How to Solve Any Triangle: First, Forget the Law of Sines and the Law of Cosines

2003 ◽  
Vol 96 (6) ◽  
pp. 448-449
Author(s):  
Lin McMullin
Keyword(s):  
Computer Algebra ◽  
Newton’S Method ◽  
Newton's Method ◽  
Graphing Calculators ◽  
Computer Algebra Systems ◽  
Mathematics Courses ◽  
Mathematical Problems ◽  
The Law ◽  
Law Of Cosines

Computer algebra systems (CASs) have made, and will continue to make, changes in what is taught in mathematics courses at all levels. Just as scientific calculators made teaching computations with logarithms obsolete, CASs will render obsolete many other topics in the curriculum. Some will be formulas and procedures for computations that are no longer necessary to solve the problems for which they were originally developed. The mathematical problems will remain; we will just use more efficient ways to solve them. A good example is Newton's method for approximating the zeros of an expression. Using Newton's method to find roots by hand has been rendered obsolete by graphing calculators that can either find the roots exactly or do the approximations faster and more accurately.

The Constant Feature: Spanning K–12 Mathematics

2004 ◽  
Vol 97 (3) ◽  
pp. 198-204
Author(s):  
James E. Schultz
Keyword(s):  
Computer Algebra ◽  
Mathematics Learning ◽  
Graphing Calculators ◽  
Computer Algebra Systems ◽  
Teaching Mathematics ◽  
Twelfth Grade ◽  
Constant Feature ◽  
K 12

When I reflect on my many years of teaching mathematics, one of the most enjoyable and fruitful ideas for calculator use came from an article that appeared more than twenty-five years ago (Judd 1976). It gave suggestions for using the constant feature of a simple calculator to enhance mathematics learning. I have used Judd's idea successfully in many classrooms at grades levels ranging from kindergarten through twelfth grade. This article revisits the constant feature for four-function calculators and extends it for use with graphing calculators and computer algebra systems (CASs) for a broad range of topics.

Soundoff!: A New Breed of Calculators: Do They Change the Way We Teach

1999 ◽  
Vol 92 (2) ◽  
pp. 88-89
Author(s):  
James Podlesni
Keyword(s):  
Advanced Placement ◽  
Computer Algebra ◽  
Graphing Calculators ◽  
Computer Algebra Systems ◽  
New Models ◽  
User Friendly ◽  
New Generation ◽  
The Way

A new generation of graphing calculators—for example, the TI-89 and the Casio 9970—that use computer algebra systems (CAS) are now available. Since they manipulate symbols, one could argue that they represent as big a change as the step from scientific to graphing calculators. A student “asks” the calculator to factor x2 + 5x + 6, and the calculator prints (X + 2)(X + 3). On the Advanced Placement calculus examination, existing graphing calculators allow the student to find the derivative of y = cos x at a specific x-value. In addition, the new models can “tell” the student that the derivative of cos x is −sin x. They can also provide units for numeric answers. They are apparently much more user-friendly than the existing HP-48, thereby assuring widespread use. The TI-89 is essentially a TI-92 in a TI-83 case, without the geometry package but with FLASH™, a feature that allows it to be upgraded electronically.

Soundoff: A Case against Computer Symbolic Manipulation in School Mathematics Today

1992 ◽  
Vol 85 (3) ◽  
pp. 180-183
Author(s):  
Bert K. Waits ◽  
Franklin Demana
Keyword(s):  
Mathematics Education ◽  
Computer Algebra ◽  
Graphing Calculators ◽  
School Mathematics ◽  
Computer Algebra Systems ◽  
National Council ◽  
Symbolic Manipulation ◽  
Symbol Manipulation ◽  
Evaluation Standards ◽  
Exploration Tool

The National Council of Teachers of Mathematics and leaders in mathematics education must move vigorously to build a consensus for acceptance of the Curriculum and Evaluation Standards (NCTM 1989). One important assumption of the Curriculum and Evaluation Standards is that all students should use computers and graphing calculators on a regular basis in school mathematics. The symbol-manipulating ability of such computer algebra systems (CAS) as the IBM Math Exploration Tool Kit, Mathematics™, and Derive™ can be used today in school mathematics to do algebra. However, we take exception to the use of computer symbol manipulation in school mathematics today for two important reasons.

Ideas behind Computer Algebra and Their Use in the Classroom

2005 ◽  
Vol 34 (2) ◽  
pp. 177-188
Author(s):  
Arthur Nunes-Harwitt
Keyword(s):  
Computer Algebra ◽  
Computer Algebra System ◽  
Lesson Plan ◽  
Computer Algebra Systems ◽  
Mathematics Courses ◽  
Simple Computer

Computer algebra systems are being used more and more frequently in mathematics courses of all levels. For instructors to use these systems effectively, they need to have an idea of how the systems work. To illuminate the mechanics, the implementation of a simple computer algebra system will be described. Further, if instructors understand the methods used by computers, they may find the ideas involved useful for human students even without computers. A lesson plan will be described that is aimed at students with little or no algebra background followed by a discussion of the author's experience using this lesson in the classroom.

Optimal Power Flow Using Newton’s Method

2012 ◽  
Vol 3 (2) ◽  
pp. 167-169
Author(s):  
F.M.PATEL F.M.PATEL ◽  
◽  
N. B. PANCHAL N. B. PANCHAL
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Power Flow ◽  
Optimal Power Flow ◽  
Optimal Power

An Efficient Sixth-Order Convergent Newton-Type Iterative Method for Nonlinear Equations

2012 ◽  
Vol 220-223 ◽  
pp. 2585-2588
Author(s):  
Zhong Yong Hu ◽  
Fang Liang ◽  
Lian Zhong Li ◽  
Rui Chen
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Efficiency Index ◽  
Sixth Order ◽  
Type Method ◽  
Second Derivatives ◽  
Better Than

In this paper, we present a modified sixth order convergent Newton-type method for solving nonlinear equations. It is free from second derivatives, and requires three evaluations of the functions and two evaluations of derivatives per iteration. Hence the efficiency index of the presented method is 1.43097 which is better than that of classical Newton’s method 1.41421. Several results are given to illustrate the advantage and efficiency the algorithm.

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