| Code |
16031
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| Year |
1
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| Semester |
L0
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| ECTS Credits |
1
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| Workload |
T(17H)
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| Scientific area |
Mathematics
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Entry requirements |
- to be a High-School student, attending the Portuguese level " 3º ciclo do Ensino Básico" or "Ensino Secundário" ;
- to be a student of Mathematics (Licence degree, Master degree, or PhD degree), or a student in related courses, such as Teaching Mathematics or any other related course in Sciences.
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Learning outcomes |
The main goal of the course is to study polynomial functions. In the first part of the course, we shall start by studying the basic properties of these functions, such as the precise definitions, the elementary algebraic operations between polynomials, the Fundamental Theorem of Algebra, and polynomial equations. Then, we shall focus the basic properties of polynomials in the study of tangents to polynomial curves and in the introduction to the study of derivatives.
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Syllabus |
Section I – Elementary properties of polynomial functions
1. Definitions
2. Algebraic operations
3. General results on zeros; the Fundamental Theorem of Algebra
Section II – Polynomial equations
1. Equations of degree less than or equal to four
2. Equations of degree greater than or equal to five
Section III – The use of the algebra of polynomial to introduce the concept of derivative
1. Tangents to polynomial curves
2. The derivative of polynomial functions
Section IV – Divided- Difference operators
1. Definitions and the main framework within the theory of polynomials
2. The derivative within the divided-difference operator setting
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Main Bibliography |
• Range, M. (2018) Using high school algebra for a natural approach to derivatives and continuity, The Mathematical Gazette 102, no. 555, pp. 435-446.
• Sultan, A. e Artzt, A.L. (2011). The Mathematics that every secondary school math teacher needs to know, New York, 2011 (primeira edição).
• Rebocho, M.N. (2022). Divided-difference operators from the geometric point of view. Formal and Analytic Solutions of Differential Equations, pp. 301 - 324, Singapore, World Scientific. DOI: 10.1142/9781800611368_0015
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Language |
Portuguese. Tutorial support is available in English.
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