The aim of the course is to provide students with a base of knowledge of mathematics and a basic training in calculus to prepare the students for further study in mathematics and for gainful employment of mathematics in economic, financial and statistical fields.
Knowledge and understanding: students should know basic calculus and linear algebra.
Applying knowledge and understanding: students should be able to apply the discussed mathematical techniques to the analysis and solution of economic and financial problems.
Making judgements: students should be able to recognize the techniques required to solve the mathematical model which describes a problem arising in economics, management and finance.
Communication skills: students should clearly describe the methodologies adopted for solving the exercises in the written exam, and answer in a clear and reasoned way to the questions of the oral exam.
Learning skills: students should be able to show a good learning ability, by widening, for example, their knowledge with use of relevant bibliographic references .
Basic concepts of set theory. Equation of a straight line. Linear and quadratic equations and inequalities.
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)
Multivariate functions: 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.
Course organization: classroom lessons, exercise sessions. Additional material is made available through the e-learning online platform Moodle, where slides used at lesson can be found, together with exercises and self-evaluation tests.
Lang S. (2002) Short calculus. Springer-Verlag, New York.
For students who speak Italian, the main reference is represented by the following book:
De Angelis P.L. (2015), Matematica di base. Giappichelli Editore, Torino
The final exam consists of written part and an oral part. The written part contains two exercises. The former requires to represent the graph of a function. The latter concerns one of the following: linear algebra, function of several variables, non-linear equations, limits. During the written part, books are forbidden. The calculator is required. If the written part mark is sufficient, the student will hold the oral part. Both the written and the oral part marks contribute to the final mark