledge of mathematics and the most suitable calculation techniques
to address the application of mathematics to economics, finance and
Knowledge and understanding: The student should exhibit knowledge of mathematical tools and ability to identify those suitable for modeling and solving economic, statistical and financial problems. Faced with a more complex problem, the student has to be able to analyze and solve every part of it, interpret the obtained results and provide the solution to the original problem.
Applying knowledge and understanding: The student has to be able to select and apply mathematical tools to economics, statistics and finance.
Making judgments: The student has to be able to define the mathematical model of applicative problems, apply the proper mathematical tools to solve them and interpret the solutions in different contexts.
Communication: The student has to be able to express and formalize mathematical
concepts. He has to be able to explain the techniques learned to solve exercises.
Lifelong learning skills: The student has to develop the ability of mathematical reasoning. He has to be able to use mathematical concepts, procedures and tools to describe, explain and predict economic
and financial phenomena.
Set theory. Naturals, integers, rational and real numbers. Elements of
analytical geometry. Algebraic equations and inequalities of degree 1 and 2.
S. Lang (2002) Short calculus. Springer-Verlag, New York
The course content can be approximatively split into the following three blocks:
I block (24 hours)
Functions: basic concepts; minimum and maximum, infimum and supremum; monotonic function; graph.
Functions: power and radix; exponential and logarithmic; absolute value; trigonometric and inverse trigonometric functions.
Limits: definition; theorems; continuity; evaluation of limits.
II block (24 hours)
Differentiation: derivative; differentiation rules; higher-order derivatives.
Applications of differentiation: minimum and maximum evaluation; convexity; De L’Hospital rule; sketching graphs of functions.
Non-linear equations: bisection method.
III block (24 hours)
Functions of several variables: basic concepts; partial derivatives; gradient; maximum and minimum of a function of two variables.
Linear algebra: vectors; matrices; matrix operations; determinant; rank; linear dependence; systems of linear equations; Gauss elimination method.
Integration: indefinite and definite integral; techniques of integration.
The course includes frontal lessons, during which the themes of the program are discussed, and exercises in attendance. The student can practice and consolidate his skills in the course section on the E-learning
platform of the University.
P. DE ANGELIS, Matematica di base, Giappichelli ed. (Seconda edizione).
Lang S. (2002) Short calculus. Springer-Verlag, New York
Students are required to take a written exam. The exam includes multiple choice questions (part 1) and exercises (part 2); students motivate the chosen techniques for solving exercises. The number of exercises in part 2 ranges between 1 and 3 and depends on their complexity. The colloquium is optional.