Polynomials

Polynomials - CSE 1400 Applied Discrete Mathematics...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: CSE 1400 Applied Discrete Mathematics Polynomials Department of Computer Sciences College of Engineering Florida Tech Fall 2011 Polynomials 1 Constants 1 Linear Polynomials 2 Quadratic Polynomials 2 The Power Basis 3 The Binomial Theorem 4 Horners Rule for Evaluating Polynomials 4 Taylor Polynomials 5 Falling Factorial Powers 5 Rising Factorial Powers 7 Problems on Polynomials 8 Abstract Polynomial functions are computationally primitive and form bases for approximating more complicated functions. Polynomials Polynomials are important because 1 . They are easy to evaluate. 2 . They can approximate arbitrarily well many more complex func- tions. If f is a continuous real-valued function on [ a , b ] and if any e > 0 is given, then there exists a polynomial p on [ a , b ] such that | f ( x )- p ( x ) | < e for all x in [ a , b ] . In words, any continuous function on a closed and bounded interval can be uniformly approximated on that interval by polynomials to any degree of accuracy. Low degree polynomials p ( x ) are studied in college algebra. College Instances of polynomials include p ( x ) = 3 x + 2 p ( x ) = x 2- x- 1 p ( x ) = x 2- 4 p ( x ) = x 3 + x 2 + x + 1 algebra studies how to solve polynomial equations p ( x ) = 0. and The zeros of polynomials can be com- puted. 3 x + 2 = at x =- 2/3 x 2- x- 1 = at x = 1 5 2 x 2- 4 = at x = 2 x 3 + x 2 + x + 1 = at x =- 1, i students learn to graph polynomial equations p ( x ) = y in a Cartesian coordinate system. cse 1400 applied discrete mathematics polynomials 2 Constants C onstants are polynomials . Constants are polynomials of de- gree . There are famous, important constants. , Zero 1 , One 2 1.414213, The square root of 2 = ( 1 + 5 ) /2 1.618033, The golden ratio 3.141592, pi e 2.718281, Euler s or Napiers constant 0.577215, The Euler-Mascheroni constant Linear Polynomials P olynomials that grow by a constant increment are called linear . A linear polynomial p ( x ) is written The zero of the equation p ( x ) = 0 is x = m- 1 b . p ( x ) = mx + b for some slope m R , m 6 = 0 and y- intercept b R . These functions are called first degree polynomials....
View Full Document

This note was uploaded on 02/11/2012 for the course MTH 2051 taught by Professor Shoaff during the Fall '11 term at FIT.

Page1 / 9

Polynomials - CSE 1400 Applied Discrete Mathematics...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online