Program, Semester Week 5

Polynomials and Recursion

This week will finalize our study of polynomials. The division algorithm for polynomials will be treated for determination of the multiplicity of a root of a polynomial.

Another topic that will be covered this week is recursive functions. These are functions that in their definitions refer to themselves - a recursive definition. Such functions often turn out to be useful for representing mathematical as well as physical behaviour, since it is not uncommon that states in a process depend on previous states. Summation notation and “dot” notation will be introduced from this foundation.

Key Terms

The division algorithm. Factor of a polynomial and the factorized form of a polynomial. Multiplicity of a root. Recursive definition. “Dot” or ellipsis notation \(\ldots\) and summation notation \(\sum\).

Preparation and Syllabus

This week will cover Sections 4.5 and 4.6 from Chapter [04 - Polynomials] as well as Sections 5.1 through 5.3 from Chapter [05 - Recursion and induction].

Opgaver

Exercises for Long Day.

Exercises for Short Day.