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Abstract(s)
Nesta dissertação apresenta-se um estudo sobre polinómios. Os principais tópicos a serem focados são: o Teorema Fundamental da Álgebra; a resolução de equações polinomiais (dedução da solução de equações de grau dois, três e quatro, bem como a aplicação de alguns métodos numéricos para equações de grau maior que quatro); o uso da álgebra elementar de polinómios para o estudo de tangentes a curvas polinomiais, bem como a introdução do cálculo de derivadas; o estudo de operadores às diferenças divididas com a propriedade fundamental de resultarem num polinómio de grau n - 1 quando aplicados a um polinómio de grau n.
In this work it is presented a study about polynomials. The main topics to be focused are as follows: the Fundamental Theorem of Algebra; the solution of polynomial equations (to deduce the solutions of the polynomial equations of degrees two, three and four, and also to apply numerical methods to find approximate solutions of polynomial equations of degree higher than four); the use of standard properties of polynomial algebra to study tangents to polynomial curves, as well as to introduce the calculus of derivatives; the study of divided-difference operators with the fundamental property of giving a polynomial of degree n - 1 when applied to a polynomial of degree n.
In this work it is presented a study about polynomials. The main topics to be focused are as follows: the Fundamental Theorem of Algebra; the solution of polynomial equations (to deduce the solutions of the polynomial equations of degrees two, three and four, and also to apply numerical methods to find approximate solutions of polynomial equations of degree higher than four); the use of standard properties of polynomial algebra to study tangents to polynomial curves, as well as to introduce the calculus of derivatives; the study of divided-difference operators with the fundamental property of giving a polynomial of degree n - 1 when applied to a polynomial of degree n.
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Keywords
Equações Polinomiais Operadores Às Diferenças Divididas Polinómios Tangentes