INTRODUCTION TO MATHEMATICS
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 statistics.
Expected learning outcomes
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, statistical and financial issues. Faced with a more complex problem, the student should 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 should be able to choose and apply mathematical tools to economics, statistics and finance.
Making judgements: The student should 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 should be able to answer the oral test questions, showing his ability to express and formalize mathematical concepts. He should be able to explain the techniques learned to solve the questions of the written exam.
Lifelong learning skills: The student should develop the ability of mathematical reasoning. He should 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. Equations and inequalities of the 1st and 2nd grade.
P. DE ANGELIS, Matematica di base, Giappichelli ed. (II edition):chapters I – II – III – IV – V (except par. 8) – VI – VII – VIII (except par. 9) –IX – X – XI – XII – XIII – XV – XVI (pag. 383-386, 403-404 except par. 4.I) –XVII.
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 at the "Parthenope" University. The course is loaded among the courses of "Economics and Management".
P. DE ANGELIS, Matematica di base, Giappichelli,
LANG S. (2002) Short calculus. Springer-Verlag, New York.
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 topics: 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. The written part is considered sufficient (18/30) if the student answers correctly to the exercise on the graph function. The second exercise assigns up to 12 points if the answer is correct. Both the written and the oral part marks contribute to the final mark through the arithmetic average.
If both the oral answers are insufficient the exam is not passed.
Due to Covid-19, the exam will be held in the presence or online depending on the indications of the University.
Furthermore, in the case of exam online, the student must demonstrate that he has acquired theoretical knowledge, passing a multiple-choice test consisting of 10 questions, and theoretical-practical skills by carrying out an exercise with the theoretical motivations regarding the method of resolution adopted
The course is uploaded on the E-learning platform of the University