Master's Dissertation
DOI
10.11606/D.55.2017.tde-23032017-145755
Document
Author
Full name
Vanessa Priscila Nicolussi Marques
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2016
Supervisor
Committee
Artioli, Vanessa Rolnik (President)
Bonotto, Everaldo de Mello
Hernandez, Michelle Fernanda Pierri
Silva, Sônia Cristina Poltroniere
Title in Portuguese
Polinômios e aproximações de função
Keywords in Portuguese
Aproximações de funções
Funções polinomiais
Interpolação polinomial
Polinômios
Abstract in Portuguese
Title in English
Polynomials and function approximations
Keywords in English
Function approximations
Least square method
Polynomial functions
Polynomial interpolation
Polynomials
Abstract in English
Polynomials have characteristics and properties that make them very important, modelling nature and daily problems or serving as a tool to solve problems, or even to achieve more advanced mathematical results. The curriculum of São Paulo state suggests a sequence of contents to be worked, leading the student to learning about polynomials from both the theoretical and the applications point of views. The polynomials teaching is done in a spiral way from the 7th year of elementary school to the 3rd year of high school, that is, its contents are gradually worked during the school years, always being resumed and deepened in accordance with the appropriate school time. This work aims to contribute to the training of basic education Mathematics teachers introducing them a solid theory of polynomials concerning about definition, properties, algebraic operations, polynomial functions, polynomial graphics and already at a more advanced level, derivative and integral of polynomials. In addition, we review the concepts of vector spaces, linear independence, base, projections and orthogonality. The presented theory is then used in the study of function approximations by polynomials. Among the forms of approach, we present the Taylor polynomial, the polynomial interpolation and polynomial fit by the least square method. Throughout the text we present applications in daily life such as the calculation of the polynomial that describes a taxi ride, the 95 formula for retirement and the the profit curve of an ice cream shop due to the price of their ice cream.