Precalculus 2: Polynomials and rational functions, the name of the course is Precalculus 2: Polynomials and rational functions in mathematics, which was published by Yodami Academy. The topics that you will get to know at the end of this course:
1. Course introduction
2. General presentation with big picture and few spoilers
3. Powers, expressions and polynomials
4. Linear equations and system of equations
5. Quadratic polynomial
6. Factoring polynomials is like finding zeros of polynomials
7. Factoring polynomials: school versus reality
8. Polynomial equations and inequalities
9. Some topics of calculus
10. Drawing (design) of polynomials
11. More advanced topics on polynomials
12. Rational functions and their domains
13. Illustrative equations and inequalities
15. Drawing (design) of rational functions
16. Decomposing partial fractions
17. More advanced topics about logical functions
18. A few words about power functions and algebraic functions
19. Additional items
A detailed description of the content of the course along with all 211 videos and their titles and with the texts of all 160 problems solved in this course is included in the source file “List_of_all_Videos_and_Problems_Precalculus_2.pdf”.
Who is this course suitable for?
- Students who plan to study Algebra, Calculus or Real Analysis
- High school students curious about university mathematics
- Everybody who wants to brush up their high school maths and gain a deeper understanding of the subject
- College and university students studying advanced courses, who want to understand all the details (concerning polynomials or rational functions) they might have missed in their earlier education
- Students wanting to learn about polynomials, for example for their College Algebra class.
What you will learn in Precalculus 2: Polynomials and rational functions Course :
- How to solve problems concerning polynomials or rational functions (illustrated with 160 solved problems) and why these methods work.
- Definition and basic terminology for polynomials: variable, coefficient, degree; a brief repetition about powers with rational exponents, and main power rules.
- Arithmetical operations (addition, subtraction, multiplication) on polynomials; the polynomial ring R[x].
- Completing the square for solving second degree equations and plotting parabolas; derivation of the quadratic formula.
- Polynomial division: quotient and remainder; three methods for performing the division: factoring out the dividend, long division, undetermined coefficients.
- Vieta’s formulas for quadratic and cubic polynomials; Binomial Theorem (proof will be given in Precalculus 4) as a special case of Vieta’s formulas.
- The Remainder Theorem and The Factor Theorem with many applications; the proofs, based on the Division Theorem (proven in an article), are presented.
- Ruffini-Horner Scheme for division by monic binomials of degree one, with many examples of applications; the derivation of the method is presented.
- And ……
Course details :
Precalculus 2: Polynomials and rational functions Course Content :
High-school mathematics, mainly arithmetic
Precalculus 1: Basic notions (mainly the concept of function and related concepts; sets; logic)
You will get a very brief introduction to *systems of linear equations* in this course (in Section 4), just enough for the needs of our applications (methods by undetermined coefficients, e.g. for partial fraction decomposition)
You will get a very brief introduction to *complex numbers* in this course (in Section 5), just enough for the needs of our applications (factoring polynomials)
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