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Keywords: Polynomial
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- Abstract: Welcome to the NROC Introductory Algebra course. This curriculum emphasizes a multi-representational approach to algebra, with concepts, results, and problems being expressed graphically, analytically, and verbally. It develops algebraic fluency by providing students with the skills needed to solve equations and perform important manipulations with numbers, variables, equations, and inequalities. In addition, the course develops proficiency with operations involving monomial and polynomial expressions. The main unifying themes of the course include understanding, writing, solving, and graphing linear equations, systems of linear equations and inequalities, quadratic equations, and rational equations.
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- Abstract: With your mouse, drag data points and their error bars, and watch the best-fit polynomial curve update instantly. You choose the type of fit: linear, quadratic, cubic, or quartic. The reduced chi-square statistic shows you when the fit is good. Or you can try to find the best fit by manually adjusting fit parameters.
(Complete Item Description)
- Abstract: Elementary Algebra is a work text that covers the traditional topics studied in a modern elementary algebra course. It is intended for students who (1) have no exposure to elementary algebra, (2) have previously had an unpleasant experience with elementary algebra, or (3) need to review algebraic concepts and techniques.
- Subject:
Mathematics and Statistics
- Grade Level:
Secondary
- Collection:
Connexions
(Complete Item Description)
- Abstract: Learn about conservation of energy with a skater dude! Build tracks, ramps and jumps for the skater and view the kinetic energy, potential energy and friction as he moves. You can also take the skater to different planets or even space!
(Complete Item Description)
- Abstract: Learn about graphing polynomials. The shape of the curve changes as the constants are adjusted. View the curves for the individual terms (e.g. y=bx ) to see how they add to generate the polynomial curve.
(Complete Item Description)
- Abstract: This collection of modules considers factoring very high degree polynomials with random coefficients. It looks particularly at the Lindsey-Fox algorithm and describes the program written by Jim Fox.
- Subject:
Mathematics and Statistics, Science and Technology
- Grade Level:
Post-secondary
- Collection:
Connexions
(Complete Item Description)
- Abstract: Horner's method is a standard minimum arithmetic method for evaluating and deflating polynomials. It can also efficiently evaluate various order derivatives of a polynomial, therefore is often used as part of Newton's method. This note tries to develop the various techniques called Horner's method, nested evaluation, and synthetic division in a common framework using a recursive structure and difference equations. There is a similarity to GOERtzel's algorithm for the DFT, Z-transform inversion by division, and Pade's and Prony's methods. This approach also allows a straight forward explanation of "stability" or numerical errors of the algorithms. Matlab implementations are given. This note came from the work of the "Polynomial Club" at Rice: Burrus, Fox, Sitton, and Treitel.
- Subject:
Mathematics and Statistics, Science and Technology
- Grade Level:
Post-secondary
- Collection:
Connexions
(Complete Item Description)
- Abstract: Lagrange's interpolation formula is a simple and clever method for finding the unique polynomial of order L that exactly passes through L+1 distinct samples of a signal.
- Subject:
Science and Technology
- Grade Level:
Post-secondary
- Collection:
Connexions
(Complete Item Description)
- Abstract: The program which implements the Lindsey-Fox algorithm that factors high degree polynomial is organized in three stages. Jim Fox is the primary author and architect of the program.
- Subject:
Mathematics and Statistics, Science and Technology
- Grade Level:
Post-secondary
- Collection:
Connexions
(Complete Item Description)
- Abstract: Factoring a high degree polynomial has been considered a difficult problem since the beginning of mathematics. We describe the strategies used to attack this problem. The results are from a group called the "Polynomial Club" (Jim Fox, Sidney Burrus, Gary Sitton, and Sven Treitel)
- Subject:
Mathematics and Statistics, Science and Technology
- Grade Level:
Post-secondary
- Collection:
Connexions
(Complete Item Description)
- Abstract: This module describes the method of partial fraction expansion, in which a ratio of polynomials can be split into a sum of small polynomials.The Heaviside cover-up method is discussed in detail with examples.Finding a partial fraction expansion in matlab is also discussed.
- Subject:
Science and Technology
- Grade Level:
Post-secondary
- Collection:
Connexions
(Complete Item Description)
- Abstract: This module will introduce rational functions and describe some of their properties. In particular, it will discuss how rational functions relate to the z-transform and provide a useful tool for characterizing LTI systems.
- Subject:
Mathematics and Statistics, Science and Technology
- Grade Level:
Post-secondary
- Collection:
Connexions
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