INTRODUCTION TO MATHEMATICS
The course aims to provide the basic knowledge of mathematics and the most suitable calculation techniques to adequately address the application of mathematics to economics, finance and statistics.
Knowledge and understanding: The student should be able to prove knowledge of mathematical tools and ability to identify those suitable for modeling and solving economic, financial and corporate issues.
Applying knowledge and understanding: The student should be able to demonstrate knowledge of mathematical tools and ability to identify those suitable for modeling and solving economic, financial and statistical issues. The student should be able to read and interpret the graph of a one-variable function in all its aspects, solve problems of determining absolute and relative maximums and minimums, and be able to apply the main integration techniques.
Making judgements: The student has to develop a critical ability to formulate a problem in a mathematical approach, apply the tools of the discipline and interpret the mathematical solution in different contexts.
Communication: The student has to be able to clearly and comprehensively argue the theoretical and practical topics of the course, showing that he/she is able to express and formalize mathematical concepts and explain the techniques learned for carrying out the 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 useful for describing, explaining and predicting economic and financial phenomena. Through the autonomous development of exercises, subsequently verified in the classroom, the student will master the application of the knowledge acquired by integrating them with the professional skills that characterize the courses of his/her university career.
Set theory. Naturals, integers, rational and real numbers. Elements of analytical geometry. Equations and inequalities of the 1st and 2nd grade.
These prerequisites will be widely used during the course and, where necessary, explanations and further material will be provided on which to resume the theory and practice.
Block I (24 hours)
Numerical functions: main definitions; minimum and maximum, lower and upper bounds; monotone functions; graphic.
Elementary functions: power function; root function; exponential function; logarithmic function; absolute value function; trigonometric and inverse trigonometric functions.
Infinitesimal calculus: definition of limit; basic theorems on limits; continuous functions; calculation of limits.
Block II (24 hours)
Differential calculus: derivative of a function; derivatives of elementary functions; rules for calculating derivatives; derivatives of a higher order. Application of differential calculus: search for the absolute maximum and minimum of a function; concavity and convexity. Graph representation of a function.
Block II (24 hours)
Functions of several variables: diagram; partial derivatives; gradient vector; research and classification of extremal points.
Elements of linear algebra: vectors; matrices; matrix calculation; determinant of a matrix; rank of a matrix; linearly independent vectors; systems of linear equations, classification and resolution; method of elimination of Gauss.
Outline of integral calculus: indefinite integral; definite integral; immediate integrals, integration by parts and by substitution.
Numerical functions. Elementary functions. Differential calculus. Functions of several variables. Elements of linear algebra. Outline of integral calculus.
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 at the "Parthenope" University.
• P. DE ANGELIS, Matematica di base, Giappichelli
• LANG S. (2002) Short calculus. Springer-Verlag, New York
The assessment is based on written examination and an oral interview. The student should be able to demonstrate acquired theoretical knowledge and theoretical-practical skills, by answering a test consisting of multiple choice questions and supporting the performance of exercises with the theoretical motivations regarding the methods of resolution chosen. The time to complete the test is one hour. During the exam the use of notes, books and informatics devices -smartphone, tablet, pc, ecc.- is not allowed. The evaluations of the oral exam, expressed out of thirty, and that of the written test contribute with equal weight to the definition of the final grade.
The evaluations of the written and oral tests contribute to the definition of the final grade. Due to Covid-19, the exams will be held in the presence or at a distance according to the indications of the University.
During the course there are two partial tests, one in the middle of the semester and one at the end. These tests will be structured in a similar way to the written test. The final mark will be determined as the average of the marks of the two tests. The achievement of a minimum of 18 points determines admission to the oral exam.